How to factor a polynomial equation?

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Hello,

The Casio FX-300ES does not handle symbolic algebra. So it cannot factor a general polynomial expression. The methods can be found in any book on Algebra.

However if you are interested in approximate factorization of quadratic and cubic polynomials, you can use the calculator to do that. It can solve aX^3 +bX^2+cX+d =0 and the quadratic equations.

If you want to factor a cubic polynomial P3(X) = aX^3+bX^2+cX+d , you write the corresponding cubic equation as **aX^3+bX^2+cX=d =0** , then you divide all terms of the equation by** a** to obtain**X^3+(b/a)X^2+(c/a)X+(d/a)=0.**

You use the calculator to solve (approximately) this equation.

Suppose you find the 3 roots **X1,X2,and X3.** Then the polynomial X^3+(b/a)X^2+(c/a)X+(d/a) can be cast in the factored form (X-X1)(X-X2)(X-X3) and the original polynomial P3(X) can be written as**P3(X) = a*(X-X1)(X-X2)(X-X3) **

You can handle the quadratic polynomial the same way.

P2(X) =a*(X-X1)(X-X2) where X1, X2 are the two real roots

Hope it helps.

Posted on Oct 17, 2009

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Posted on Jan 02, 2017

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Use the quadratic formula, or factor the quadratic polynomial. Once factored into a product of two first degree binomials, the roots are obtained by setting (in TURN) each binomial factor equal to zero.

May 02, 2014 | Casio fx-300ES Calculator

This calculator is unable to factor a polynomial expression.

In general there are a few factoring methods

In general there are a few factoring methods

**Factor by grouping terms****Factor by completing the square**(quadratic polynomial)**Factor by finding two integers such their sum is equal to the coefficient of the middle term, and their product is equal to the third (constant term)**. This is valid for a quadratic polynomial where the leading coefficient (of the x^2 term) is equal to 1.**X^2+SX+P**

Jul 31, 2012 | Casio FX-115ES Scientific Calculator

No it cannot factor. It does not do symbolic manipulations.If you know a bit of theory of polynomials you can find the roots of the polynomial equation. The calculator has a Solve utility. Once you have the roots, you can use your knowledge about polynomials to carry out the factorization procedure.

Aug 31, 2011 | Casio fx-300ES Calculator

Sorry, but no! it is not capable of factoring anything. It can however solve for the roots of a polynomial equation.Write your polynomial as P(X)= a(X² +(b/a)X+c/a) =0. Use the calculator to solve the polynomial equation X² +(b/a)X+c/a =0 and find the roots X1, and X2. You will then be able to write the original polynomial as P(X)=a(X-X1)(X-X2). Beware that by using the calculator, the values of the roots are approximate.

Mar 14, 2011 | Casio fx-300ES Calculator

Natively, the calculator cannot factor polynomials because it does not have a Computer Algebra System or (CAS). You can however find the roots of the polynomial equation P(x)=0 and factor approximately.

On the Internet, there is a program which you can download and transfer to your calculator. Here is the link (the page is in French).

On the Internet, there is a program which you can download and transfer to your calculator. Here is the link (the page is in French).

Dec 09, 2010 | Casio FX-9750GPlus Calculator

The short story is that this calculator does have a computer algebra system or CAS and thus cannot factor polynomials with arbitrary (unknown) coefficients or known coefficients.

However if the coefficients are given you can ,if you are willing to travel that way, factor approximately a polynomial P(x).

Basically, the idea is that any polynomial P(X) of degree n can be written in the factored form (X-x_1)(X-x_2)...(X-x_n), where x_1, x_2, x_3,...x_n are the roots (real or complex) of the equation P(X)=0.

The procedure ( for a 3rd degree polynomial) is as follows: (the fixYa site parser will remove the plus signs, so I am writing the whole word plus instead of the mathematical sign

If you want to factor a cubic polynomial P3(X) = aX^3 plus bX^2 plus cX plus d , you write the corresponding cubic equation as**aX^3 plus bX^2 plus cX plus d =0** , then you divide all terms of the equation by** a** to obtain

**X^3 plus (b/a)X^2 plus (c/a)X plus (d/a)=0.**

You use the calculator to solve (approximately) this equation.

Suppose you find the 3 roots**X1,X2,and X3.**
Then the polynomial X^3 plus (b/a)X^2 plus (c/a)X plus (d/a) can be cast in the
factored form (X-X1)(X-X2)(X-X3) and the original polynomial P3(X) can
be written as

**P3(X) = a*(X-X1)(X-X2)(X-X3) **

You can handle the quadratic polynomial the same way.

P2(X) =a*(X-X1)(X-X2) where X1, X2 are the two real roots.

To find the various roots you must use the solve( application.

However if the coefficients are given you can ,if you are willing to travel that way, factor approximately a polynomial P(x).

Basically, the idea is that any polynomial P(X) of degree n can be written in the factored form (X-x_1)(X-x_2)...(X-x_n), where x_1, x_2, x_3,...x_n are the roots (real or complex) of the equation P(X)=0.

The procedure ( for a 3rd degree polynomial) is as follows: (the fixYa site parser will remove the plus signs, so I am writing the whole word plus instead of the mathematical sign

If you want to factor a cubic polynomial P3(X) = aX^3 plus bX^2 plus cX plus d , you write the corresponding cubic equation as

You use the calculator to solve (approximately) this equation.

Suppose you find the 3 roots

You can handle the quadratic polynomial the same way.

P2(X) =a*(X-X1)(X-X2) where X1, X2 are the two real roots.

To find the various roots you must use the solve( application.

Nov 11, 2010 | Casio FX-9750GPlus Calculator

The short story is that this calculator does have a computer algebra system or CAS and thus cannot factor polynomials with arbitrary (unknown) coefficients or known coefficients.

However if the coefficients are given you can ,if you are willing to travel that way, factor approximately a polynomial P(x).

Basically, the idea is that any polynomial P(X) of degree n can be written in the factored form (X-x_1)(X-x_2)...(X-x_n), where x_1, x_2, x_3,...x_n are the roots (real or complex) of the equation P(X)=0.

The procedure ( for a 3rd degree polynomial) is as follows:

If you want to factor a cubic polynomial P3(X) = aX^3 bX^2 cX d , you write the corresponding cubic equation as**aX^3 bX^2 cX d =0** , then you divide all terms of the equation by** a** to obtain

**X^3 (b/a)X^2 (c/a)X (d/a)=0.**

You use the calculator to solve (approximately) this equation.

Suppose you find the 3 roots**X1,X2,and X3.**
Then the polynomial X^3 (b/a)X^2 (c/a)X (d/a) can be cast in the
factored form (X-X1)(X-X2)(X-X3) and the original polynomial P3(X) can
be written as

**P3(X) = a*(X-X1)(X-X2)(X-X3) **

You can handle the quadratic polynomial the same way.

P2(X) =a*(X-X1)(X-X2) where X1, X2 are the two real roots.

However if the coefficients are given you can ,if you are willing to travel that way, factor approximately a polynomial P(x).

Basically, the idea is that any polynomial P(X) of degree n can be written in the factored form (X-x_1)(X-x_2)...(X-x_n), where x_1, x_2, x_3,...x_n are the roots (real or complex) of the equation P(X)=0.

The procedure ( for a 3rd degree polynomial) is as follows:

If you want to factor a cubic polynomial P3(X) = aX^3 bX^2 cX d , you write the corresponding cubic equation as

You use the calculator to solve (approximately) this equation.

Suppose you find the 3 roots

You can handle the quadratic polynomial the same way.

P2(X) =a*(X-X1)(X-X2) where X1, X2 are the two real roots.

Sep 11, 2010 | Casio FX-9750GPlus Calculator

You cannot factor a polynomial with the help of this calculator. It does not have a Computer Algebra System or CAS. You can factor it approximately.

- You can however rewrite the equation 7k^2+23k+6=0 in the canonical form X^2+ (23/7)X+(6/7)=0
- Calculate its discriminant Delta= (23/7)^2-4*(6/7), which is positive, meaning that real solutions exist.
- Calculate the two roots x1 and x2 (approximately).
- The polynomial can be factored as (X-x1)(X-x2)

May 05, 2010 | Casio FX-9750GPlus Calculator

Hello,

Sorry, but you cannot use this calculator to factorize a general polynomial.

1. It does not know symbolic algebra.

2. It can only manipulate numbers.

However if you have polynomials of degree 2 or 3, with numerical coefficients (no letters) you can set [MODE] to equation and use the equation solver to find the real roots of 2nd degree or 3rd degree polynomials. Assuming that your polynomials have real roots (X1, X2) for the polynomial of degree 2, or (X1, X2, X3) for the polynomial of degree 3, then it is possible to write

P2(X) =a*(X-X1)(X-X2)

P3(X)= a(X-X1)(X-X2)(X-X3)

This is an approximate factorization, except if your calculator configured in MathIO, has been able to find exact roots (fractions and radicals)

where a is the coefficient of the highest degree monomial aX^2 +...

or aX^3 +....

But I have a hunch that this is not what you wanted to hear.

Good luck.

Sorry, but you cannot use this calculator to factorize a general polynomial.

1. It does not know symbolic algebra.

2. It can only manipulate numbers.

However if you have polynomials of degree 2 or 3, with numerical coefficients (no letters) you can set [MODE] to equation and use the equation solver to find the real roots of 2nd degree or 3rd degree polynomials. Assuming that your polynomials have real roots (X1, X2) for the polynomial of degree 2, or (X1, X2, X3) for the polynomial of degree 3, then it is possible to write

P2(X) =a*(X-X1)(X-X2)

P3(X)= a(X-X1)(X-X2)(X-X3)

This is an approximate factorization, except if your calculator configured in MathIO, has been able to find exact roots (fractions and radicals)

where a is the coefficient of the highest degree monomial aX^2 +...

or aX^3 +....

But I have a hunch that this is not what you wanted to hear.

Good luck.

Mar 08, 2009 | Casio fx-300ES Calculator

Hello,

Sorry, but you cannot use this calculator to factor a general polynomial.

1. It does not know symbolic algebra.

2. It can only manipulate numbers.

However if you have polynomials of degree 2 or 3, with numerical coefficients**
(no letters) **you can set [MODE] to **Equation **and use the equation solver
to find the real roots of 2nd degree or 3rd degree polynomials.
Assuming that your polynomials have real roots (X1, X2) for the
polynomial of degree 2, or (X1, X2, X3) for the polynomial of degree 3,
then it is possible to write

**P2(X) =a*(X-X1)(X-X2)**

P3(X)= a(X-X1)(X-X2)(X-X3)

where a is the coefficient of the highest degree monomial aX^2 +...

or aX^3 +....

This is an approximate factorization, except if your calculator configured in MathIO, has been able to find exact roots (fractions and radicals)

While the [MODE][5:Equation] only handles quadratic and cubic equations, the [SHIFT][SOLVE=] solver finds the roots of arbitarry expressions (not limited to polynomials). In principle you can use it to find the roots of an expression. If it is a polynomial of dgree higher that 3 you can factor it (approximately).

But I have a hunch that this is not what you wanted to hear.

Hope it helps.

Sorry, but you cannot use this calculator to factor a general polynomial.

1. It does not know symbolic algebra.

2. It can only manipulate numbers.

However if you have polynomials of degree 2 or 3, with numerical coefficients

P3(X)= a(X-X1)(X-X2)(X-X3)

where a is the coefficient of the highest degree monomial aX^2 +...

or aX^3 +....

This is an approximate factorization, except if your calculator configured in MathIO, has been able to find exact roots (fractions and radicals)

While the [MODE][5:Equation] only handles quadratic and cubic equations, the [SHIFT][SOLVE=] solver finds the roots of arbitarry expressions (not limited to polynomials). In principle you can use it to find the roots of an expression. If it is a polynomial of dgree higher that 3 you can factor it (approximately).

But I have a hunch that this is not what you wanted to hear.

Hope it helps.

Dec 09, 2008 | Casio fx-300ES Calculator

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