Question

Factorise x square minus x minus 2

Answer 1

Answer: The factors of $x^{2} -x-2$ are  $(x-2)(x+1)$ respectively.

Step-by-step explanation:

Given:We have given $x^{2} -x-2$.

To find:We have to find factors of $x^{2} -x-2$.

Explanation:

Step 1:As we have given  $x^{2} -x-2$.To find the factor given expression we have to write middle term -x into two terms such that the multiplication of two terms should be equal to product of first term and and third term and their addition or subtraction should be the middle term.

Step 2:So the multiplication of two term should be $-2x^{2}$ and their addition or subtraction should be $-x$.

Step 3:So we have,

                         ⇒ $x^{2} -x-2$.

                         ⇒  $x^{2} -2x+x-2$

                         ⇒  $x(x-2)+1(x-2)$

                         ⇒  $(x-2)(x+1)$

∴ The factors of $x^{2} -x-2$ are  $(x-2)(x+1)$ respectively.

Splitting the Middle Term for Factoring Quadratics

The sum of the roots of the equation $a x^{2} + bx + c = 0$ can be given by,

α+β = -b/a

The product of the roots in the equation $a x^{2} + bx + c = 0$  can be given by,

α.β = c/a

We split the middle term b of the quadratic equation $a x^{2} + bx + c = 0$such that when we try to factorize quadratic equations. We determine the factor pairs of the product of a and c such that their sum is equal to b.

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Answer 2

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Step-by-step explanation:

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