Question

What are the factors of x2 – x – 6? Check all that apply. X – 6 x 6 x – 3 x – 2 x 2 x 1 x – 1.

Answer 1

Answer:

The factors are x-3 and x+2, and the roots are 3 and -2.

Step-by-step explanation:

x^2-x-6 can be factored in the following way:

(x-3)(x+2)

The factors are x-3 and x+2, and the roots are 3 and -2.

Answer 2

Factored form of an expression is writing it in the terms of multiplication of factors. The factors of given expression are: (x-3) and (x+2)

How to factorize a quadratic polynomial with single variable?

Quadratic polynomial with single variables are expressible in the form

$ax^2 + bx + c$

where x is the variable and a,b,c are constants.

Its factored form is

$\dfrac{1}{4a^2} \times (2ax +b-\sqrt{b^2 - 4ac})(2ax +b+ \sqrt{b^2 - 4ac})$

For the given case, the expression given to us is $x^2 - x - 6$

Comparing it with the standard form of quadratic expression  $ax^2 + bx + c$, we get: a = 1. b = -1. and c = -6

Using the aforesaid formula, we get:

$=\dfrac{1}{4a^2} \times (2ax +b-\sqrt{b^2 - 4ac})(2ax +b+ \sqrt{b^2 - 4ac})\\\\=\dfrac{1}{4}\times(2x -1 - \sqrt{1 +24})(2a -1 + \sqrt{1 + 24})\\\\=\dfrac{1}{4} \times (2x - 1-5)(2x - 1 + 5)\\\\=(x -3)(x+2)$

Thus, The factors of given expression are: (x-3) and (x+2)

Learn more about factors here;

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