Question

Which of the following represents the factorization of the trinomial below?x2 – X-20A. (x-4)(x-5)B. (X + 4)(x-5)oC. (x-2)(x-10)0D. (x+2)(x-10)

Answer 1

(x+4)(x-5)

Explanation:

Second order polynomial in the following format:

ax² + bx + c = 0

Has roots x¹ and x².

Can be factored as:

(x - x¹)(x - x²)

So, we have to find the roots.

Finding the roots:

Bhaskara formula, which is:

`x=(-b\pm√(b^2-4ac))/(2a)`

In the polynomial given in this question:

a = 1, b = -1, c = -20

So

`x=(-(-1)\pm√((-1)^2-4\ast1\ast(-20)))/(2)=(1\pm√(81))/(2)`

The roots are:

`x^1=(1+9)/(2)=5,x^2=(1-9)/(2)=-4`

The factored form is:

(x - x¹)(x - x²) = (x - (-4))(x - 5) = (x+4)(x-5)