Question

Identify the factors of x^2-8x-20

O (x+4)(x-5)
O (x+5)(x-4)
O (x-10)(x+2)
O ( x-2)(x+10)

Answer 1

Answer: So, the correct factorization is (x - 10)(x + 2), which matches option D:

O (x-2)(x+10)

Step-by-step explanation: To factor the quadratic expression x^2 - 8x - 20, you need to find two binomials whose product equals the given expression. To do this, we can first try to find two numbers that multiply to the constant term (-20) and add up to the coefficient of the linear term (-8).

The two numbers that fit these criteria are -10 and +2 because (-10) * (+2) = -20 and (-10) + (+2) = -8.

So, we can write the expression as:

x^2 - 10x + 2x - 20

Now, you can factor by grouping:

x^2 - 10x + 2x - 20 = (x^2 - 10x) + (2x - 20)

Now factor each group:

x(x - 10) + 2(x - 10)

Now, you can factor out the common factor of (x - 10):

(x - 10)(x + 2)

So, the correct factorization is (x - 10)(x + 2), which matches option D:

O (x-2)(x+10)