Question

Factor the trinomial below.

x2 – 3x – 40

A. (x + 5)(x + 8)
B. (x + 5)(x – 8)
C. (x – 5)(x – 8)
D. (x – 5)(x + 8)

Answer 1

Two numbers that can multiply to equal 40 but subtract to equal - 3.
$40 = 8 \times 5 \\ - 8 + 5 = - 3 \\ \\ (x - 8)(x + 5)$

Answer 2

Answer:

B. (x + 5)(x – 8)

Step-by-step explanation:

For any given quadratic expression, consider it along side the general form of a quadratic equation ax² + bx + c = 0

To factorize, the factors of the product of a and c will have to add up to give a sum equivalent to b. Then an only then can the expression be factorized.

For x2 – 3x – 40

a = 1, b= -3 and c = -40

The product of a and c is -40 and the factors of this product that add up to b are - 8 and 5. Therefore;

x2 – 3x – 40 = x2 – 8x + 5x – 40

= x(x - 8) +5(x - 8)

= (x -8)(x + 5)