Question

Consider this expression
x^2 + x - 72

Replace the values of a and b to rewrite the given expression

(x + a)(x+b)

Answer 1

Answer:

$\displaystyle \large{(x + 9)(x - 8)}$

The value of a is 9 and b is -8

Step-by-step explanation:

$\displaystyle \large{(x + a)(x + b) = {x}^{2} + (a + b)x + ab}$

We need to find two numbers that add up or subtract off to 1.

Then we also use the same two numbers that multiply and get -72.

Let's see:-

• 9 and -8 seem like correct values.

Because 9+(-8) is 9-8 = 1

And 9(-8) is -72.

Therefore:

$\displaystyle \large{ {x}^{2} + x - 72 = (x + 9)(x - 8)}$

The value of a is 9 and the value of b is -8 according to form of (x+a)(x+b)

Answer 2

Answer:

(x + 9)(x - 8)

Step-by-step explanation:

x² + x - 72

Consider the factors of the constant term (- 72) which sum to give the coefficient of the x- term (+ 1)

The factors are + 9 and - 8 , since

9 × - 8 = - 72 and 9 - 8 = 1 , then

x² + x - 72 = (x + 9)(x - 8)

with a = 9 and b = - 8