Question

Select the correct answer. What is the complete factorization of x2 + 2x − 63? A. (x + 21)(x − 3) B. (x − 9)(x + 7) C. (x + 9)(x − 7) D. (x − 21)(x + 3)

Answer 1

Answer is C. ( x + 9) (x -7 )

Step by step using “complete the Square” method

x^2 + 2x -63 = 0

Isolate variables, add 63 to both sides

x^2 +2x = 63

Find 1/2 of x and square it a= 1^2 = 1

Add 1 to both sides of the equation

x^2 + 2x +1 = 63 + 1
Simplify

x^2 + 2x +1 = 64

Now you can factor both sides

( x + 1) ^2 on the left - explanation
( x + 1) (x + 1) distributed = x^2 + 2x +1

Now take square root of both sides

√ (x + 1)^2 = √64

x + 1 = +- 8
Subtract 1 from both sides

x = -1 +- 8

So

x = -1 + 8
x = 7 or ( x - 7)
x = -1 -8
x = -9 or ( x + 9)

So C. Is your correct answer

Answer 2

C is correct

Explanation:

x² + 2x - 63

= x² +9x - 7x - 63

= x(x+9)-7(x+9)

= (x + 9)(x - 7)

∴ C is correct