What is the value of (x + 2)(x - 3) + 5, when x² - x - 6 = - 4 ?

A.) -2

B.) -1

C.) 1

D.) 2

E.) 3

A.) -2

B.) -1

C.) 1

D.) 2

E.) 3

**Solve the equation x² - x - 6 = - 4, for x, and then substitute the value(s) into (x + 2)(x - 3) + 5**

x² - x - 6 = - 4

x² - x - 2 = 0 {added 4 to each side}

(x - 2)(x + 1) = 0 {factored into two binomials}

x - 2 = 0 or x + 1 = 0 {set each factor equal to 0}

x = 2 or x = -1 {added 2 in first equation and subtracted 1 in second equation}

Beginning to get worried because you just got 2 solutions for x,

and the answer choices only show 1 number?? Read on!

(x + 2)(x - 3) + 5

= (2 + 2)(2 - 3) + 5 {substituted 2 in for x}

= 4(-1) + 5 {worked inside parentheses}

= - 4 + 5 {multiplied}

= 1 {added}

(x + 2)(x - 3) + 5

= (-1 + 2)(-1 - 3) + 5 {substituted -1 in for x}

= 1(-4) + 5 {worked inside parentheses}

= -4 + 5 {multiplied}

= 1 {added}

**C.) 1**

**- Algebra House**