Question

Part A: Write the expression x2 + 2x - 24 as a product of two linear expressions. Show your work and justify each step. (5 points)

Part B: Rewrite x2 - 8x + 16 as a square of a linear expression. (3 points)

Part C: Do the expressions in parts A and B have a common factor? Justify your answer. (2 points)

Answer 1

well factor the expression in part A

look at the constant term -24... find the factors of -24 that add to -2...

the larger factor is negative

then written in linear form its

(x + factor 1)(x + factor 2)

part B

this is a perfect square, which means the linear factors are identical...

so find the factors of 16 that add to -8... both factors are negative and the same value.

so its written (x + factor1)(x + factor2) or ( x + factor1)^2

part C should be obvious if you factor correctly