Question

Two students, Tony and Mike, factored the trinomial 8x2 − 12x − 8. Tony factored it as 4(x − 2)(2x + 1) and Mike factored it as (x − 2)(8x + 4). Indicate which student factored the trinomial completely and which student did not, and explain why. (10 points)

Answer 1

Tony and Mike, factored the trinomial $8x^2 - 12x - 8$

Tony factored it as 4(x - 2)(2x + 1) and

Mike factored it as (x - 2)(8x + 4)

$8x^2 - 12x - 8$

GCF is 4. We factor out 4

$4(2x^2 - 3x - 2)$

2*-2=-4. We find out two factors whose product is -4  and sum is -3

two factors are -4  and 1. Split middle term -3x using two factors

$4(2x^2 - 4x + 1x - 2)$

Group first two terms and last two terms

$4[(2x^2 - 4x) + (1x - 2)]$

Factor out GCF from each group

$4[2x(x - 2) + 1(x - 2)$

4(2x+1)(x-2)

Tony factored it correctly

Mike factored it as (x − 2)(8x + 4)

Mike factor 8x+4 further. GCF of 8 and 4 is 4

So it becomes 4(2x+1)

Mike not factored it completely