Solutions

Problem Set #5:

1. Factor each quadratic below (there are no "duds" among them)

a) x² + x - 56 = (x+8)(x-7)

b) x² - 81 = (x+9)(x-9)

c) x² – 6x – 91 = (x-13)(x+7)

d) x² + 7x = (x)(x+7)

e) x³ – 6x² – 40x = x(x-10)(x+4)

2. Factor each below as much as possible. Your answers may be checked by expanding them and comparing to the original expression.

a) x² – 5x - 24 =(x-8)(x+3)

b) x⁶ – 100x⁴ = x⁴ (x-10)(x+10)

c) x² + 7x + 10 = (x+2)(x+5)

d) x² – 121 = (x+11)(x-11)

e) x² -12x + 35 = (x-5)(x-7)

f) x² + 16 = x² + 16

g) x² + 100x =x(x+100)

h) 5x³ -125x = 5x(x-5)(x+5)

i) x⁴ – 625 = (x+5)(x-5)(x² + 25)

j) 100 – 4x² = (10-2x)(10+2x) = -4(x-5)(x+5) as well

k) x⁴ + 25x² = x²(x² + 25)