Assignment #2
Solution
d. 2 numbers are +6 and -1
2𝑥 2 + 6𝑥 − 𝑥 − 3
(2𝑥 2 + 6𝑥)(−𝑥 − 3)
2𝑥(𝑥 + 3) − 1(𝑥 + 3)
(2𝑥 − 1)(𝑥 + 3)
h. 2 numbers are +3 and +8
6𝑥 2 + 8𝑥 + 3𝑥 + 4
(6𝑥 2 + 8𝑥)(+3𝑥 + 4)
2𝑥 (3𝑥 + 4) + 1(3𝑥 + 4)
(2𝑥 + 1)(3𝑥 + 4)
l. −(15𝑥 2 + 𝑥 − 2)
the two numbers are +6 and -5
−(15𝑥 2 + 6𝑥 − 5𝑥 − 2)
−[3𝑥 (5𝑥 + 2) − 1(5𝑥 + 2)]
−(3𝑥 − 1)(5𝑥 + 2)
p. 6(3𝑥 2 − 5𝑥 + 2)
the two numbers are -3 and -2
6(3𝑥 2 − 3𝑥 − 2𝑥 + 2)
6[3𝑥 (𝑥 − 1) − 2(𝑥 − 1)
6(3𝑥 − 2)(𝑥 − 1)
h. let 𝑎 = 2𝑥 2 − 3𝑥, and 𝑏 = 2𝑥 − 5
therefore, (2𝑥 2 − 3𝑥)2 − (2𝑥 − 5)2 becomes 𝑎2 − 𝑏2 which is a difference of squares
𝑎2 − 𝑏2 = (𝑎 + 𝑏)(𝑎 − 𝑏)
[(2𝑥 2 − 3𝑥) + (2𝑥 − 5)][(2𝑥 2 − 3𝑥) − (2𝑥 − 5)]
[2𝑥 2 − 3𝑥 + 2𝑥 − 5][2𝑥 2 − 3𝑥 − 2𝑥 + 5]
[2𝑥 2 − 𝑥 − 5][2𝑥 2 − 5𝑥 + 5]