Question

3 poi
Ahn
16) Factorise (a) x² +3x2-x-3
(b) x2-7-30​

Answer 1

ANSWER

Let p(x)=x3+3x2−x−3

p(x) is a cubic polynomial, so it may have three linear factors.

The constant term is -3. The factors of -3 are -1, 1, -3 and 3.

p(−1)=(−1)3+3(−1)2−(−1)−3=−1+3+1−3=0

∴(x+1) is a factor of p(x).

p(1)=(1)3+3(1)2−1−3=1+3−1−3=0

∴(x−1) is a factor of p(x).

p(−3)=(−3)3+3(−3)2−(−3)−3=−27+27+3−3=0

∴(x+3) is a factor of p(x).

The three factors of p(x) are (x + 1), (x - 1) and (x - 3)

∴x3+3x2−x−3=(x+1)(x−1)(x+3).