factorise x^3 + 2x^2 - 11x - 12
Answers
Answered by
17
Answer:
(x-3), (x+4) and (x+1)
Step-by-step explanation:
You can factorize this polynomial using Factor Theorem.
p(x) = x³+2x²-11x-12
Let g(x) = (x+1)
Let (x+1) = 0
= x = -1
p(1) = -1³+2 x -1²- 11 x -1 -12
p(1) = -1 + 2 x 1 - 11 x -1 - 12
p(1) = -1 + 2 +11 - 12
p(1) = 1 + 11 - 12
p(1) = 12-12
p(1) = 0
Therefore, (x+1) is a factor of p(x).
Now, let us divide p(x) by g(x) using long division.
When we do this, We get q(x) = x²+x-12 (quotient)
Now, let us factorize q(x):
x²+x-12
= x²-3x+4x-12
= x(x-3)+4(x-3)
= (x-3)(x+4)
Therefore, The factors of p(x) are (x-3), (x+4) and (x+1)
Answered by
1
Step-by-step explanation:
here is your answer. hope it helps you
Attachments:

Similar questions