Question

Factorise : x3 + 2x2 - 11x - 12

Answer 1

Answer:

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(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)

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Answer 2

Answer ✍

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1: -11x-12

Group 2: x3+2x2

Pull out from each group separately :

Group 1: (11x+12) • (-1)

Group 2: (x+2) • (x2)

Hope it helps you ❤⤴️