Question

Using factor theorem factorise
x 3 + 2x² 11x-12​

Answer 1

Given Equation :

• x³ + 2x² - 11x - 12

Let us take random numbers from 0, to find the roots of the given equation.

Let us first take x = -1

⟹ (-1)³ + 2(-1)² - 11(-1) - 12

⟹ -1 + 2 + 11 - 12

⟹ 0

So, we get ( x + 1 ) as one of the root of the given polynomial.

Now, let us divide the given polynomial with ( x + 1 )

Refer to the attachment for the long division.

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The quotient we got is x² + x - 12

Let us solve this equation by the method called splitting the middle term.

$⟹ {x}^{2} + x - 12$

$⟹ {x}^{2} + 4x - 3x - 12$

$⟹ x(x + 4) - 3(x + 4)$

$⟹ (x + 4)(x - 3)$

$\sf{ \red{x = - 4}}$

$\sf{ \blue{x = 3}}$

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Hence the factors of the polynomial x³ + 2x² - 11x - 12 are :

• ( x + 1 )
• ( x + 4 )
• ( x - 3 )

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