Question

Using factor theorem, factorize each of the following polynomial:
x³+2x²-x-2

Answer 1

Answer:

x^3 + 2x^2 - x - 2 = 0

=> x^2(x + 2) - 1(x + 2) = 0

=> (x^2 - 1)(x + 2) = 0

=> x = -2, 1, -1

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Answer 2

$\underline \mathbb{QUESTION}$

Using factor theorem, factorize each of the following polynomial:

x³+2x²-x-2

$\underline \mathbb{SOLUTION}$

${x}^{3} - 2 {x}^{2} - x + 2$

$\bold\green{\underline{Let,}}$

$p(x) = {x}^{3} - 2 {x}^{2} - x + 2$

$\bold{\huge{\fbox{\color{Red}{By\:trial}}}}$

$p(1) = (1) {}^{3} - 2(1) {}^{2} - (1) + 2$

$= > 1 - 2 - 1 + 2 = 0$

$\bold{\fbox{\color{Red}{By\:factor\:theorem}}}$

$\bold\green{\underline{x-1\:is\:a\:factor\:of\:p(x)}}$

${x}^{3} - 2 {x}^{2} - x + 2$

$= > {x}^{2} (x - 1) - x(x - 1) - 2(x - 1)$

$= > (x - 1)( {x}^{2} - x - 2 )$

$= > (x - 1)( {x}^{2} - 2x + x - 2)$

$= > (x - 1)x(x - 2) + 1(x - 2)$

$= > (x - 1)(x - 2)(x + 1)$

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