Question

x⁴-2x³-7x²+8x+12



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Answer 1

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• Factorise the polynomial.

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Given quartic polynomial,

$\sf {x}^{4} - 2 {x}^{3} - 7 {x}^{2} + 8x + 12$

$\sf = {x}^{4} + {x}^{3} - 3 {x}^{3} - 3 {x}^{2} - 4 {x}^{2} - 4x + 12x + 12$

$\sf = {x}^{3} (x + 1) - 3 {x}^{2} (x + 1) - 4x(x + 1) + 12(x + 1)$

$\sf = (x + 1)( {x}^{3} - 3 {x}^{2} - 4x + 12)$

$\sf = (x + 1)( {x}^{2}(x - 3) - 4(x - 3))$

$\sf = (x + 1)((x - 3)( {x}^{2} - 4)$

$\sf = (x + 1)(x - 3)(x + 2)(x - 2)$

$\star\:\:\:\sf\large\underline\blue{Answer:-}$

• $\sf (x + 1)(x - 3)(x + 2)(x - 2)$