Factorize $x^{3} + x^{2} - 17 x + 15$

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Solution

$x^{3} + x^{2} - 17 x + 15$
$\Rightarrow x^{3} - x^{2} + 2 x^{2} - 2 x - 15 x + 15$
$\Rightarrow x^{2} (x - 1) + 2 x (x - 1) - 15 (x - 1)$
Take common out the tern (x-1)
$\Rightarrow (x - 1) (x^{2} + 2 x - 15)$
$\Rightarrow (x - 1) (x^{2} - 3 x + 5 x - 15)$
$\Rightarrow (x - 1) x (x - 3) + 5 (x - 3)$
$\Rightarrow (x - 1) (x - 3) (x + 5)$

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Factorize: x³ + x² - 17x + 15

Q. Which of the following are factors of

f (x) = x^{3} - x^{2} - 17 x - 15

Question 24
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(i) $2 x^{3} - 3 x^{2} - 17 x + 30$

(ii) $x^{3} - 6 x^{2} + 11 x - 6$

(iii) $x^{3} + x^{2} - 4 x - 4$

(iv) $3 x^{3} - x^{2} - 3 x + 1$

Question 24
Factorise
(i) $2 x^{3} - 3 x^{2} - 17 x + 30$

(ii) $x^{3} - 6 x^{2} + 11 x - 6$

(iii) $x^{3} + x^{2} - 4 x - 4$

(iv) $3 x^{3} - x^{2} - 3 x + 1$

Q. Find the degree of the following polynomial.

x^{3} + 17 x - 21 - x^{2}

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Factorize x3+x2−17x+15

x3+x2−17x+15⇒x3−x2+2x2−2x−15x+15⇒x2(x−1)+2x(x−1)−15(x−1)Take common out the tern (x-1)⇒(x−1)(x2+2x−15)⇒(x−1)(x2−3x+5x−15)⇒(x−1)x(x−3)+5(x−3)⇒(x−1)(x−3)(x+5)

Factorize $x^{3} + x^{2} - 17 x + 15$