Question

factories x cube+13x square+ 32x+ 20
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Answer 1

Step-by-step explanation:

Let, f (x) = x3 + 13x2 + 32x + 20 The factors of the constant term + 20 are ± ± 1, ± ± 2, ± ± 4, ± ± 5, ± ± 10 and 20 Putting x = -1, we have f (-1) = (-1)3 + 13 (-1)2 + 32 (-1) + 20 = -1 + 13 – 32 + 20 = 0 So, (x + 1) is a factor of f (x) Let us now divide f (x) = x3 + 13x2 + 32x + 20 by (x + 1) to get the other factors of f (x) Using long division method, we get x3 + 13x2 + 32x + 20 = (x + 1) (x2 + 12x + 20) x2 + 2x + 20 = x2 + 10x + 2x + 20 = x (x + 10) + 2 (x + 10) = (x + 10) (x + 2) Hence, x3 + 13x2 + 32x + 20 = (x + 1) (x + 10) (x + 2)Read more on Sarthaks.com - https://www.sarthaks.com/1072873/using-factor-theorem-factorize-each-of-the-following-polynomial-x-3-13x-2-32x-20

Answer 2

$\small\bf{\underline{\green{verified \: answer✔}}}$

$x {}^{3} + 13x + 32x + 20$

$x {}^{3} + x {}^{2} + 12x {}^{2} + 32x + 20$

$x {}^{2} (x + 1) + 12x { }^{2} +(12 + 20)x + 20$

$x {}^{2} (x + 1) + 12x {}^{2} + 12x + 20 x + 20$

$x {}^{2} (x + 1) + 12x(x + 1) + 20(x + 1)$

$(x + 1) (x {}^{2} + 12x + 20)$

$(x + 1)(x {}^{2} + 10x + 2x + 20)$

Given:-

( x + 1 ) [x(x+10)+2(X+10)]

(x+1)(x+10)(x+2)