Question

Factors of (x5 – 9x2 – 2x – 4) are​

Answer 1

Given data:

The expression $x^{5}-9x^{2}-2x-4$

To find:

We have to factorize the given term

Step-by-step explanation:

Here, $x^{5}-9x^{2}-2x-4$

$=x^{5}+2x^{4}+4x^{3}-2x^{4}-4x^{3}-8x^{2}-x^{2}-2x-4$

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

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

This is the required factorization.

Final answer:

$x^{5}-9x^{2}-2x-4=(x^{2}+2x+4)(x^{3}-2x^{2}-1)$

Note:

Since there is no $x^{4}$ and $x^{3}$ terms in the given expression, we must include them in the expression using $a-a=0$ concept.

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Answer 2

$Given data:</p><p></p><p>The expression x^{5}-9x^{2}-2x-4x5−9x2−2x−4</p><p></p><p>To find:</p><p></p><p>We have to factorize the given term</p><p></p><p>Step-by-step explanation:</p><p></p><p>Here, x^{5}-9x^{2}-2x-4x5−9x2−2x−4</p><p>=x^{5}+2x^{4}+4x^{3}-2x^{4}-4x^{3}-8x^{2}-x^{2}-2x-4=x5+2x4+4x3−2x4−4x3−8x2−x2−2x−4</p><p>=x^{3}(x^{2}+2x+4)-2x^{2}(x^{2}+2x+4)-1(x^2+2x+4)=x3(x2+2x+4)−2x2(x2+2x+4)−1(x2+2x+4)</p><p>=(x^{2}+2x+4)(x^{3}-2x^{2}-1)=(x2+2x+4)(x3−2x2−1)</p><p>This is the required factorization.</p><p></p><p>Final answer:</p><p></p><p>x^{5}-9x^{2}-2x-4=(x^{2}+2x+4)(x^{3}-2x^{2}-1)x5−9x2−2x−4=(x2+2x+4)(x3−2x2−1)</p><p>$