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# Need to calculate:The factorization of x^{3}+8x^{2}-3x-24. # Need to calculate:The factorization of x^{3}+8x^{2}-3x-24.

Question
Polynomial factorization asked 2021-01-06
Need to calculate:The factorization of $$x^{3}+8x^{2}-3x-24$$.

## Answers (1) 2021-01-07
Formula used:
The factors of a polynomial can be find by taking a common factor and this method is called factor by grouping,
$$ab+ac+bd+cd=a(b+c)+d(b+c)$$
$$=(a+d)(b+c)$$
Or,
$$ab-ac+bd-cd=a(b-c)+d(b-c)$$
$$=(a+d)(b-c)$$
Calculation:
Consider the polynomial $$x^{3}+8x^{2}—3x—24$$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$$x^{3}+8x^{2}—3x—24=(x^{3}+8x^{2})—(3x+24)$$
$$=x^{2}(x+8)-3(x+8)$$
As, $$(x+8)$$ is the common factor of the polynomial,
The polynomial can be factorized as,
$$x^{2}(x+8)—3(x+8)=(x+8)(x^{-3})$$
Therefore, the factorization of the polynomial $$x^{3}+8x^{2}—3x—24\ is\ (x + 8)(x^{2}-3)$$.

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