# Need to calculate:The factorization of x^{3}-7x^{2}+4x-28. Question
Polynomial factorization Need to calculate:The factorization of $$x^{3}-7x^{2}+4x-28$$. 2021-01-11
Formula used:
The factors of a polynomial can be found 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 $$x^{3}—7x^{2}+4x-28$$.
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
$$x^{3}-7x^{2}+4x-28=(x^{3}-7x^{2})+(4x-28)$$
$$=x^{2}(x-7)+4(x-7)$$
As, $$(x-7)$$ is the common factor of the polynomial,
The polynomial can be factorized as,
$$x^{3}-7x^{2}+4x-28=x^{2}(x-7)+4(x-7)$$
$$=(x-7)(x^2+4)$$
Therefore, the factorization of the polynomial is $$(x — 7)(x^{2} +4)$$.

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