Need to calculate:The factorization of x^{3}-7x^{2}+4x-28.

Question
Polynomial factorization
asked 2021-01-10
Need to calculate:The factorization of \(x^{3}-7x^{2}+4x-28\).

Answers (1)

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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