Need to calculate:The factorization of 2x^{3}-8x^{2}-9x+36.

Need to calculate:The factorization of 2x^{3}-8x^{2}-9x+36.

Question
Polynomial factorization
asked 2020-11-23
Need to calculate:The factorization of \(2x^{3}-8x^{2}-9x+36\).

Answers (1)

2020-11-24
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 \(2x^{3}-8x^{2}-9x+36\).
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
\(2x^{3}-8x^{2}-9x+36=(2x^{3}-8x^{2})-(9x-36)\)
\(=2x^{2}(x-4)-9(x-4)\)
As, \((x-4)\) is the common factor of the polynomial,
The polynomial can be factorized as,
\(2x^{2}(x-4)-9(x-4)=(x-4)(2x^{2}-9)\)
Therefore, the factorization of the polynomial \(2x^{3}-8x^{2}-9x+36\) is \((x-4)(2x^{2}-9)\).
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