Need to calculate:The factorization of the polynomial, 2x^{4}+6x^{2}+5x^{2}+15.

Dillard 2021-02-22 Answered
Need to calculate:The factorization of the polynomial, 2x4+6x2+5x2+15.
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Expert Answer

liannemdh
Answered 2021-02-23 Author has 106 answers
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,
abac+bdcd=a(bc)+d(bc)
=(a+d)(bc)
Calculation:
Consider the provided polynomial,
2x4+6x2+5x2+15
Since, this is a four term polynomial, factorization of this polynomial can be find with the help of factor by grouping as,
2x4+6x2+5x2+15=(2x4+6x2)+(5x2+15)
=2x2(x2+3)+5(x2+3)
As, (x2+3) is the common factor of the polynomial,
Therefore, the polynomial can be factorized as,
2x4+6x2+5x2+15=2x2(x2+3)+5(x2+3)
=(x2+3)(2x2+5)
Hence, the factorization of the polynomial 2x4+6x2+5x2+15 is (x2+3)(2x2+5).
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