Need to calculate:The factorization of x^{3}+4x^{2}+3x+12.

defazajx 2021-03-09 Answered
Need to calculate:The factorization of x3+4x2+3x+12.
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Expert Answer

izboknil3
Answered 2021-03-10 Author has 99 answers

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,
abac+bdcd=a(bc)+d(bc)
=(a+d)(bc)
Calculation:
Consider the polynomial x3+4x2+3x+12.
This is a four term polynomial, factorization of this polynomial can be found by factor by grouping as,
x3+4x2+3x+12=(x3+4x2)+(3x+12)
=x2(x+4)+3(x+4)
As, (x+4) is the common factor of the polynomial,
The polynomial can be factorized as,
x3+4x2+3x+12=x2(x+4)+3(x+4)
=(x+4)(x2+3)
Therefore, the factorization of the polynomial x3+4x2+3x+12 is (x+4)(x2+3).

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