Need to calculate: The factorization of the polynomial ax^{2}+ay+bx^{2}+by.

Ernstfalld 2021-03-06 Answered
Need to calculate: The factorization of the polynomial ax2+ay+bx2+by.
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Expert Answer

Tasneem Almond
Answered 2021-03-07 Author has 91 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, ax2+ay+bx2+by.
This is a four terms polynomial, factorization of this polynomial can be found by factor by grouping as,
ax2+ay+bx2+by=(ax2+ay)+(bx2+by)
=a(x2+y)+b(x2+y)
As, (x2+y) is the common factor of the polynomial factor it out as follows,
ax2+ay+bx2+by=a(x2+y)+b(x2+y)
=(x2+y)(a+b)
The factorization of the polynomial ax2+ay+bx2+ by is (x2+y)(a+b).
Check the result as follows,
(x2+y)(a+b)=x2a+x2b+ya+yb
=ax2+bx2+ay+by
=ax2+ay+bx2+by
Thus, the factorization of the polynomial ax2+ay+bx2+ by is (x2+y)(a+b).
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