Factor each polynomial completely. If the polynomial cannot be factored,

Josh Sizemore 2021-12-14 Answered
Factor each polynomial completely. If the polynomial cannot be factored, say it is prime.
8x2+88x+80
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Expert Answer

Bukvald5z
Answered 2021-12-15 Author has 33 answers
Step 1
We have to factorize the polynomial:
8x2+88x+80
Factorizing the polynomial by middle term splitting method
Here,
80×8
For middle term,
80+8=88
Step 2
Therefore,
8x2+88x+80=8x2+80x+8x+80
=8x(x+10)+8(x+10)
=(x+10)(8x+8)
=(x+10)×8(x+1)
=8(x+1)(x+10)
Hence, factorized form of the expression is 8(x+1)(x+10).
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Jenny Bolton
Answered 2021-12-16 Author has 32 answers
There are many ways of factorize a polynomial. Key point is to find out the common factor from whole polynomial. Sometimes it is easy to form groups of terms in such a way that there is always one factor common in several groups. Then with the help of distributive property common factor can be factored out of each group. This technique of factorization is called factor by grouping. Sometimes there is no common factor coefficient in middle term. In such case, it is known as prime polynomial.
Objective is factor the polynomial 8x2+88x+80. It cannot be factored, then it is prime polynomial.
It is obviously seen first common factor is 8 in the polynomial. Take it as common factor then solve it further as given below:
8x2+88x+80=8(x2+11x+10)
=8(x2+10x+x+10)
=8(x(x+10)+1(x+10))
=8(x+10)(x+1)
Hence, the factor of 8x2+88x+80 polynomial is 8(x+10)(x+1). Since it has three factors, since. The is not a prime polynomial.
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