Factor each polynomial. 6x^{3}+3x^{2}y+2xz^{2}+yz^{2}

Sam Longoria 2021-12-12 Answered
Factor each polynomial. 6x3+3x2y+2xz2+yz2
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Expert Answer

Ella Williams
Answered 2021-12-13 Author has 28 answers
Step 1
To factor the polynomial 6x3+3x2y+2xz2+yz2, first take the common factor 3x2 from the first two terms and z2 from the last two terms, and then take out the common term (2x+y) from the resulting expression to get the factorized form of the equation, that is;
6x3+3x2y+2xz2+yz2=3x22x+3x2y+2xz2+yz2
=3x2(2x+y)+z2(2x+y)
=(2x+y)(3x2+z2)
Step 2
Now to check the obtained result, expand the expression by cross multiplication and check whether it forms the initial polynomial, as follows;
(2x+y)(3x2+z2)=2x(3x2)+2x(z2)+y(3x2)+y(z2)
=6x3+2xz2+3yx2+yz2
Therefore the factorized form of the polynomial 6x3+3x2y+2xz2+yz2 is (2x+y)(3x2+z2)

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Pademagk71
Answered 2021-12-14 Author has 34 answers

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