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What are the different types of factoring polynomials?
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by
WinpossibleUser3718
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what are the different types of factoring polynomials?
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Responses
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There are many types of factoring polynomial, following are the basic types of factoring.
Type 1
Factoring out the greatest common factor from the polynomial
Ex. 5x^3 + 10 X^2
= 5x^2(x + 2)
Type 2
When there is no common factor of all terms in polynomial then grouping is done to find the factor
Ex. 3ax + 6ay + 4x + 8y
= 3a(x + 2y) + 4(x + 2y)
Now this two terms have a common factor i.e. (x + 2y)
(x + 2y) (3a + 4) |
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by
Winpossible
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Sep 03, 10 01:06PM PST
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More to the answer:
Type 3
Factoring the difference of two perfect squares. In this we use the property of a factor i.e.
x^2 – y^2 = (x + y)(x – y)
Ex.
2x*(y^2)*(z^3) – 18(x^3)*z
= 2xz{ (y^2)*(z^2) – 9(x^2)}
= 2xz{(yz)^2 – (3x)^2}\
= 2xz(yz + 3x)(yz - 3x)
Type 4
Factoring the sum or difference in two perfect cubes. Using the property of factor.
Sum: x^3 – y^3 = (x – y)(x^2 + xy + y^2)
Difference: x^3 + y^3 = (x + y)(x^2 - xy + y^2)
Ex.
8x^3 + 27x^3
= (2x)^3 +(3y)^3
= (2x + 3y){(2x)^2 - (2x)*(3y) + (3y)^2}
= (2x + 3y){4x^2 – 6xy + 9y^2}
Related video lessons:
Factoring Trinomial
Factoring
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by
Winpossible
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Sep 03, 10 01:11PM PST
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