Download FACTORING POLYNOMIALS

FACTORING POLYNOMIALS
I.
Is there a common factor?
2x – 8
=
2(x – 4)
2
=
xy2(x – 3)
5(x – y) + n(x – y)
=
(x – y )(5 + n)
2 2
x y – 3xy
II.
Is it a binomial? If so, is it the
A. Difference of two squares?
a2 – b2
=
(a + b)(a – b)
9x2 – 25y2
=
(3x + 5y)(3x – 5y)
(a + b)2 – 25
OR
=
=
[(a + b) + 5][(a + b) – 5]
(a + b + 5)(a + b-5)
B. Sum of two squares? a2 + b2 does not factor (it is prime.)
C. Sum of two cubes?
a 3 + b3
=
(a + b)(a2 – ab + b2)
8x3 + 27y3
=
(2x + 3y)(4x2 – 6xy + 9y2)
a3 – b3
=
(a – b)(a2 + ab + b2)
x3 – 64
=
(x – 4)(x2 + 4x + 16)
D. Difference of two cubes?
E. None of these? It does not factor (it is prime)
III.
Is it a trinomial? If so, is it. . .
A. Square of a binomial (often referred to as a Perfect Square Trinomial)?
a2 + 2ab + b2
=
(a + b)(a + b)
x2 + 6x + 9
OR
=
=
(x + 3)(x + 3)
(x + 3)2
4x2 – 20xy + 25y2
=
(2x – 5y)2
(OVER)
B. Is a = 1? Use REVERSE FOIL or trial-and-error method
x2 + 7x + 12
=
(x + 3)(x + 4)
2
=
(x – 3)(x – 4)
2
=
(x + 6)(x – 3)
2
=
(x – 6)(x + 3)
x – 7x + 12
x + 3x – 18
x – 3x – 18
C. Is a  1? Use AC GROUPING or trial-and-error method.
(See handout on Factoring Ax2 + Bx + C)
IV.
Does it have four terms. If so, will it. . .
A. Group (first two terms together, last two terms together)
5a – 5b – xa + xb
=
=
=
(5a – 5b) + (-xa + xb)
5(a – b) – x(a – b)
(a – b)(5 – x)
x3 – 3x2 + 2x – 6
=
=
=
(x3 – 3x2) + (2x – 6)
x2(x – 3) + 2(x – 3)
(x – 3)(x2 + 2)
B. Group (first three terms together)
x2 + 6x + 9 – y2
=
=
=
(x2 + 6x + 9) – y2
(x + 3)2 – y2
[(x + 3) + y][(x + 3) – y]
C. Group (last three terms together)
y2 – x2 + 6x – 9
=
=
=
y2 – (x2 – 6x + 9)
y2 – (x – 3)2
[y + (x – 3)][y – (x – 3)]
BE SURE YOUR ANSWER IS FACTORED COMPLETELY.