Algebra and General Mathematics: Factoring

(Last Updated On: February 5, 2020)

FACTORING

Factoring is the process of writing polynomial as a product.

COMMON MONOMIAL FACTOR

cx + cy = c(x + y)

FACTORING SPECIAL POLYNOMIAL FORMS

Difference of Two Squares

x2 – y2 = (x + y) (x – y)

Perfect Square Trinomial  x2 + 2xy + y2 = (x + y)2

x2 – 2xy + y2 = (x – y)2

Sum or Difference of Two Cubes

x3 + y3 = (x + y) (x2 – xy + y2)

x3 – y3 = (x – y) (x2 + xy + y2)

OTHER TRINOMIALS

x2 + (a + b)x + ab = (x + a) (x + b)acx2 + (ad +bc)x + bd = (ax + b) (cx + d)

FACTORING BY GROUPING

ac + bc + ad + bd = c(a + b) + d(a + b)                        = (a + b) (c + d)

FACTORING (x2 ± y2)

x4 – y4 = (x – y) (x + y) (x2 + y2)x5 + y5 = (x + y) (x4 – x3y + x2y2 – xy3 + y4)

x5 – y5 = (x – y) (x4 + x3y + x2y2 + xy3 + y4)

x6 – y6 = (x – y) (x + y) (x2 + xy + y2) (x2 – xy + y2)

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