Algebra and General Mathematics: Factoring

Review notes in Factoring topic in Algebra and General Mathematics. This will help you prepare in taking the Engineering Board Exam or simply reviewing for your Algebra subject.

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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