Algebra and General Mathematics: Factoring

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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