UNIT 3 QUADRATIC FUNCTIONS SECTION 1 FACTORING FACTORING

UNIT 3 – QUADRATIC FUNCTIONS SECTION 1 – FACTORING

FACTORING REVIEW • Supplemental Packet p. 32 • Factor using GCF • 9 x 4 + 3 x 3 + 12 x 2 = • GCF: Greatest Common Factor • Each shares a 3 and x 2 • Divide 3 x 2 out of each term • = 3 x 2 (3 x 2 + x + 4)

FACTORING REVIEW • Practice: • 1) 10 x – 15 x 3 GCF: 5 x • = 5 x(2 – 3 x 2) • 2) 2 x 5 – 4 x 3 GCF: 2 x 3 • = 2 x 3(x 2 – 2 x) • 3) 6 c 3 – 12 c 2 d 2 + 3 cd • 3 cd(2 c 2 – 4 cd + 1)

FACTORING REVIEW • Factor Trinomials (a = 1) • x 2 + 5 x – 6 • = (x + 6)(x – 1) • Check by multiplying • x 2 – 1 x + 6 x – 6 • x 2 + 5 x - 6

FACTORING REVIEW • Practice: • 1) (c + 7)(c – 5) • 7 times -5 = -35 • Outer -5 c + inner 7 c = 2 c • 2) (x – 9)(x + 2) • 3) (x – 8)

FACTORING REVIEW • Factor Trinomials (a ≠ 1) • 6 x 2 + 7 x - 5 • = (6 x ) (x ) • Break up the 6 x 2, then the -5 • = (6 x - 5) (x + 1) • This does NOT work since outer 6 x + inner -5 x does not equal 7 x

FACTORING REVIEW • 6 x 2 + 7 x - 5 • = (6 x ) (x ) • Break up the 6 x 2, then the -5 • Try 3 and 2 instead of 6 and 1 • = (3 x - 5) (2 x + 1) • This does NOT work since outer 3 x + inner -10 x = -7 x and we need +7 x

FACTORING REVIEW • 6 x 2 + 7 x - 5 • = (6 x ) (x ) • Switch signs • = (3 x + 5) (2 x - 1) • This does work since outer -3 x + inner 10 x = +7 x

FACTORING REVIEW • Practice: • 1) (2 x + 1)(x + 7) • Outer 14 x + Inner 1 x = 15 x • 2) (3 x + 4)(x - 3) • Outer -9 x + Inner 4 x = -5 x

FACTORING REVIEW • Factoring a 2 – b 2 • Example: x 2 – 81 = • Break up the x 2 and 81, but the middle term is 0 x, it cancelled out. • This can only be done using 9 and -9 • = (x + 9)(x – 9)

FACTORING REVIEW • Practice: • 1) (x + 8)(x – 8) • 2) (6 x + 11)(6 x – 11) • *Note we are simply using the square root of each number. • 3) (8 x 3 + 7 y 2 w 4) (8 x 3 – 7 y 2 w 4)

FACTORING REVIEW • Factoring a 2 + 2 ab + b 2 • Example: x 2 + 8 x + 16 = • Break up the x 2 and 16, but the middle term of 8 x, is twice that of the square root of 16. • √ 16 = 4 4(2) also = 8 • = (x + 4)2

FACTORING REVIEW • Factoring a 2 + 2 ab + b 2 • Practice: • 1) √ 36 = 6 6(2) = 12 • = (x – 6)2 • 2) (4 x + 1)2 • Note: we are again using square root. • 3) (x 3 – 8 y)2

FACTORING REVIEW • Factoring Completely • ALWAYS look for a GCF first • 1) 9(x 2 + 10 x – 11) = 9(x + 11)(x – 1) • 2) 3 x(x 2 + 14 x + 49) = 3 x(x + 7)2 • 3) 10 x 3(4 x 2 – 81) • = 10 x 3(2 x + 9)(2 x – 9)

FACTORING REVIEW • PRACTICE pages: • Supplemental Packet p. 34 - 36

FACTORING REVIEW • SOLVE BY FACTORING • Supplemental packet p. 37 • Example: 3 x 2 – 8 x + 5 = 5 x + 15 • Step 1: Set the equation equal to 0 • 3 x 2 – 8 x + 5 = 5 x + 15 • -5 x - 15 -5 x – 15 • 3 x 2 – 13 x - 10 = 0

FACTORING REVIEW • SOLVE BY FACTORING • Step 2: Factor • 3 x 2 – 13 x - 10 = 0 • (3 x + 2)(x – 5) = 0 • Step 3: Solve • 3 x + 2 = 0 x – 5 = 0 • x = -2/3 x=5

FACTORING REVIEW • Practice: Supplemental packet p. 38