Factoring and Solving Quadratics (Review)

Factoring and Solving Quadratics (Review)

Factoring (when a=1)

• If the expression looks like x²+bx+c

• Use the x-game ("c" goes on top, "b" goes on bottom)

• Find what multiplies to make the top, but adds/subtracts to make the bottom

• Pay attention to +/-!!

Multiple Choice

Factor
x²+12x+35

• (x+5)(x+7)
• (x+4)(x+3)
• (x+7)(x-5)
• Prime

Multiple Choice

Factor
x² -16x + 48

• (x - 12)(x - 4)
• (x + 6)(x - 8)
• (x + 12)(x - 4)
• (x -16)(x - 3)

Multiple Choice

Factor
k² - 2k - 24

• (k+4)(k-6)
• (k+4)(k+6)
• (k+6)(k-1)
• (k-4)(k+6)

Factoring (when  $a\ne1$  )

• If the expression looks like  $ax^2+bx+c$  

• Use the x-game, but MULTIPLY a times c to get the number that goes on top; b still goes on bottom

• Don't forget to SLIDE & DIVIDE to get your final answer

• Pay attention to +/-!!

Multiple Choice

Factor:

2m² + 3m − 9

• 2(m + 3)(m − 3)

• (2m − 3)²

• (m + 3)(2m − 3)

• (2m + 3)(m − 3)

Solving a Quadratic Equation

• Make sure that the equation is set =0 (everything is on one side)

• Identify a, b, and c

• Use the quadratic formula and a calculator

• Remember to get BOTH answers!

Multiple Choice

Solve
x² + 2x - 24 = 0

• x = -6, x = 4
• x = 6, x = -4
• x = 12, x = -2
• x = 8, x = -3

Multiple Choice

Solve
6x² + 17x + 12 = 0

• x = -4/3, x = -3/2
• x = 9, x = 8
• x = 4, x = 3
• x = -4, x = -3

Multiple Choice

Solve:
x² - 49 = 0

• x = -7, x = 7
• x = -7
• x = 7
• x = -7, x = 1

Multiple Choice

Solve using the Quadratic Formula

6x² - 52 = 11x

• x = 4, -2.17

• x = -4, 2.17

• x = -3.71, -1.88

• x = 3.71, 1.88