Grade: 9 Subject: Math (Algebra I) Unit: Introduction to Quadratics Lesson: 3 of 6 SAT: AdvancedMath ACT: Math

Guided Practice

Learning Objectives

In this guided practice lesson, you will:

Work through these 10 problems. Click each question to reveal the answer and explanation.

Question 1: Factor: x^2 + 5x + 6

Answer: (x + 2)(x + 3)

Solution: Find two numbers that multiply to 6 and add to 5. Those numbers are 2 and 3. Check: (x+2)(x+3) = x^2 + 5x + 6.

Question 2: Factor: x^2 - 7x + 12

Answer: (x - 3)(x - 4)

Solution: Find two numbers that multiply to 12 and add to -7. Those are -3 and -4. Check: (x-3)(x-4) = x^2 - 7x + 12.

Question 3: Factor: x^2 - 9

Answer: (x + 3)(x - 3)

Solution: This is a difference of squares: a^2 - b^2 = (a+b)(a-b). Here, x^2 - 9 = x^2 - 3^2 = (x+3)(x-3).

Question 4: Solve: x^2 + 6x + 8 = 0

Answer: x = -2 or x = -4

Solution: Factor: (x+2)(x+4) = 0. Set each factor to zero: x+2=0 gives x=-2, x+4=0 gives x=-4.

Question 5: Solve using quadratic formula: x^2 - 4x - 5 = 0

Answer: x = 5 or x = -1

Solution: a=1, b=-4, c=-5. x = (4 +/- sqrt(16+20))/2 = (4 +/- 6)/2. So x = 5 or x = -1.

Question 6: Factor: 2x^2 + 7x + 3

Answer: (2x + 1)(x + 3)

Solution: Find factors of 2*3=6 that add to 7: 1 and 6. Rewrite: 2x^2 + x + 6x + 3. Factor by grouping: x(2x+1) + 3(2x+1) = (2x+1)(x+3).

Question 7: Factor: x^2 + 2x - 15

Answer: (x + 5)(x - 3)

Solution: Find two numbers that multiply to -15 and add to 2. Those are 5 and -3.

Question 8: Solve: x^2 - 16 = 0

Answer: x = 4 or x = -4

Solution: Factor: (x+4)(x-4) = 0. Or solve directly: x^2 = 16, so x = +/-4.

Question 9: Factor completely: 3x^2 - 12

Answer: 3(x + 2)(x - 2)

Solution: First factor out GCF: 3(x^2 - 4). Then factor difference of squares: 3(x+2)(x-2).

Question 10: Solve: x^2 + 4x + 4 = 0

Answer: x = -2 (double root)

Solution: Factor: (x+2)^2 = 0. This is a perfect square trinomial. x = -2 is the only solution (with multiplicity 2).