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Over Lesson 8–3
A. A
B. B
C. C
D. D
(m – 4)(m – 9)
Factor m2 – 13m + 36.
Over Lesson 8–3
A. A
B. B
C. C
D. D
{–2, 10}
Solve y2 – 8y – 20 = 0.
Over Lesson 8–3
A. A
B. B
C. C
D. D
{–6, –2}
Solve x2 + 8x = –12.
Over Lesson 8–3
A. A
B. B
C. C
D. D
(p4 – 14)(p4 + 6)
What are the factors of p8 – 8p4 – 84?
• Factor trinomials of the form ax2 + bx + c.
• Solve equations of the form ax2 + bx + c = 0.
• prime polynomial
Factor ax2 + bx + c
A. Factor 5x2 + 27x + 10.In this trinomial, a = 5, b = 27, and c = 10. You need to find two numbers with a sum of 27 and with a product of 5 ● 10 or 50. Make an organized list of the factors of 50 and look for the pair of factors with the sum of 27.
1, 50 51
2, 25 27 The correct factors are 2 and 25.
Factors of 50 Sum of Factors
Divide these factors by the leading coefficient and reduce
Factor ax2 + bx + c
2551
= (5x + 2)(x + 5)
Answer: (5x + 2)(x + 5)
Factor ax2 + bx + c
B. Factor 4x2 + 24x + 32.
The GCF of the terms 4x2, 24x, and 32 is 4. Factor this term first.
4x2 + 24x + 32 = 4(x2 + 6x + 8) DistributiveProperty
Now factor x2 + 6x + 8. Since the lead coefficient is 1, find the two factors of 8 whose sum is 6.
1, 8 9
2, 4 6 The correct factorsare 2 and 4.
Factors of 8 Sum of Factors
Factor ax2 + bx + c
Answer: So, x2 + 6x + 4 = (x + 2)(x + 4). Thus, the complete factorization of 4x2 + 24x + 32 is 4(x + 2)(x + 4).
A. A
B. B
C. C
D. D
(3x + 5)(x + 7)
A. Factor 3x2 + 26x + 35.
A. A
B. B
C. C
D. D
2(x + 2)(x + 5)
B. Factor 2x2 + 14x + 20.
Factor ax2 – bx + c
Factor 24x2 – 22x + 3.In this trinomial, a = 24, b = –22, and c = 3. Since b is negative, m + p is negative. Since c is positive, mp is positive. So m and p must both be negative. Therefore, make a list of the negative factors of 24 ● 3 or 72, and look for the pair of factors with the sum of –22.
–1, –72 –73
–2, –36 –38
–3, –24 –27
–4, –18 –22 The correct factorsare –4 and –18.
Factors of 72 Sum of Factors
Factor ax2 – bx + c
24x2 – 22x + 3 = 24x2 + mx + px + 3 Write the pattern.
= (4x – 3)(6x – 1) DistributiveProperty
= 24x2 – 4x –18x + 3 m = –4 and p = –18
= (24x2 – 4x) + (–18x + 3) Group terms with common factors.
= 4x(6x – 1) + (–3)(6x –1) Factor the GCF.
Answer: (4x – 3)(6x – 1)
A. A
B. B
C. C
D. D
(2x – 3)(5x – 4)
Factor 10x2 – 23x + 12.
Determine Whether a Polynomial is Prime
Factor 3x2 + 7x – 5.
In this trinomial, a = 3, b = 7, and c = –5. Since b is positive, m + p is positive. Since c is negative, mp is negative, so either m or p is negative, but not both. Therefore, make a list of all the factors of 3(–5) or –15, where one factor in each pair is negative. Look for the pair of factors with a sum of 7.
–1, 15 14
1, –15 –14
–3, 5 2
3, –5 –2
Factors of –15 Sum of Factors
Determine Whether a Polynomial is Prime
There are no factors whose sum is 7. Therefore, 3x2 + 7x – 5 cannot be factored using integers.
Answer: 3x2 + 7x – 5 is a prime polynomial.
Solve Equations by Factoring
ROCKETS Mr. Nguyen’s science class built a model rocket for a competition. When they launched their rocket outside the classroom, the rocket cleared the top of a 60-foot high pole and on its descent landed in a nearby tree. If the launch pad was 2 feet above the ground, the initial velocity of the rocket was 64 feet per second, and the rocket landed 30 feet above the ground, how long was the rocket in flight? Use the equation h = –16t2 + vt + h0.
h = –16t2 + vt + h0 Vertical motion model
30 = –16t2 + 64t + 2 h = 30, v = 64, h0 = 2
0 = –16t2 + 64t – 28 Subtract 30 from each side.
Solve Equations by Factoring
0 = –4(4t2 – 16t + 7) Factor out –4.
0 = 4t2 – 16t + 7 Divide each side by –4.
0 = (2t – 7)(2t – 1) Factor 4t2 – 16t + 7.
2t – 7 = 0 or 2t – 1 = 0 Zero Product Property
2t = 7 2t = 1 Solve each equation.
Solve Equations by Factoring
Answer: 3.5 seconds
again on its way down. Thus, the rocket was in flight for 3.5 seconds before landing.
A. A
B. B
C. C
D. D
When Mario jumps over a hurdle, his feet leave the ground traveling at an initial upward velocity of 12 feet per second. Find the time t in seconds it takes for Mario’s feet to reach the ground again. Use the equation h = –16t2 + vt + h0.
