If (ax + 2)(bx + 7) = 15x^2 + cx + 14 for all values of x, and a + b = 8, what are the two possible

Q: What is the correct answer for SAT Maths?

The correct answer is D. Expand the left side of the equation: (ax + 2)(bx + 7) = abx^2 + 7ax + 2bx + 14 = abx^2 + (7a + 2b)x + 14. Comparing this to 15x^2 + cx + 14, we can equate the coefficients: 1) ab = 15 2) 7a + 2b = c We are also given a + b = 8. From a + b = 8, we can express b as b = 8 - a. Substitute this into ab = 15: a(8 - a) = 15 8a - a^2 = 15 a^2 - 8a + 15 = 0 Factor the quadratic equation: (a - 3)(a - 5) =

Q: If (ax + 2)(bx + 7) = 15x^2 + cx + 14 for all values of x, and a + b = 8, what are the two possible values for c?

The correct answer is D. Expand the left side of the equation: (ax + 2)(bx + 7) = abx^2 + 7ax + 2bx + 14 = abx^2 + (7a + 2b)x + 14. Comparing this to 15x^2 + cx + 14, we can equate the coefficients: 1) ab = 15 2) 7a + 2b = c We are also given a + b = 8. From a + b = 8, we can express b as b = 8 - a. Substitute this into ab = 15: a(8 - a) = 15 8a - a^2 = 15 a^2 - 8a + 15 = 0 Factor the quadratic equation: (a - 3)(a - 5) =

Q: What are the options for this SAT Maths question?

A. 3 and 5 · B. 6 and 35 · C. 10 and 21 · D. 31 and 41

Question

If (ax + 2)(bx + 7) = 15x^2 + cx + 14 for all values of x, and a + b = 8, what are the two possible values for c?

FirstInTest · Accepted Answer

Expand the left side of the equation:
(ax + 2)(bx + 7) = abx^2 + 7ax + 2bx + 14 = abx^2 + (7a + 2b)x + 14.
Comparing this to 15x^2 + cx + 14, we can equate the coefficients:
1) ab = 15
2) 7a + 2b = c
We are also given a + b = 8.
From a + b = 8, we can express b as b = 8 - a. Substitute this into ab = 15:
a(8 - a) = 15
8a - a^2 = 15
a^2 - 8a + 15 = 0
Factor the quadratic equation: (a - 3)(a - 5) = 0. So, a = 3 or a = 5.
Case 1: If a = 3, then b = 8 - 3 = 5. Substitute these values into the equation for c:
c = 7a + 2b = 7(3) + 2(5) = 21 + 10 = 31.
Case 2: If a = 5, then b = 8 - 5 = 3. Substitute these values into the equation for c:
c = 7a + 2b = 7(5) + 2(3) = 35 + 6 = 41.
Thus, the two possible values for c are 31 and 41.

Answer

3 and 5

Answer

6 and 35

Answer

10 and 21

Answer

31 and 41

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