The polynomial p(x) = ax^3 + bx + 6 has remainder 0 when divided by x - 1 and remainder 12 when divided by x - 2. What is a?

1 p(1) = a + b + 6 = 0 \Rightarrow a + b = -6. p(2) = 8a + 2b + 6 = 12 \Rightarrow 8a + 2b = 6 \Rightarrow 4a + b = 3. Subtract: 3a = 9, a = 3. Hmm, that gives a = 3. Choice index 3 is the right answer; let me set a = 3 at index 0.

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Acemy

Nonlinear Equations in One Variable and Systems of Equations

SAT Math· difficulty 5/5

p(x) = ax^3 + bx + 6

A
$3$
B
$1$
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C
$2$
D
$-1$

Explanation

p(1) = a + b + 6 = 0 \Rightarrow a + b = -6

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