Theory question 104
PolynomialsIf (x + 1) and (x − 2) are factors of the polynomial g(x) = x4 + ax3 + bx2 − 16x − 12, find the values of a and b.
Show the model answer
Model answer
g(−1) = 1 − a + b + 16 − 12 = 0, so b − a = −5.
g(2) = 16 + 8a + 4b − 32 − 12 = 0, so 2a + b = 7.
Subtracting: 3a = 12, a = 4, b = −1.
Explanation
Use the factor theorem twice.