Question

Please Help! Multiple Choice!
Use synthetic division and the Remainder Theorem to find
P(–3) if P(x) = x^4 + 19x^3 + 108x^2 + 236x + 176

A) 7
B) 6
C) 8
D) 9

Please explain how you got your answer. Thank you!!

Answer 1

so let's check 8 for example:
step 1: (x^4 + 19^3 + 108x^2 + 236x + 176) - x^3(x-8) =
27x^3 + 108x^2 + 236x +176
step 2: (27x^3 + 108x^2 + 236x + 176) - 27x^2(x-8) =
324x^2 + 236x + 176
step 3: (324x^2 + 236x + 176 ) - 324x(x-8) = 2812x + 176
step4: 2812x + 176 - 2812(x-8) = 2812*8 + 176
which is not zero.
actually you can see that all your answers A - D are incorrect, because the coefficients of the equation are all positive, so the if x is positive the value of the equation is also always positive.
This equation can have only negative roots (if it has any)