Question

Given that the polynomial x³+ax-3x+4
Is divided by x-2 and the reminder is 14.Find the value of a

Answer 1

Step-by-step explanation:

$p(x) = {x}^{3} + ax - 3x + 4 \\ p(x) = 2 \\ p(2) = {2}^{3} + a \times 2 - 3 \times 2 + 4 \\ p(2) = 8 + 2a - 6 + 4 \\ p(2) = 2a + 6 \\ but \: p(2) = 14 \\ 2a + 6 = 14 \\ 2a = 14 - 6 \\ 2a = 8 \\ a = \frac{14}{2} \\ a = 7$

Answer 2

Answer:

x-2=0

x=2

then ,

x³+ax-3x+4=0

(2)³+a(2)-3(2)+4=0

8+2a-6+4=0

8-2+2a=0

6+2a=0

2a=-6

a=-6÷2

a=-3