Question

Ax^3+bx^2+x-6has x+2 as a facter and leave remaunder 4when divide by x-2 .,find a and b

Answer 1

$\textbf{\huge{ANSWER:}}$

p (x) = ax^3 + bx^2 + x - 6 ...(1)

Factor = x + 2
=》x + 2 = 0
=》x = (-2) ...(2)

Remainder 4 when (1) is divided by x - 2
x - 2 = 0
=》 x = 2 ...(3)

(1) ÷ (2)

=》 a (-2)^3 + b (-2)^2 + (-2) - 6 = 0

=》 (-8a) + 4b - 8 = 0

=》 4 ( -2a + b -2 ) = 0

=》 (-2a) + b -2 = 0

=》 b = 2a + 2 .....(4)

(1) ÷ (3)

=》 a (2)^3 + b (2)^2 + 2 - 6 = 4

=》 8a + 4b - 4 = 4

=》 4 ( 2a + b) = 8

=》 2a + b = 2

=》 b = 2 - 2a ...(5)


b = b

Therefore,

(4) = (5)

=》2a + 2 = 2 - 2a

=》$\textbf{a = 0}$

Put the value of (a) in (4):

=》 2(0) + 2 = b

=》 $\textbf{b = 2}$

Hope it Helps!! :)

Answer 2

hey there ,,,

a= 0 and b = 2 ,,

solution told in attachment !!

hope it helps!!

All the best ,,,