Question

The polynomial p(x) = x4–2x 2+ bx + 3 when divided by x –2 leaves the remainder 23. Find the value of b.

Answer 1

Answer:

6

Step-by-step explanation:

For 0 of x-2=

                   x-2=0

                   ⇒x=2

By remainder theorem-

$x^{4}-2x^{2} +bx+3 \\=>(2)^{4} -(2)(2)^{2} +(b)(2)+3=23\\=>16-8+2b+3=23\\=>11+2b=23\\=>2b=23-11\\=>b=\frac{12}{2} \\\\=>6$

Answer 2

Answer:

6

Step-by-step explanation:

For 0 of x-2=

x-2=0

⇒x=2

By remainder theorem-

\begin{gathered}x^{4}-2x^{2} +bx+3 \\= > (2)^{4} -(2)(2)^{2} +(b)(2)+3=23\\= > 16-8+2b+3=23\\= > 11+2b=23\\= > 2b=23-11\\= > b=\frac{12}{2} \\\\= > 6\end{gathered}

x

4

−2x

2

+bx+3

=>(2)

4

−(2)(2)

2

+(b)(2)+3=23

=>16−8+2b+3=23

=>11+2b=23

=>2b=23−11

=>b=

2

12

=>6