Question

When p(x)=9x4-45x3+37x2+x+2

is divided by x-2, a student can
determine the remainder by
evaluating p(2). What is the
value of p(2)?

Answer 1

The value:

• 
  `p\left(2\right)=-32`

Explanation:

Given the function

`p\left(x\right)=9x^4-45x^3+37x^2+x+2`

substituting x=2 to get p(2)

`p\left(2\right)=9\left(2\right)^4-45\left(2\right)^3+37\left(2\right)^2+\left(2\right)+2`

`\mathrm{Remove\:parentheses}:\quad \left(a\right)=a`

`p\left(2\right)=9\cdot \:2^4-45\cdot \:2^3+37\cdot \:2^2+2+2`

`\mathrm{Add\:the\:numbers:}\:2+2=4`

`p\left(2\right)=2^4\cdot \:9+2^2\cdot \:37+4-2^3\cdot \:45`

`p\left(2\right)=144+148+4-360`

`p\left(2\right)=-64`

`p\left(2\right)=-32`

Thus, the value:

• 
  `p\left(2\right)=-32`