Question

Use synthetic substitution to find g(4) and g(-5) for the function g(x) = 3x4 - 5x2 + 7x - 7

Answer 1

`g(4)=709`

`g(-5) = 1708`

Explanation:

Step 1: Find g(4)

Substitution Method:

`g(4)=3(4)^4-5(4)^2+7(4)-7`

`g(4)=3(256)-5(16)+28-7`

`g(4)=768-80+28-7`

`g(4)=709`

Synthetic Division:

`\begin{array}{rrrrrr}\multicolumn{1}r{4} & {3} & 0 & -5 & 7 & -7\\\cline{2-6} & & 12& 48 & 172 & 716\\\cline{2-6} & 3 & 12& 43 & 179 & \multicolum 709\end{array}`

Answer:
`g(4)=709`

Step 2: Find g(-5)

`g(-5)=3(-5)^4-5(-5)^2+7(-5)-7`

`g(-5)=3(625)-5(25)-35-7`

`g(-5) = 1875-125-35-7`

`g(-5) = 1708`

Synthetic Division:

`\begin{array}{rrrrrr}\multicolumn{1}r{-5} & {3} & 0 & -5 & 7 & -7\\\cline{2-6} & & -15& 75& -350& 1715\\\cline{2-6} & 3 & -15& 70& -343& \multicolum 1708\end{array}`

Answer:
`g(-5) = 1708`