Question

if $h(x) = 5x^{3} - 26x^{2} + 5x$, use synthetic division to find $h(5)$.

Explanation:

Step1: Set up synthetic division

We are dividing \(h(x) = 5x^3 - 26x^2 + 5x + 0\) (we add the constant term 0) by \(x - 5\), so we use 5 as the root. The coefficients of the polynomial are 5, -26, 5, 0.
Set up the synthetic division as:

$$
LATEXBLOCK0
$$

Step2: Perform synthetic division

• Bring down the leading coefficient 5.
• Multiply 5 by 5 to get 25, add to -26: \(-26 + 25=-1\).
• Multiply -1 by 5 to get -5, add to 5: \(5 + (-5) = 0\).
• Multiply 0 by 5 to get 0, add to 0: \(0+0 = 0\).

The last number in the bottom row is the remainder, which is \(h(5)\) by the Remainder Theorem.

Answer:

0