Question

Evaluate polynomials using synthetic division ADF If p(u)=2ᵘ⁴-28ᵘ²-24u-17, use synthetic division to find p(4). Submit

Answer 1

To evaluate the polynomial p(u)=2u⁴-28u²-24u-17 using synthetic division, follow the steps: identify terms, arrange in descending order, set up the table, perform synthetic division, obtain the result.

Step-by-step explanation:

To evaluate the polynomial p(u)=2ᵘ⁴-28ᵘ²-24u-17 using synthetic division, we need to follow these steps:

1. Identify the constant term and the coefficients of the powers of u.
2. Arrange them in descending order.
3. Set up the synthetic division table.
4. Perform the synthetic division using the given value, in this case, 4.
5. The resulting value will be the evaluated polynomial.

Let's go through these steps:

Step 1:

Constant term: -17

Coefficients of u⁴: 2

Coefficients of u³: 0 (since u³ is not present)

Coefficients of u²: -28

Coefficients of u: -24

Step 2:

Arranging them in descending order: 2ᵘ⁴-28ᵘ²-24u-17

Step 3:

Synthetic division table:

u | 2 -28 -24 -17
4

Step 4:

Performing synthetic division:

u | 2 -28 -24 -17
4 | 8 -80 -416 -1752

Step 5:

The resulting value is -1752.

Therefore, p(4) = -1752.