Question

question 4 of 24 step 1 of 1 use synthetic division to determine if the given value for k is a zero of this polynomial. if not, determine p(k). p(x) = 11x⁴ − 28x³ − 10x² + 53x − 18; k = 2 answer 2 points keypad keyboard shortcuts selecting an option will display any text boxes needed to complete your answer. is k a zero of this polynomial? yes no

Explanation:

Step1: Set up synthetic division

For \( p(x) = 11x^4 - 28x^3 - 10x^2 + 53x - 18 \) and \( k = 2 \), the coefficients are \( 11, -28, -10, 53, -18 \). Bring down the first coefficient:

$$
LATEXBLOCK0
$$

Step2: Multiply and add

Multiply \( 11 \) by \( 2 \) to get \( 22 \), add to \( -28 \): \( -28 + 22 = -6 \)

$$
LATEXBLOCK1
$$

Step3: Repeat multiplication and addition

Multiply \( -6 \) by \( 2 \) to get \( -12 \), add to \( -10 \): \( -10 + (-12) = -22 \)

$$
LATEXBLOCK2
$$

Step4: Continue the process

Multiply \( -22 \) by \( 2 \) to get \( -44 \), add to \( 53 \): \( 53 + (-44) = 9 \)

$$
LATEXBLOCK3
$$

Step5: Final multiplication and addition

Multiply \( 9 \) by \( 2 \) to get \( 18 \), add to \( -18 \): \( -18 + 18 = 0 \)

$$
LATEXBLOCK4
$$

The remainder is \( 0 \), so \( k = 2 \) is a zero.

Answer:

Yes