Use synthetic division to determine if the given value for $k$ is a zero of this polynomial. If not, determine $p (k)$ .
$p (x) = 4 x^{4} - 12 x^{3} - 8 x^{2} + 46 x - 28; k = 2$
Answer
Selecting an option will display any text boxes needed to complete your answer.
Is k a zero of this polynomial?
Yes O No

Answer

Expert–verified

Hide Steps

Answer

$Yes, k is a zero of this polynomial.$

Steps

Step 1 ：Given the polynomial $p (x) = 4 x^{4} - 12 x^{3} - 8 x^{2} + 46 x - 28$ and $k = 2$

Step 2 ：To determine if $k$ is a zero of the polynomial, we substitute $k$ into the polynomial. If the result is zero, then $k$ is a zero of the polynomial.

Step 3 ：Substituting $k = 2$ into the polynomial, we get $p (k) = 4 (2)^{4} - 12 (2)^{3} - 8 (2)^{2} + 46 (2) - 28$

Step 4 ：Solving the above expression, we find that $p (k) = 0$

Step 5 ：Since $p (k) = 0$ , we conclude that $k = 2$ is a zero of the polynomial.

Step 6 ： $Yes, k is a zero of this polynomial.$

Use synthetic division to determine if the given value for k is a zero of this polynomial. If not, determine p(k).p(x)=4x4−12x3−8x2+46x−28;k=2AnswerSelecting an option will display any text boxes needed to complete your answer.Is k a zero of this polynomial?Yes O No

Answer

Popular Problems