Question

Is synthetic division to determine if they given value of K is zero of the polynomial

Answer 1

If k = 4 is a zero of this polynomial, that means we have p(4) = 0.

Also, using the Remainder theorem, we know that (x - 4) will be a factor of the polynomial, so dividing the polynomial by this factor results in a remainder of zero.

So, calculating the synthetic division, we have:

So the quotient of the division is 2x² + 4x + 11 and the remainder is 36.

Since the remainder is not zero, so k is not a zero of the polynomial.

Answer: No

p(k) = 36