College Algebra: Use synthetic division to determine if the given value for k is a zero of this polynomial

Question

Use synthetic division to determine if the given value for k is a zero of this polynomial. If not, determine p(k). p(x)=7x4−21x3−9x2+53x−14;k=2

is k a zero for this polynomial?

Answer 1

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2 | 7 -21 -9 53 -14

14 -14 -46 14

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7 -7 -23 7 0

P(2) = 7*16 - 21*8 - 9*4 + 53*2 -14

= 112 - 168 - 36 + 106 - 14

= 0

YES