The expression x^4-16 is equivalent to the product of (x+2) and p(x) which expression could represent p(x)
1 answer:
Easy
differnce of 2 perfect squares
a²-b²=(a+b)(a-b)
in this case
x⁴=(x²)²
16=4²
(x²)²-4²=(x²+4)(x²-4)
x²-4 can be factored since 4=2²
x²-2²=(x+2)(x-2)
complete factored form is
(x²+4)(x+2)(x-2)
gegroup to seperate (x+2)
(x+2)[(x²+4)(x-2)]
(x+2)p(x)
p(x)=(x²+4)(x-2)
expanded
p(x)=x³-2x²+4x-8
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