All the real zeros of the given polynomial are integers.

dedica66em 2021-12-19 Answered
All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in factored form.
P(x)=x3+12x2+48x+64
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Expert Answer

Cheryl King
Answered 2021-12-20 Author has 36 answers
Step 1
Definition used -
Real zeros of a cubic polynomial -
We can factor a given cubic polynomial using the grouping method. Then we will equate all factors to 0 and solve for x. Those values of x are real zeros.
Step 2
Given -
P(x)=x3+12x2+48x+64
x3+12x2+48x+64=0
x3+4x2+8x2+32x+16x+64=0
x2(x+4)+8x(x+4)+16(x+4)=0
(x+4)(x2+8x+16)=0
(x+4)(x+4)(x+4)=0
x+4=0, x+4=0, x+4=0
x=-4
Step 3
Polynomial in factored form can be written as-
P(x)=(x+4)3

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jgardner33v4
Answered 2021-12-21 Author has 35 answers
P(x)=x3+12x2+48x+64
=(x+4)(x2+8x+16)
=(x+4)(x+4)2
=(x+4)3
Real zeroes (x=-4 is root with multiplicity 3)
x=-4, -4, -4
P(x)=(x+4)3=(x+4)(x+4)(x+4)

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