Form a polynomial whose zeros and degree are given.

Question

Form a polynomial whose zeros and degree are given.

​Zeros:

−7​,

multiplicity​ 1;   

−4​,

multiplicity​ 2; degree 3

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Part 1

Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.

​f(x)=enter your response here

​(Simplify your​ answer.)

Answer 1

x=-7

x+7 = 0

x+7 is one factor

x=-4

x+4 = 0

x+4 is another factor

since it has multiplicity 2,

put an exponent of 2 with it to get

(x+4)^2

now multiply the factors together

f(x) = (x+7)(x+4)^2

= (x+7)(x^2 + 8x +16)

= x^3 +15x^2 +72x + 112