Question

Zeros: -3, multiplicity 1; -4, multiplicity 2; degree 3

Answer 1

The polynomial of degree 3 if we have zeros: -3, multiplicity 1; -4, multiplicity 2 is $x^3+11x^2+40x+48$

Step-by-step explanation:

We need to find the polynomial of degree 3 if we have zeros: -3, multiplicity 1; -4, multiplicity 2

Multiplicity tells how many times that zero occur:

s0 zeros are: -3,-4,-4

or we can write as: x=-3,x=-4 and x=-4

or x+3=0, x+4=0, x+4=0

Multiplying all terms to find the polynomial of degree 3:

$(x+3)(x+4)(x+4)\\=(x(x+4)+3(x+4))(x+4)\\=(x^2+4x+3x+12)(x+4)\\=(x^2+7x+12)(x+4)\\=x(x^2+7x+12)+4(x^2+7x+12)\\=x^3+7x^2+12x+4x^2+28x+48\\=x^3+7x^2+4x^2+12x+28x+48\\=x^3+11x^2+40x+48$

So, the polynomial of degree 3 if we have zeros: -3, multiplicity 1; -4, multiplicity 2 is $x^3+11x^2+40x+48$

Keywords: Factors of polynomials

Learn more about factors of polynomials at:

• brainly.com/question/1464739
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• brainly.com/question/1414350

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