The polynomial of degree 3 if we have zeros: -3, multiplicity 1; -4, multiplicity 2 is [tex]x^3+11x^2+40x+48[/tex]
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:
[tex](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[/tex]
So, the polynomial of degree 3 if we have zeros: -3, multiplicity 1; -4, multiplicity 2 is [tex]x^3+11x^2+40x+48[/tex]
Keywords: Factors of polynomials
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