Question

Form a polynomial whose zeros and degree are given. ​Zeros: 2​, multiplicity​ 1; 4​, multiplicity​ 2; degree 3

Answer 1

Answer:

If the polynomial is degree 3, then it is of the form y = Ax3 + Bx2 +Cx + D

And if the zeros are -2 with multiplicity of 1, then the factor is (x+2)1 = x+2

The other zero is -4 with multiplicity of 2, so it's factor is (x+4)2 = x2 +8x+16

So in general, if we let A = 1, then the polynomial is y = (x+2)(x+4)2 which multiplies out to

(x+2)(x2+8x+16) = x3 + 8x2 + 16x + 2x2 + 16x + 32

Combining like terms gives the polynomial:

y = x3 +10x2 + 32x + 32

If A is not 1, then y = A(x3 +10x2 + 32