Algebra homework

Question

Create a polynomial with roots -3 and 5 of multiplicity of 2. What is the degree of the polynomial, write in standard form.

Answer 1

From the wording of the problem, it is not clear if the multiplicity of 2 applies to both zeros or just to the zero of 5. I will assume the latter. (In any case, you will see the method.)

Zeros: -3; and 5 with multiplicity of 2

f(x) = A(x + 3)(x - 5)²

where A is real and A ≠ 0. Note the multiplicity is the exponent in (x - z)ⁿ, where z is a zero and n is the multiplicity of z. Now expand f(x) into standard form and finish from here.

Answer 2

Create a polynomial with roots -3 and 5 of multiplicity of 2. What is the degree of the polynomial, write in standard form.

With roots of -3 and -5. the factors are (x + 3) and (x + 5)

Multiply them to get:

x^2 + 8x + 15

I assume that "multiplicity of 2" means we multiply the whole thing by 2:

2x^2 + 16x + 30