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homework assignment 3.6: zeros of polynomials
score: 0/12 answered: 0/12
question 1
write the factored form of the polynomial function with real coefficients, a lead coefficient of 1, and zeros of $-4$, $-4$, $3$, and $2$.
$y(x) = $
question help: video read written example

Explanation:

Step1: Relate zeros to factors

If $r$ is a zero of a polynomial, then $(x-r)$ is a factor. For the zero $-4$ (multiplicity 2), the factors are $(x-(-4))$ twice; for zeros 3 and 2, the factors are $(x-3)$ and $(x-2)$.

Step2: Multiply factors with lead coefficient

The lead coefficient is 1, so multiply all factors together:
$y(x) = (x+4)(x+4)(x-3)(x-2)$
We can write the repeated factor with an exponent:
$y(x) = (x+4)^2(x-3)(x-2)$

Answer:

$y(x) = (x+4)^2(x-3)(x-2)$