A student is asked to find a polynomial f (x) of degree four with the zeros 2, - 3, 0, and - 7. What factors would the student multiply together to find f (x) ? You do not need to multiply the factors out, just list them!

Question

Delgado

Mathematics

21 February, 23:44

A student is asked to find a polynomial f (x) of degree four with the zeros 2, - 3, 0, and - 7. What factors would the student multiply together to find f (x) ? You do not need to multiply the factors out, just list them!

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Answers (1)

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Emmy Stark · Answer 1

(x-2), (x+3), x and (x + 7)

Step-by-step explanation:

Here, the zeros of the polynomial are 2, - 3, 0 and - 7.

Let's consider a case of a quadratic equation where x = 5 is a solution. This means that x + 5 is a factor of that quadratic equation.

Now, let's apply same approach to this polynomial. If x = 2 is a solution, then x - 2 is a factor. If x = - 3, then, x + 3 is a factor. If x = 0, this means x itself is a solution and lastly, if x = - 7 is a solution, that means x + 7 is a factor.

Thus, the factors to multiply together are; (x-2), (x+3), x and (x + 7)