# f(x) = x^3 - x^2 - 21x + 45, x + 5 is a factor. Use synthetic division and solve the resulting quadratic quotient to find all zeros (x intercepts).

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### 1 Answer

Factor `x^3-x^2-21x+45` using synthetic division knowing that x+5 is a factor:

If x+5 is a factor, then -5 is a root.

-5 | 1 -1 -21 45

-5 30 -45

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1 -6 9 0

The quotient is `x^2-6x+9` ; this is a perfect square trinomial and factors as `(x-3)^2`

So f(x) factors as f(x)=(x+5)(x-3)(x-3)

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The zeros (x-intercepts, roots) of f(x) are -5 and 3 (3 is a double root.)

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The graph: