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f(x) = x^3 - x^2 - 21x + 45, x + 5 is a factor.  Use synthetic division and solve the...

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kristenmarieb... | Student, Grade 10 | Valedictorian

Posted July 23, 2013 at 7:06 PM via web

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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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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 23, 2013 at 7:36 PM (Answer #1)

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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
     -------------------
        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:

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