Complete the steps to factor the polynomial. One root of f(x) = x³ + x² – 22x – 40 is 5. If 5 is a root of the function, then is a

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1. Answer:

   If one root of a cubic is known (and verified), then we can do a synthetic division and factor the remaining quadratic expression.

   f(x)=x^3+x^2-22x-40

   f(5)=125+25-22(5)-40=0 so x-5 is a factor

   Now do the synthetic division

   5 | +1 +1 -22 -40

   ——————–

   1 6 8 0

   The resulting quadratic is x^2+6x+8 which can be factored into

   (x+2)(x+4)

   The complete factorization is therefore

   f(x)=x³ + x² – 22x – 40 = (x-5)(x+2)(x+4)

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