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simplify the function

+1 vote

f(x)= { 5 x^3 +21 x^2+ 14 x+ 40 }/{ x + 4 }?

asked Feb 11, 2013 in PRE-ALGEBRA by johnkelly Apprentice

1 Answer

+2 votes

f(x) =(5x3 + 21x2 + 14x + 40) / (x + 4)

Consider: 5x3 + 21x2 + 14x + 40.

If p/q is a rational zero, then p is a factor of 40 and q is a factor of 5.

The possible values of p is -4.

The possible values for q is -4.

So, p/q = -4

Make a table for the synthetic division and test possible real zeros.

    p/q

5

21

14

40

-4

5

1

10

0

Since f(-4)   =   0,   x  = - 4 is a zero. The depressed polynomial is  5x2 + x + 10 = 0.

Therefore f(x) = (x - 4)(5x2 + x + 10) / (x + 4) = 5x2 + x + 10

f(x) = 5x2 + x + 10.

answered Feb 11, 2013 by richardson Scholar

Since, f(- 4) =   0, x = - 4 is a zero. The depressed polynomial is  5x2 + x + 10 = 0.

So, f(x) = [(x + 4)(5x2 + x + 10)]/(x + 4) = 5x2 + x + 10.

∴ f(x) = 5x2 + x + 10.

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