Math question from Algebra 2

Question

Knowing that f(4) = 0, find all the zeros of f(x) = x³ -13x² +44x -32

Answer 1

divide the cubic by x-4

with long or synthetic division

x=4 is one zero

4 1 -13 44 -32

4 -36 32

1 -9 8 0

which leaves a quadratic as the quotient, remainder= 0

x^2 - 9x +8 = 0

(x-8)(x-1) = 0

x=1, 8

zeroes are 1, 4 and 8

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Answer 2

f(x) = x³ – 13x² + 44x – 32

Using long division to factor out (x –4) will give you a factorable quadratic.

1. The leading term of you quadratic will be x²
2. You will subtract x²(x –4) = x³ – 4x² from f(x) to get –9x² + 44x – 32
3. The second term of you quadratic will be – 9x
4. You will then subtract –9x(x –4) = –9x² + 36x from –9x² + 44x – 32 to get 8x – 32

It shouldn't be too difficult to find the last term of you quadratic from here. Once you do, you factor it to find the other two roots of the equation.

Hope this helps.

Answer 3

Use long division to divide f(x) by x-4.

Then factor the quotient to find the other 2 roots.