Please help me on algebra 2

Question

If x-1 is a factor of x3-6x2+11x-6, find the remaining factors of the polynomial.

Answer 1

Hi Taylor,

There are a few ways that you can approach this problem, depending on the way that you prefer to factor. However, given the set up of the problem I would recommend using synthetic division to start. In order to do this you would need to identify all of the coefficients that would go along the top. The value of x will go at the top left.

1 | 1 -6 11 -6

|

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We then start by bringing the first number down.

1 | 1 -6 11 -6

|

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1

Multiple the number we brought down by the value on the outside. (1x1). Place that number under the second coefficient.

1 | 1 -6 11 -6

| 1

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1

Add the numbers together.

1 | 1 -6 11 -6

| 1

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1 -5

Repeat the process.

1 | 1 -6 11 -6

| 1 -5 6

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1 -5 6 0

Add back in your x's, starting one degree lower than the original equation.

x² - 5x + 6

Factor as normal.

(x - 3) (x - 2)

Helpful Quadratic Factoring Hint:

If the second sign is positive both factors have the same sign in the middle. If the second sign is negative each factor has a different sign.