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Warm up Use synthetic division to divide (4x3 – 3x2 + 2x + 1)/ (x – 1) (x3 – x2 – 6)/(x + 2)

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**Dividing a polynomial by a monomial**

(4y5 – 6y4 + 12y3 – 8y2) / (4y2)

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**Dividing a polynomial by a polynomial using long division**

(6x2 + x – 2)/ (2x – 1)

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**Dividing a polynomial by a polynomial using synthetic division**

(2t2 + 13t + 15)/ (t + 5)

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Factor by grouping x3 + x2 – x – 1

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Factor by grouping 2x3 – 3x2 – 2x + 3

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**Sum and difference of two cubes**

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Factor the following x y3 – 125

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Factor the following 4x5 – 32x2 2x7 + 54x4

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Factor theorem The expression x-a is a linear factor of a polynomial if and only if the value a is a zero of the related function. --How do you find out if a is a zero of the function?

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**Factor theorem Is -2 a zero of the following function?**

Y = x3 + x2 – 2x

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**Factor theorem Is -5 a zero of the following function?**

Y = x3 + 9x2 + 15x -25

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**Factor theorem Is 3 a zero of the following function?**

If yes then find the other remaining zeros Y = x3 - 9x2 + 27x – 27

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**Write a polynomial function in standard form with the given zeros**

X = 5, 6, 7 X = -2, 0, 1

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**Write a polynomial function in standard form with the given zeros**

X = -5, -5, 1 X = 3,3,3

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6.5 Warm Up 1.Factor 8x 3 + 125. 2.Factor 5x 3 + 10x 2 – x – 2. 3.Factor 200x 6 – 2x 4. 4.Find the product of (2x – 3)(2x – 5). 5.Find the product of (5x.

6.5 Warm Up 1.Factor 8x 3 + 125. 2.Factor 5x 3 + 10x 2 – x – 2. 3.Factor 200x 6 – 2x 4. 4.Find the product of (2x – 3)(2x – 5). 5.Find the product of (5x.

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