The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.

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The Factor Theorem

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Factoring Polynomials 1. Common Factoring: 4x + 8 = 4(x + 2)

Transcript of The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.

Page 1: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.

The Factor Theorem

Page 2: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.

• To factor an expression means to re-write it as a product……

10 = 5 X 2

Page 3: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.

Factoring Polynomials

1. Common Factoring:

4x + 8 = 4(x + 2)

Page 4: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.

Factoring Polynomials2. Trinomial Factoring:

x2 + 5x + 6 = (x + 2)(x + 3)

If we can not find integer factors, we use the quadratic formula….

Page 5: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.

Cubic formula?....

• There is an analogous formula for polynomials of degree three:

• The solution of ax3+bx2+cx+d=0 is

Page 6: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.
Page 7: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.

A quartic equation, or equation of the fourth degree, is an equation consisting in equating to zero a quartic polynomial, of the form

where a ≠ 0.

Page 8: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.
Page 9: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.

Ya.so, we need an easier way…

Page 10: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.

Complete the following:

(x – 1) x3 + 2x2 – 1x - 2

Find the value of the function at the roots…

Page 11: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.

So…

To factor a polynomial, use trial and error to determine which values for b result in f(b) = 0

In other words, if f(b) = 0, then x – b is a factor

Page 12: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.
Page 13: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.
Page 14: The Factor Theorem. To factor an expression means to re-write it as a product…… 10 = 5 X 2.

+/- 1+/- 2

+/- 3+/- 6

+/- 9+/- 16


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Remainder and Factor Theorem

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