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Section 5.3. Example 1. a.Add 2 x 3 – 5 x 2 + 3 x – 9 and x 3 + 6 x 2 + 11 in a vertical format. b.Add 3 y 3 – 2 y 2 – 7 y and -4 y 2 + 2 y – 5 in a horizontal format. b.(3 y 3 – 2 y 2 – 7 y ) + (-4 y 2 + 2 y – 5) 3 y 3 – 2 y 2 – 4 y 2 – 7 y + 2 y – 5

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Section 5.3

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Section 5 3

Section 5.3


Example 1

Example 1

  • a.Add 2x3 – 5x2 + 3x – 9 and x3 + 6x2 + 11 in a vertical format.

  • b.Add 3y3 – 2y2 – 7y and -4y2 + 2y – 5 in a horizontal format.


Section 5 3

  • b.(3y3 – 2y2 – 7y) + (-4y2 + 2y – 5)

  • 3y3 – 2y2 – 4y2 – 7y + 2y – 5

  • 3y3 – 6y2 – 5y – 5

a.

3x3 + x2 + 3x + 2


Example 2

Example 2

  • a.Subtract 3x3 + 2x2 – x + 7 from

  • 8x3 – x2 – 5x + 1 in a vertical format.

  • b.Subtract 5z2 – z + 3 from 4z2 + 9z – 12 in horizontal format.


Section 5 3

  • b.(4z2 + 9z – 12) – (5z2 – z + 3)

  • 4z2 + 9z – 12 – 5z2 + z – 3

  • 4z2 – 5z2 + 9z + z – 12 – 3

  • -z2 + 10z – 15

  • Do Guided Practice #1 and #2.

a.

5x3 − 3x2 − 4x − 6


Example 3

Example 3

  • a.Multiply -2y2 + 3y – 6 and y – 2 in a vertical format.

  • b.Multiply x + 3 and 3x2 – 2x + 4 using the box method.


Section 5 3

a.

4y2 − 6y + 12

-2y3 + 3y2 − 6y

-2y3 + 7y2 − 12y +12


Section 5 3

b.(x + 3)(3x2 – 2x + 4)

= 3x3 + 7x2 – 2x + 12

3x2

-2x

4

-2x2

4x

3x3

x

-6x

3

9x2

12


Example 4

Example 4

  • Multiply x – 5, x + 1, and x + 3.

  • (x – 5)(x + 1)(x + 3) = (x2 – 4x – 5)(x + 3)

  • =x3 – x2 – 17x – 15

x2

-4x

-5

-4x2

-5x

x3

x

-12x

3

3x2

-15

Read the key concept on p. 347.


Example 5

Example 5

  • a.(3t + 4)(3t – 4) =

  • b.(8x – 3)2 =

  • c.(pq + 5)3 =

(3t)2 – 42 = 9t2 – 16

(8x)2 – 2(8x)(3) + (-3)2

= 64x2 – 48x + 9

(pq)3 + 3(pq)2(5) + 3(pq)(5)2 + (5)3

= p3q3 + 15p2q2 + 75pq + 125

Do Guided Practice #3, #4, and #5.

HW: pp. 349-351 (4-48 mult. of 4, 54, 56, 58)


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