Warm-Up Collect like terms and arrange in descending order. 5 minutes 1) 4x 3 + 6x 4 – 2x 4 + 8x 2) 3x – 5x + 5 + 2x 0 3) Evaluate 4x 3 + x 2 – 2 for x.

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Presentation transcript:

Warm-Up Collect like terms and arrange in descending order. 5 minutes 1) 4x 3 + 6x 4 – 2x 4 + 8x 2) 3x – 5x x 0 3) Evaluate 4x 3 + x 2 – 2 for x = 0 and x = 1

Addition / Subtraction of Polynomials Objectives: To add polynomials To subtract polynomials

Example 1 Add (5x 2 + 3x + 4) + (3x 2 + 5) = 8x 2 + 3x+ 9

Example 2 Add (7x 2 y 3 + xy) + (1 – 2x 2 y 3 ) = 5x 2 y 3 + xy+ 1

Practice 1) (3x 2 + 2x – 2) + (-2x 2 + 5x + 5) Add. 2) (31x 4 + x 2 + 2x – 1) + (-7x 4 + 5x 3 – 2x + 2) 3) (4a 2 b – 5a + 3) + (-2a 2 b – 2a – 4)

Example 3 Add. (2x 4 – 5x 2 + 4x + 5) + (5x 4 + 7x 3 – 2x 2 – 2x) 2x 4 + 0x 3 – 5x 2 + 4x + 5 5x 4 + 7x 3 – 2x 2 – 2x + 0 7x 4 + 7x 3 – 7x 2 + 2x+ 5

Example 4 Add. (-3x 4 y 3 + 6x 3 y 3 – 6x 2 + 5xy 5 + 1) + (5x 5 – 3x 3 y 3 – 5xy 5 ) -3x 4 y 3 + 6x 3 y 3 – 6x 2 + 5xy x 5 - 3x 3 y 3 - 5xy 5 5x 5 – 3x 4 y 3 + 3x 3 y 3 – 6x 2 + 1

Practice 1) (-2m 3 – 5m 2 – 2m – 4) + (m 4 – 6m 2 + 7m – 10) Add. 2) (-3x 4 y 3 – 5xy + 2) + (x 4 y 3 + x 2 + 2xy + 5)

Subtraction of Polynomials Objectives: To subtract polynomials

Example 1 Subtract. (5x 2 + 3x - 2) - (2x 2 + 1) = 5x 2 + 3x x = 3x 2 + 3x - 3

Example 2 Subtract. (2x 2 y 2 + 3xy 3 – 4y 4 ) - (x 2 y 2 – 5xy 3 + 3y – 2y 4 ) = 2x 2 y 2 + 3xy 3 – 4y 4 - x 2 y 2 + 5xy 3 – 3y + 2y 4 = x 2 y 2 + 8xy 3 – 2y 4 – 3y

Practice 1) (5x 4 + 4) – (2x 2 – 1) Subtract. 2) (-7m 3 + 2m + 4) – (-2m 3 – 4) 3) (-3a 2 b 4 + 5ab - 4) - (-4a a 2 b 4 – 2a - 6)

Example 3 Subtract. (8x 3 + 6x 2 – 3x + 5) – (5x 3 – 3x 2 + 2x – 4) 8x 3 + 6x 2 – 3x x 3 + 3x 2 - 2x + 4 3x 3 – 9x 2 - 5x + 9

Example 4 Subtract. (2a 4 b + 5a 3 b 2 – 4a 2 b 3 ) – (4a 4 b + 2a 3 b 2 – 4ab) 2a 4 b + 5a 3 b 2 – 4a 2 b 3 -4a 4 b - 2a 3 b 2 + 4ab -2a 4 b + 3a 3 b 2 – 4a 2 b 3 + 4ab

Practice 1) (-2m 3 – 5m 2 – 2m – 4) - (m 4 – 6m 2 + 7m – 10) Subtract. 2) (-3x 4 y 3 – 5xy + 2) - (x 4 y 3 + x 2 + 2xy + 5)

RULE! In order to add or subtract, you must have …. The same BASE and the same EXPOENNT!

Example You can add 3x 2 + 2x 2 together You CAN NOT add 3x 3 + 2x 2 together!