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5 minutes. Warm-Up. Collect like terms and arrange in descending order. 1) 4x 3 + 6x 4 – 2x 4 + 8x. 2) 3x – 5x + 5 + 2x 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.
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5 minutes Warm-Up Collect like terms and arrange in descending order. 1) 4x3 + 6x4 – 2x4 + 8x 2) 3x – 5x + 5 + 2x0 3) Evaluate 4x3 + x2 – 2 for x = 0 and x = 1
Addition / Subtraction of Polynomials Objectives: To add polynomials To subtract polynomials
Example 1 Add (5x2 + 3x + 4) + (3x2 + 5) = 8x2 + 3x + 9
Example 2 Add (7x2y3 + xy) + (1 – 2x2y3) = 5x2y3 + xy + 1
Practice Add. 1) (3x2 + 2x – 2) + (-2x2 + 5x + 5) 2) (31x4 + x2 + 2x – 1) + (-7x4 + 5x3 – 2x + 2) 3) (4a2b – 5a + 3) + (-2a2b – 2a – 4)
Example 3 Add. (2x4 – 5x2 + 4x + 5) + (5x4 + 7x3 – 2x2 – 2x) 2x4 + 0x3 – 5x2 + 4x + 5 5x4 + 7x3 – 2x2 – 2x + 0 7x4 + 7x3 – 7x2 + 2x + 5
Example 4 Add. (-3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1) + (5x5 – 3x3y3 – 5xy5) -3x4y3 + 6x3y3 – 6x2 + 5xy5 + 1 5x5 - 3x3y3 - 5xy5 5x5 – 3x4y3 + 3x3y3 – 6x2 + 1
Practice Add. 1) (-2m3 – 5m2 – 2m – 4) + (m4 – 6m2 + 7m – 10) 2) (-3x4y3 – 5xy + 2) + (x4y3 + x2 + 2xy + 5)
Subtraction of Polynomials Objectives: To subtract polynomials
Example 1 Subtract. (5x2 + 3x - 2) - (2x2 + 1) = 5x2 + 3x - 2 - 2x2 - 1 = 3x2 + 3x - 3
Example 2 Subtract. (2x2y2 + 3xy3 – 4y4) - (x2y2 – 5xy3 + 3y – 2y4) = 2x2y2 + 3xy3 – 4y4 - x2y2 + 5xy3 – 3y + 2y4 = x2y2 + 8xy3 – 2y4 – 3y
Practice Subtract. 1) (5x4 + 4) – (2x2 – 1) 2) (-7m3 + 2m + 4) – (-2m3 – 4) 3) (-3a2b4 + 5ab - 4) - (-4a3 + 11a2b4 – 2a - 6)
Example 3 Subtract. (8x3 + 6x2 – 3x + 5) – (5x3 – 3x2 + 2x – 4) 8x3 + 6x2 – 3x + 5 -5x3 + 3x2 - 2x + 4 3x3 – 9x2 - 5x + 9
Example 4 Subtract. (2a4b + 5a3b2 – 4a2b3) – (4a4b + 2a3b2 – 4ab) 2a4b + 5a3b2 – 4a2b3 -4a4b - 2a3b2 + 4ab -2a4b + 3a3b2 – 4a2b3 + 4ab
Practice Subtract. 1) (-2m3 – 5m2 – 2m – 4) - (m4 – 6m2 + 7m – 10) 2) (-3x4y3 – 5xy + 2) - (x4y3 + x2 + 2xy + 5)
RULE! • In order to add or subtract, you must have …. • The same BASE and the same EXPOENNT!
Example • You can add 3x2 + 2x2 together • You CAN NOT add 3x3 + 2x2 together!