EXAMPLE 1 Add polynomials vertically and horizontally a

EXAMPLE 1 Add polynomials vertically and horizontally a. Add 2 x 3 – 5 x 2 + 3 x – 9 and x 3 + 6 x 2 + 11 in a vertical format. SOLUTION a. 2 x 3 – 5 x 2 + 3 x – 9 + x 3 + 6 x 2 + 11 3 x 3 + x 2 + 3 x + 2

EXAMPLE 1 Add polynomials vertically and horizontally b. Add 3 y 3 – 2 y 2 – 7 y and – 4 y 2 + 2 y – 5 in a horizontal format. (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 = 3 y 3 – 6 y 2 – 5 y – 5

EXAMPLE 2 Subtract polynomials vertically and horizontally a. Subtract 3 x 3 + 2 x 2 – x + 7 from 8 x 3 – x 2 – 5 x + 1 in a vertical format. SOLUTION a. Align like terms, then add the opposite of the subtracted polynomial. 8 x 3 – x 2 – 5 x + 1 – (3 x 3 + 2 x 2 – x + 7) 8 x 3 – x 2 – 5 x + 1 + – 3 x 3 – 2 x 2 + x – 7 5 x 3 – 3 x 2 – 4 x – 6

EXAMPLE 2 Subtract polynomials vertically and horizontally b. Subtract 5 z 2 – z + 3 from 4 z 2 + 9 z – 12 in a horizontal format. Write the opposite of the subtracted polynomial, then add like terms. (4 z 2 + 9 z – 12) – (5 z 2 – z + 3) = 4 z 2 + 9 z – 12 – 5 z 2 + z – 3 = 4 z 2 – 5 z 2 + 9 z + z – 12 – 3 = –z 2 + 10 z – 15

GUIDED PRACTICE for Examples 1 and 2 Find the sum or difference. 1. (t 2 – 6 t + 2) + (5 t 2 – t – 8) ANSWER 6 t 2 – 7 t – 6 2. (8 d – 3 + 9 d 3) – (d 3 – 13 d 2 – 4) ANSWER 8 d 3 + 13 d 2 + 8 d + 1