Polynomials : Polynomials
Adding and Subtracting Polynomials : Adding and Subtracting Polynomials
Adding Polynomials : Adding Polynomials To add polynomials, combine like terms. + + + = = 2 2 2 Does not =
Example : Example Add (-7z2 + 9z – 3) + (8z2 – 6z + 9) (-7z2 + 9z – 3) + (8z2 – 6z + 9) = -7z2 + 8z2 + 9z – 6z – 3 + 9 = 1z2 + 3z + 6 = z2 + 3z + 6 Rearrange the terms so that the like terms are grouped together. Add like terms. 1z2 = z2
Finding the Opposite of a Polynomial : Finding the Opposite of a Polynomial When a negative sign precedes parentheses, we find the opposite of the expression by changing the sign of each term inside the parentheses.
Example : Example Simplify. –(–5a + 3b – 7c) –(–5a + 3b – 7c) = We change the sign of each term 5a 3b 7c – +
Subtracting Two Polynomials : Subtracting Two Polynomials To subtract two polynomials, change the sign of each term in the second polynomial and then add.
Example : Example Perform the operations indicated.
(3a2 + 4a – 7) – (7a2 – 2a – 5) = 3a2 + 4a – 7 + (– 7a2) + 2a + 5 A – sign in front of parentheses indicates we are subtracting. We change the sign of terms that were inside parentheses, then add. = 3a2 + 4a – 7 + (– 7a2) + 2a + 5 Simplify by combining like terms. = -4a2 + 6a – 2
Multiplying Polynomials : Multiplying Polynomials
Example : Example Multiply. -2y(5y2 + 3y – 8) -2y(5y2 + 3y – 8) = -2y(5y2) – 2y(3y) – 2y(– 8) Multiply each term by -2y = -10y3 – 6y2 + 16y
Example : Example Multiply. (3x + 1)(x - 2) First
F Outer
O Inner
I Last
L 3x2 - 6x x - 2 (3x + 1)(x – 2) = 3x2 – 5x - 2 Combine like terms.
I hope you enjoyed this short presentation on Polynomials : I hope you enjoyed this short presentation on Polynomials