Page 353 - Algebra 1

To add or subtract polynomials, combine like terms. Polynomials can be added vertically or horizontally.
Adding Polynomials
Add the polynomials. Write the answer in standard form.
a. (-8x3 +4x2 +x+1)+(3x3 -2x2 +7) SOLUTION
Example
3
-8x3 +4x2 +x+1
+3x3 - 2x2 + 7
-5x3 +2x2 +x+8 Add like terms.
The polynomial -5x3 + 2x2 + x + 8 is in standard form.
b. (x+10+2x3)+(3x2 -7x-2) SOLUTION
Arrange like terms in columns.
Math Language
Like terms, such as -8x3 and 3x3, have the same variables raised to the same powers.
(x+10+2x3)+(3x2 -7x-2) x+10+2x3 +3x2 -7x-2
2x3 + 3x2 + x - 7x - 2 + 10
2x3 + 3x2 - 6x + 8
Removeparentheses.
Arrange with like terms together. Combine like terms.
The polynomial 2x3 + 3x2 - 6x + 8 is in standard form. Subtracting Polynomials
Subtract the polynomials. Write the answer in standard form.
Example
4
Caution
Remember to multiply each term in the parentheses by -1.
-1(2x2 - x + 8).
a. (6x2 +4x+2)-(2x2 -x+8) SOLUTION
(6x2 +4x+2)-(2x2 -x+8) -2x2 + x - 8
6x2 + 4x + 2 +-2x2 + x-8 4x2 + 5x - 6
Find the opposite of the second polynomial.
Arrange like terms in columns.
Add like terms.
338 Saxon Algebra 1
The polynomial 4x2 + 5x - 6 is in standard form.