Adding Polynomials by Collecting Like Terms

0:00How do we add these two polynomials?

0:03A polynomial is made of terms joined by plus and minus signs. The first has three terms: x squared, two x and minus four.

0:13Algebra tiles model terms. A big square is x squared, a strip is x, and a small square, called a unit tile, is one. Pink tiles are negative.

0:26The first polynomial is one x squared tile, two x tiles and four negative unit tiles.

0:34The second is two x squared tiles, three negative x tiles and four negative unit tiles.

0:41Like terms have the same variable and power, so their tiles match. Collect them into groups: x squared terms, x terms and constants, which have no x.

0:52The number in front of a term is its coefficient. Add them: one x squared plus two x squared is three x squared.

1:01A positive and a negative x tile make a zero pair, because x plus minus x is zero.

1:09Remove both zero pairs. One negative x tile is left, so two x minus three x is minus x.

1:18All eight unit tiles are negative, so there are no zero pairs. Minus four minus four is minus eight.

1:26Do not combine x squared terms with x terms: their tiles are different sizes.

1:32So the sum is three x squared minus x minus eight.

1:38Check with x equals two: the first polynomial is four and the second is minus two, so together they make two.

1:47Our answer gives twelve minus two minus eight, which is also two.

1:52To add polynomials, collect like terms and add their coefficients.