In this section, algebraic tiles are used to factor trinomials.

Find the factors of 2x² − 7x + 6.

• First, create a rectangular diagram with the tiles for the trinomial.

• Then, find the factors from the rectangular diagram.
  • There are two large squares therefore one of the x's have a coefficient of 2.

  (2x   )(x   )

  • There are 3 green shaded rectangular columns of tiles on the right side so the constant in the first factor is a -3.

  (2x − 3)(x   )

  • There are 2 rows of green shaded rectangular tiles at the bottom so the constant in the second factor is a -2.

  (2x − 3)(x − 2)

  The factors of 2x²− 7x + 6 are (2x − 3)(x − 2).

Example: Use algebra tiles to show the factorization of x²+ x − 2

The factors of x² + x − 2 are Interactive popup. Assistance may be required.

Check Your Answer

(x − 1)(x + 2)