Question

The expression 40x2 – 65x + 50 represents the sum of the interior angles of a regular pentagon in degrees. If the interior angles of the pentagon are equal, which expression represents the measure of two angles?

2x2(20 – 32x + 25x2)
2(8x2 – 13x +10)
5x2(8x2 – 13x + 10)
5(3x2 – 8x + 5)
Factor –7x3 + 21x2 + 3x – 9 by grouping. What is the resulting expression?

(3 – 7x)(x2 – 3)
(7x – 3)(3 + x2)
(3 – 7x2)(x – 3)
(7x2 – 3)(3 + x)
Which model represents the factors of x2 + 9x + 8?

An algebra tile configuration. 7 tiles are in the Factor 1 spot: 1 is labeled + x and 6 are labeled +. 4 tiles are in the Factor 2 spot: 1 is labeled + x and 3 are labeled +. 28 tiles are in the Product spot: 1 is labeled + x squared, 9 are labeled + x, 9 are labeled +, and 9 are labeled negative.
An algebra tile configuration. 5 tiles are in the Factor 1 spot: 1 is labeled + x and 4 are labeled +. 3 tiles are in the Factor 2 spot: 1 is labeled + x and 2 are labeled +. 15 tiles are in the Product spot: 1 is labeled + x squared, 6 are labeled + x, and 8 are labeled +.
An algebra tile configuration. 6 tiles are in the Factor 1 spot: 1 is labeled + x and 5 are labeled +. 4 tiles are in the Factor 2 spot: 1 is labeled + x and 3 are labeled +. 24 tiles are in the Product spot: 1 is labeled + x squared, 8 are labeled + x, 9 are labeled +, and 6 are labeled negative.
An algebra tile configuration. 9 tiles are in the Factor 1 spot: 1 is labeled + x and 8 are labeled +. 2 tiles are in the Factor 2 spot: 1 is labeled + x and 1 is labeled +. 18 tiles are in the Product spot: 1 is labeled + x squared, 9 are labeled + x, and 8 are labeled +.

Answer 1

1) Each interior angle = (40x^2 − 65x + 50)/5 = 8x^2 − 13x + 10, so two angles = 2(8x^2 − 13x + 10).

2) Factor by grouping:
-7x^3 + 21x^2 + 3x − 9 = (−7x^2)(x − 3) + 3(x − 3) = (3 − 7x^2)(x − 3).

3) x^2 + 9x + 8 = (x + 8)(x + 1). The matching tile model is the one with Factor 1: x + 8 (1 x tile and 8 + tiles) and Factor 2: x + 1 (1 x tile and 1 + tile) — the last option.