Question

Jenna constructs the model to represent 3x2 + 11x – 4. An algebra tile configuration. 0 tiles are in the Factor 1 spot. 0 tiles are in the Factor 2 spot. 20 tiles are in the Product spot in 4 columns with 5 rows. First row: 3 + x squared, 1 negative x. The last 4 rows are the same: 3 + x, 1 negative. What factors does Jenna need to model for the sides?Jenna constructs the model to represent 3x2 + 11x – 4. An algebra tile configuration. 0 tiles are in the Factor 1 spot. 0 tiles are in the Factor 2 spot. 20 tiles are in the Product spot in 4 columns with 5 rows. First row: 3 + x squared, 1 negative x. The last 4 rows are the same: 3 + x, 1 negative. What factors does Jenna need to model for the sides?

Answer 1

To find the factors, we need to factor the quadratic expression 3x^2 + 11x - 4, which results in the factors (3x – 1) and (x + 4).

Step-by-step explanation:

The question involves using algebra tiles to model a quadratic expression, which is a common method used to visualize factoring in mathematics. Jenna has a model to represent 3x2 + 11x – 4 with a configuration of 20 tiles arranged in 4 columns and 5 rows. To determine the factors that Jenna needs for the sides of her model, we need to factor the quadratic expression. In this case, we look for two binomials whose product gives Jenna's quadratic expression. After some trial and error or systematic factoring, we would find that the correct factors are (3x – 1) and (x + 4), as these factors when multiplied will yield Jenna's original expression.