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? (3x 1) and (x – 4) (3x – 1) and (x 4) (3x – 2) and (x 2) (3x 2) and (x – 2).

Answer 1

Factored form of an expression is writing it in the terms of multiplication of factors. The factors of given expression are: (3x-1) and (x-4)

How to find the factors of a quadratic expression?

If the given quadratic expression is of the form $ax^2 + bx + c$,

then its factored form is given by $(x - \alpha)(x-\beta)$

such that

$b =\alpha+\beta\\ac = \alpha \times \beta$

For the given case, the expression is $3x^2 + 11x - 4$

If we take

$\alpha = 12\\\beta = -1$, then we get 12-1 = 11, and 12 times -1 = -12 = -4 times 3

Thus,

$3x^2 + 11x - 4 = 3x^2 + 12x - x - 4 = 3x(x-4) + 1(x-4) = (3x-1)(x-4)\\3x^2 + 11x - 4 = (3x-1)(x-4)$

(these factors represent the side length of the region whose area is modeled by the considered expression since area of rectangle is product of its length and width (assuming region was rectangle) ).

Thus, The factors of given expression are: (3x-1) and (x-4)

Learn more about factors of a quadratic expression here:

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