Question

jenna constructs the model to represent \\(3x^2 + 11x - 4\\).
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)\\)

Explanation:

Identify the polynomial and its factors

The polynomial represented by the algebra tiles is:

$$ 3x^2 + 11x - 4 $$

We factor this quadratic expression:

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

Verify with the algebra tile model

• The top side (Factor 1) represents \(3x - 1\), consisting of three \(+x\) tiles and one \(-1\) tile.
• The left side (Factor 2) represents \(x + 4\), consisting of one \(+x\) tile and four \(+1\) tiles.
• Multiplying these dimensions yields:
• Three \(+x^2\) tiles: \(3x \cdot x = 3x^2\)
• Twelve \(+x\) tiles: \(3x \cdot 4 = 12x\)
• One \(-x\) tile: \(-1 \cdot x = -x\)
• Four \(-1\) tiles: \(-1 \cdot 4 = -4\)
• Combining the \(x\) terms: \(12x - x = 11x\), which matches the model.
• Thus, the factors are \((3x - 1)\) and \((x + 4)\).

Answer:

• (3x + 1) and (x - 4)
• (3x - 1) and (x + 4) (Correct answer)
• (3x - 2) and (x + 2)
• (3x + 2) and (x - 2)