which model represents the factors of x² + 9x + 8?
which model represents the factors of x² + 9x + 8?
Answer
Explanation:
Step1: Factor the quadratic expression
We need to factor (x^{2}+9x + 8). We look for two numbers that multiply to (8) (the constant term) and add up to (9) (the coefficient of (x)). The numbers are (8) and (1) since (8\times1=8) and (8 + 1=9). So (x^{2}+9x + 8=(x + 8)(x+1)).
Step2: Analyze the tile - model representation
In a tile - model for factoring a quadratic (ax^{2}+bx + c), the large square represents (x^{2}), the long rectangles represent (x), and the small squares represent the constant. For ((x + 8)(x + 1)), we should have one (x^{2}) - tile, (8 + 1=9) (x) - tiles, and (8\times1 = 8) unit - tiles.
Answer:
The model that has one (+x^{2}) tile, nine (+x) tiles, and eight (+) (unit) tiles represents the factors of (x^{2}+9x + 8). Without seeing the full options clearly from the image, the correct model should have these components.