Question

drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. match each division expression with the correct quotient.
division expressions:
\\(\frac{-66x^2 + 1633x - 77}{11x - 7}\\)
\\(\frac{-55x^2 + 68x - 21}{-5x + 3}\\)
\\(\frac{-14x^2 - 68x - 48}{2x + 8}\\)
tiles (quotients):
-7x - 6
-6x + 11
11x - 7
6x + 11
7x - 6
7x + 6
11x + 7
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Explanation:

Step 1: Divide \(\frac{-14x^{2}-68x - 48}{2x + 8}\)

First, factor out \(-2\) from the numerator: \(-2(7x^{2}+34x + 24)\). Then factor the quadratic in the numerator: \(7x^{2}+34x + 24=(7x + 6)(x + 4)\). The denominator is \(2x + 8 = 2(x + 4)\). Cancel out \((x + 4)\) and divide the remaining terms: \(\frac{-2(7x + 6)(x + 4)}{2(x + 4)}=-7x - 6\).

Step 2: Divide \(\frac{-55x^{2}+68x - 21}{-5x + 3}\)

Use polynomial long division or factor. Let's try factoring. The numerator: \(-55x^{2}+68x - 21 =-(55x^{2}-68x + 21)\). Factor \(55x^{2}-68x + 21=(11x - 7)(5x - 3)\). So the expression becomes \(\frac{-(11x - 7)(5x - 3)}{-(5x - 3)} = 11x - 7\) (note: original denominator is \(-5x + 3=-(5x - 3)\)).

Step 3: Divide \(\frac{-66x^{2}+163x - 77}{11x - 7}\)

Factor the numerator: \(-66x^{2}+163x - 77=-(66x^{2}-163x + 77)\). Factor \(66x^{2}-163x + 77=(6x - 11)(11x - 7)\) (wait, let's check: \((6x - 11)(11x - 7)=66x^{2}-42x - 121x + 77=66x^{2}-163x + 77\)). So the expression is \(\frac{-(6x - 11)(11x - 7)}{11x - 7}=-6x + 11\).

Answer:

• \(\frac{-14x^{2}-68x - 48}{2x + 8}\) matches \(-7x - 6\)
• \(\frac{-55x^{2}+68x - 21}{-5x + 3}\) matches \(11x - 7\)
• \(\frac{-66x^{2}+163x - 77}{11x - 7}\) matches \(-6x + 11\)