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Quadratic Factoring Practice Questions (page 2)

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Updated on Oct 3, 2011

Practice 2

1. The binomial x2 – 16 is the difference between two perfect squares. The coefficient of x, 1, is a perfect square, and the exponent of x is even. The constant, 16, is also a perfect square. The positive square root of x2 is x and the positive square root of 16 is 4.

The square root of the first term, x, plus the square root of the second term, 4, is the first factor: x + 4. The square root of the first term minus the square root of the second term is the second factor: x – 4. Therefore, x2 – 16 factors to (x + 4)(x – 4).

2. The binomial 9x2 – 81 is the difference between two perfect squares. The coefficient of x, 9, is a perfect square, and the exponent of x is even. The constant, 81, is also a perfect square. The positive square root of 9x2 is 3x, and the positive square root of 81 is 9.

The square root of the first term, 3x, plus the square root of the second term, 9, is the first factor: 3x + 9. The square root of the first term minus the square root of the second term is the second factor: 3x – 9. Therefore, 9x2 – 81 factors to (3x + 9)(3x – 9).

3. The binomial 49x4 – 100 is the difference between two perfect squares. The coefficient of x, 49, is a perfect square, and the exponent of x is even. The constant, 100, is also a perfect square. The positive square root of 49x4 is 7x2, and the positive square root of 100 is 10.

The square root of the first term, 7x2, plus the square root of the second term, 10, is the first factor: 7x2 + 10. The square root of the first term minus the square root of the second term is the second factor: 7x2 – 10. Therefore, 49x4 – 100 factors to (7x2 + 10)(7x2 – 10).

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