Component. Short Review 1. Factorize 3x + 12 2. Factorize 4x²+ 20x 3. Factorize x² + 5x+6 4. Factorize x²-9 5. Factorize 9b²-3b +2
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Component. Short Review 1. Factorize 3x + 12 2. Factorize 4x²+ 20x 3. Factorize x² + 5x+6 4. Factorize x²-9 5. Factorize 9b²-3b +2
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Answer:
1. To factorize 3x + 12, we can factor out the greatest common factor of 3. This gives us:
3(x + 4)
Therefore, 3x + 12 can be factored as 3(x + 4).
2. To factorize 4x² + 20x, we can factor out the greatest common factor of 4x. This gives us:
4x(x + 5)
Therefore, 4x² + 20x can be factored as 4x(x + 5).
3. To factorize x² + 5x + 6, we need to find two numbers that multiply to 6 and add up to 5. These numbers are 2 and 3. Therefore, we can write:
x² + 5x + 6 = (x + 2)(x + 3)
Therefore, x² + 5x + 6 can be factored as (x + 2)(x + 3).
4. To factorize x² - 9, we can use the difference of squares formula, which states that:
a² - b² = (a + b)(a - b)
In this case, a = x and b = 3. Therefore, we can write:
x² - 9 = (x + 3)(x - 3)
Therefore, x² - 9 can be factored as (x + 3)(x - 3).
5. To factorize 9b² - 3b + 2, we need to find two numbers that multiply to 18 (the product of 9 and 2) and add up to -3 (the coefficient of the middle term). These numbers are -2 and -9. Therefore, we can write:
9b² - 3b + 2 = (3b - 2)(3b - 1)
Therefore, 9b² - 3b + 2 can be factored as (3b - 2)(3b - 1).