Quadratic equations can be written in the standard form `ax^2 + bx + c = 0`, where 'a', 'b' and 'c' are real numbers and 'a' is not equal to 0.
The general method of factoring a quadratic expression is same regardless of the value of 'a'. However, depending on whether 'a' is 1, negative or greater than 1, you need to pay attention to different points while factoring.
When 'a' is greater than 1, you can factor a quadratic expression by first multiplying the values 'a' and 'c' along with their signs and then finding two numbers whose product is equal to the product of 'a' and 'c' and whose sum is equal to 'b'. Remember to take the product and 'b' with their appropriate signs.
Example: Factor `3x^2 + 2x - 1`
Find the values of 'a', 'b' and 'c':
The general method of factoring a quadratic expression is same regardless of the value of 'a'. However, depending on whether 'a' is 1, negative or greater than 1, you need to pay attention to different points while factoring.
When 'a' is greater than 1, you can factor a quadratic expression by first multiplying the values 'a' and 'c' along with their signs and then finding two numbers whose product is equal to the product of 'a' and 'c' and whose sum is equal to 'b'. Remember to take the product and 'b' with their appropriate signs.
Example: Factor `3x^2 + 2x - 1`
Find the values of 'a', 'b' and 'c':
- a = 3
- b = 2
- c = -1
Product of 'a' and 'c' `= 3 * -1 = -3`,
So you need to find two numbers whose product is -3 and sum is 2. So you get 3 and -1 because 3 times -1 is -3 and 3 plus -1 is 2.
`3x^2 + 3x - x - 1`
Factor further by grouping the first two terms and the next two terms and then factoring out their greatest common divisors,
`3x(x + 1) - 1(x + 1)`
Factor x + 1,
`(x + 1)(3x - 1)`
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