SOLUTION: Factor the polynomial completely. 9x^2 - 49
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Question 441725: Factor the polynomial completely. 9x^2 - 49
Found 2 solutions by robertb, Ex:
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
Answer by Ex(2) (Show Source): You can put this solution on YOUR website!
This is an example of a quadratic that you manually have to write in the middle variable. From there, you just Un-FOIL as usual. The LONG way follows:
1.)
- This is the base equation. Note that you cannot factor out 3 or 9 due to the fact that 49 is not divisible by 3 (4 + 9 = 13 which is not divisible by 3).
2.)
- This is the equation written in standard quadratic form. Note that the coefficient is zero.
3.)
- When unfoiling a standard quadratic (ax^2 + bx + c), you multiply a * c, then find two factors of the product that when added, make b. In this case it was 21 * (-21).
4.)
- Here you factor out the GCF of each pair of terms.
5.)
- Finally, you factor out the common binomial factors. This is the answer.
The short way:
1.)
- This quadratic is an example of what is known as a "difference of squares" meaning that it's a term squared minus another term squared or . Note that there is no middle term as in a standard quadratic formula.
2.)
- This is the factored form a difference of squares will always take once factored.
3.) a = (√9x^2) = 3x, b =(√49) = 7
- Find the root of both terms.
4.)
- Input values.
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