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Factor.
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Q. Factor.
- Identify , , : Identify , , and in the quadratic expression . Compare with .
- Find product and sum: Find two numbers whose product is () and whose sum is ().We need to find two numbers that multiply to and add up to .After checking possible pairs of factors of ( and , and ), we find that none of these pairs add up to .This means we cannot factor the quadratic expression using simple factorization methods.
- Use quadratic formula: Since the quadratic expression cannot be factored easily, we will use the quadratic formula to find the roots of the equation .The quadratic formula is .Let's calculate the discriminant first.Discriminant = = .Since the discriminant is a perfect square, we can find exact roots.
- Calculate discriminant: Calculate the roots using the quadratic formula.We have two possible values for :
- Calculate roots: Write the factored form using the roots found.The factored form of the quadratic expression is .Substitute and into the factored form.Factored form: However, we started with integer coefficients, so we should express the roots as fractions to maintain the form. (since is )Factored form: To clear the fraction, multiply each term by .Factored form:
