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Factor.
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Q. Factor.
- Identify Variables: Identify , , and in the quadratic expression . Compare with .
- Find Multiplying Numbers: Find two numbers that multiply to (which is ) and add up to (which is ).We need to find two numbers that satisfy these conditions.After checking possible pairs that multiply to ( and , and ), we see that none of these pairs add up to .This means we cannot factor the quadratic expression by simple inspection or by using integer pairs.
- Use Quadratic Formula: Since the quadratic does not factor neatly with integers, we will use the quadratic formula to find the roots of the equation .The quadratic formula is given by .Let's calculate the discriminant first: .
- Calculate Discriminant: Now we can find the roots using the quadratic formula.We have two possible values for :
- Find Roots Using Formula: Write the factored form using the roots found.The factored form of the quadratic expression is .Substitute and into the factored form:However, this does not match the original expression's coefficients, which are all integers. We made a mistake in assuming that the quadratic could be factored over the integers. Since the roots are not integers, the quadratic expression cannot be factored over the integers.
