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Solving Quadratic Equations

Solving Quadratic Equations 1.10 - Solution

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To factor a trinomial with a leading coefficient of one, think of the process as multiplying two binomials in reverse. Let's start by taking a look at the constant term. In this case, the constant term is This is a negative number, so for the product of the constant terms in the factors to be negative, these constants must have opposite signs (one positive and one negative.)

Factor Constants Product of Constants
and
and
and
and

Next, let's consider the coefficient of the linear term. We need the sum of the factors that produced the constant term to equal the coefficient of the linear term,

Factors Sum of Factors
and
and
and
and

We found the numbers whose product is and whose sum is These numbers are and We can now rewrite the given expression as a product of two factors.