Question

factor trinomials (a=1)
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question
factor.
$x^2 + x - 90$
answer attempt 1 out of 10
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Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-90\) and add up to \(1\). Let's list the factor pairs of \(90\): \(1\) and \(90\), \(2\) and \(45\), \(3\) and \(30\), \(5\) and \(18\), \(6\) and \(15\), \(9\) and \(10\). Now, we need one positive and one negative number (since their product is negative) such that their sum is \(1\). The pair \(10\) and \(-9\) works because \(10\times(-9)= -90\) and \(10 + (-9)=1\).

Step2: Factor the trinomial

Using the numbers we found, we can factor \(x^{2}+x - 90\) as \((x + 10)(x - 9)\) because when we expand \((x + 10)(x - 9)\) using the distributive property (FOIL method), we get \(x^{2}-9x + 10x-90=x^{2}+x - 90\), which matches the original trinomial.

Answer:

\((x + 10)(x - 9)\)