Question

factor trinomials (a=1)
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question
factor.
$x^2 + 4x - 45$
answer
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Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-45\) (the constant term) and add up to \(4\) (the coefficient of \(x\)). Let's list the factor pairs of \(-45\): \((-1, 45)\), \((1, -45)\), \((-3, 15)\), \((3, -15)\), \((-5, 9)\), \((5, -9)\). Among these, \(9\) and \(-5\) multiply to \(9\times(-5)= -45\) and add up to \(9 + (-5)=4\).

Step2: Factor the trinomial

Using the two numbers we found, we can factor the trinomial \(x^{2}+4x - 45\) as \((x + 9)(x - 5)\) because when we expand \((x + 9)(x - 5)\) using the distributive property (FOIL method), we get \(x^{2}-5x + 9x-45=x^{2}+4x - 45\), which matches the original trinomial.

Answer:

\((x + 9)(x - 5)\)