Answer:
she needs to find factors of -45 that add to -4
Explanation:
You want to know the error involved when looking for factors of 5x²-4x-9 by considering only factors of -9.
Quadratic factors
Consider the product of factors (ax +b)(x +d):
(ax+b)(x +d) = ax² +adx +bx +bd = ax² +(ad+b)x +bd
You will notice the two parts of the sum that is the middle term coefficient have the product abd, which is also the product of the first and last coefficients.
Sarah needs to be looking for factors of (5)(-9) = -45 that have a sum of -4.
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Additional comment
The factors Sarah needs are -9 and 5. These will give Sarah the equation ...
5x² -9x +5x -9
which can be factored pairwise to ...
x(5x -9) +1(5x -9) = (x +1)(5x -9)