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The two expressions below are equivalent. Find the values of a and b that make them equivalent.

The two expressions are:
5x^2+bx-12
(5x+a)(x-4)

User Ocelot
by
8.6k points

1 Answer

3 votes

Answer:


a=3\text{ and } b=-17

Explanation:

We are given that:


5x^2+bx-12=(5x+a)(x-4)

First, we can distribute the right-hand side:


5x(x-4)+a(x-4)

Distribute:


=5x^2-20x+ax-4a

Rewrite:


=5x^2+(-20+a)x-(4a)

Since it is equivalent to the above expression, the coefficients of the variables must match. This means that:


-20+a=b\text{ and } 12=4a

Solving for a in the second equation gives:


a=3

Therefore:


b=-20+3=-17

User Wolli
by
8.3k points

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