Solve 3t^2-10t-8=0 by factoring. Enter your answers below t= square t= square

Question

Answer 1

To solve the quadratic equation

by factoring, we need to find two numbers that multiply to \(3 \times (-8) = -24\) and add up to

.The two numbers that satisfy these conditions are

and

, because:

Next, we rewrite the middle term

using these two numbers:

Now, we factor by grouping:

We can factor out the common binomial factor \((t - 4)\):

Setting each factor equal to zero gives us the solutions:

Solving these equations, we get:

Therefore, the solutions to the equation

are:

So, the answers are:

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