Question

1. $24r^2 + 44r - 40$

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of 24, 44, and -40. The GCF of 24, 44, and 40 is 4. So we factor out 4:
$$24r^2 + 44r - 40 = 4(6r^2 + 11r - 10)$$

Step2: Factor the quadratic

Now, factor the quadratic \(6r^2 + 11r - 10\). We need two numbers that multiply to \(6\times(-10)= -60\) and add up to 11. The numbers are 15 and -4.
Rewrite the middle term using these numbers:
$$6r^2 + 15r - 4r - 10$$
Group the terms:
$$(6r^2 + 15r) + (-4r - 10)$$
Factor out the GCF from each group:
$$3r(2r + 5) - 2(2r + 5)$$
Now, factor out the common binomial factor \((2r + 5)\):
$$(3r - 2)(2r + 5)$$

Step3: Combine the factors

Putting it all together, the factored form of the original expression is:
$$4(3r - 2)(2r + 5)$$

Answer:

\(4(3r - 2)(2r + 5)\)