Factor the following expression. $$ \begin{array}{l}4 x^{2}-13 x+10 \ (4 x-[?])(x-\square)\end{array} $$

Question

UpStudy AI · Accepted Answer

To factor the quadratic expression $$ 4x^{2} - 13x + 10 $$, we look for two binomials of the form $$(4x + a)(x + b)$$ such that:

1. The product of $$a$$ and $$b$$ is $$10$$.
2. The sum of $$4b$$ and $$a$$ is $$-13$$.

Let's identify the values of $$a$$ and $$b$$:

1. Possible pairs $$(a, b)$$ that multiply to $$10$$ are:
   - $$(-1, -10)$$
   - $$(-2, -5)$$
   - $$(-5, -2)$$

2. Check which pair satisfies $$4b + a = -13$$:
   - For $$(-5, -2)$$: $$4(-2) + (-5) = -8 - 5 = -13$$

This pair works, so the factored form is:

$$
(4x - 5)(x - 2)
$$

**Answer:** 
$$
(4x - 5)(x - 2)
$$
The factored form of the expression $$4x^{2} - 13x + 10$$ is $$(4x - 5)(x - 2)$$.

Factor the following expression.