The factors of the polynomial 4x^2-7x-2 are: a) (4x+1)(x-2) b) (4x+1)(x+2) c) (4x-1)(x-2) d) (4x-1)(x+2)

## Step 1: Find factors of $ac$ that add up to $b$<br />### In the quadratic $ax^2 + bx + c$, we have $a=4$, $b=-7$, and $c=-2$. Thus, $ac = (4)(-2) = -8$. We need to find two numbers that multiply to -8 and add up to -7. These numbers are -8 and 1, since $(-8)(1) = -8$ and $-8 + 1 = -7$.<br /><br />## Step 2: Rewrite the middle term and factor by grouping<br />### Rewrite the middle term $-7x$ as $-8x + x$. The expression becomes $4x^2 - 8x + x - 2$. Now, factor by grouping: $4x(x-2) + 1(x-2)$.<br /><br />## Step 3: Factor out the common binomial<br />### Factor out the common binomial $(x-2)$ to get $(4x+1)(x-2)$.