nter the coefficients for each term in the product of -2x^2 and -5x^2-2x-7 Enter 0 as the coefficient of any terms not in the product. (x^4+1) x^3+1 x^2+1 square x+1

## Step 1: Rewrite as addition<br />### Rewrite the expression $-5x^2 - 2x - 7$ as $-5x^2 + (-2x) + (-7)$.<br /><br />## Step 2: Distribute $-2x^2$<br />### Distribute $-2x^2$ to each term inside the parentheses:<br />### $-2x^2(-5x^2) + (-2x^2)(-2x) + (-2x^2)(-7)$.<br /><br />## Step 3: Simplify each term<br />### Simplify each term by multiplying the coefficients and adding the exponents of $x$:<br />### $10x^4 + 4x^3 + 14x^2$.<br /><br />## Step 4: Identify coefficients<br />### The resulting expression is $10x^4 + 4x^3 + 14x^2 + 0x + 0$.<br />### The coefficients are 10 for $x^4$, 4 for $x^3$, 14 for $x^2$, 0 for $x$, and 0 for the constant term.