Polynomial Remainder 9A6Be4

1. **State the problem:** We need to find the remainder when the polynomial $$4x^2 - 3x - 7$$ is divided by $$x + 7$$. 2. **Recall the Remainder Theorem:** The remainder when a polynomial $$f(x)$$ is divided by $$x - a$$ is $$f(a)$$. 3. **Rewrite divisor:** Here, the divisor is $$x + 7$$ which can be written as $$x - (-7)$$, so $$a = -7$$. 4. **Evaluate the polynomial at $$x = -7$$:** $$ 4(-7)^2 - 3(-7) - 7 = 4(49) + 21 - 7 = 196 + 21 - 7 $$ 5. **Simplify:** $$ 196 + 21 - 7 = 210 $$ 6. **Conclusion:** The remainder when $$4x^2 - 3x - 7$$ is divided by $$x + 7$$ is $$210$$.