Divide. \[ \left(3 x^{2}+5 x-10\right) \div(x+3) \] Your answer should give the quotient and the remainder. Quotient: \( \square \) Remainder: \( \square \)

**Step 1: Divide the leading terms** Divide the leading term of the numerator, \(3x^2\), by the leading term of the divisor, \(x\): \[ \frac{3x^2}{x} = 3x \] So, the first term of the quotient is \(3x\). --- **Step 2: Multiply and subtract** Multiply the entire divisor by \(3x\): \[ 3x \cdot (x+3) = 3x^2 + 9x \] Subtract this from the original polynomial: \[ (3x^2 + 5x - 10) - (3x^2 + 9x) = -4x - 10 \] --- **Step 3: Divide the new leading term** Now, divide the new leading term \(-4x\) by \(x\): \[ \frac{-4x}{x} = -4 \] Add \(-4\) to the quotient. --- **Step 4: Multiply and subtract again** Multiply the divisor by \(-4\): \[ -4 \cdot (x+3) = -4x - 12 \] Subtract this from the current remainder: \[ (-4x - 10) - (-4x - 12) = 2 \] The remainder is \(2\). --- **Final Answer:** Quotient: \(3x - 4\) Remainder: \(2\)