\[ \left(3 x^{2}+26 x+36\right) \div(x+7) \] Your answer should give the quotient and the remainder. Quotient: \( \square \) Remainder: \( \square \)

Divide the polynomials by following steps: - step0: Using Long Division to Divide Polynomials: \(\left(3x^{2}+26x+36\right)\div \left(x+7\right)\) - step1: Calculate: \(\left(3x+5\right)\text{ }\textrm{remainder}\text{ }1\) To divide \( 3x^{2} + 26x + 36 \) by \( x + 7 \), we perform polynomial long division. 1. **Divide the leading term**: - The leading term of the dividend \( 3x^{2} \) divided by the leading term of the divisor \( x \) gives \( 3x \). 2. **Multiply and subtract**: - Multiply \( 3x \) by \( x + 7 \) to get \( 3x^{2} + 21x \). - Subtract this from the original polynomial: \[ (3x^{2} + 26x + 36) - (3x^{2} + 21x) = 5x + 36 \] 3. **Repeat the process**: - Now, divide the leading term \( 5x \) by \( x \) to get \( 5 \). - Multiply \( 5 \) by \( x + 7 \) to get \( 5x + 35 \). - Subtract this from \( 5x + 36 \): \[ (5x + 36) - (5x + 35) = 1 \] The division results in a quotient of \( 3x + 5 \) and a remainder of \( 1 \). Thus, the final answer is: - Quotient: \( 3x + 5 \) - Remainder: \( 1 \)