x2+5x+9 divided by x+2solution
Answer (1)
Step 1: Set up the polynomial long division.We need to divide x² + 5x + 9 by x + 2.Step 2: Divide the leading term.Divide the leading term of the numerator x² by the leading term of the denominator x:x² ÷ x = xStep 3: Multiply and subtract.Multiply x by x + 2:x(x + 2) = x² + 2xNow subtract this from the original polynomial:(x² + 5x + 9) - (x² + 2x) = 3x + 9Step 4: Repeat the process.Now divide the leading term 3x by x:3x ÷ x = 3Multiply 3 by x + 2:3(x + 2) = 3x + 6Subtract this from 3x + 9:(3x + 9) - (3x + 6) = 3Step 5: Write the final result.The division gives us a quotient of x + 3 and a remainder of 3.So, the final answer is:x + 3 + 3⁄(x + 2)
