Use polynomial long division to rewrite the following fraction in the form q(x)+d(x)r(x) where d(x) is the denominator of the original fraction, the quotient, and r(x) is the remainder.
2x+14x3−4x2+9x+6
Answer: 6 Points
2x2−3x+6
Solution
Step 1: 2x+14x3−4x2+9x+6 Step 2: 4x3÷2x=2x2 Step 3: 2x2×(2x+1)=4x3+2x2 Step 4: (4x3−4x2+9x+6)−(4x3+2x2)=−6x2+9x+6 Step 5: −6x2÷2x=−3x Step 6: −3x×(2x+1)=−6x2−3x Step 7: (−6x2+9x+6)−(−6x2−3x)=12x+6 Step 8: 12x÷2x=6 Step 9: 6×(2x+1)=12x+6 Step 10: (12x+6)−(12x+6)=0 Final Answer: 2x2−3x+6