Dividing the Polynomial
To divide the polynomial 2x² + 17x + 35 by x + 5, we can use polynomial long division. Here’s a step-by-step guide:
Step 1: Set Up the Division
Write the division in a long division format. We want to divide 2x² + 17x + 35 by x + 5.
Step 2: Divide the Leading Terms
Take the leading term of the dividend (the polynomial you’re dividing), which is 2x², and divide it by the leading term of the divisor (the polynomial you’re dividing by), which is x. This gives us:
2x² ÷ x = 2x
Step 3: Multiply and Subtract
Multiply the entire divisor (x + 5) by 2x:
2x(x + 5) = 2x² + 10x
Now, subtract this result from the original polynomial:
(2x² + 17x + 35) – (2x² + 10x) = 7x + 35
Step 4: Repeat the Process
Now, divide the leading term of the new polynomial (7x + 35) by the leading term of the divisor (x + 5):
7x ÷ x = 7
Multiply the divisor by 7:
7(x + 5) = 7x + 35
Now, subtract this from (7x + 35):
(7x + 35) – (7x + 35) = 0
Final Result
After performing the division, we find that:
2x² + 17x + 35 ÷ (x + 5) = 2x + 7
Therefore, the result of dividing 2x² + 17x + 35 by x + 5 is:
2x + 7