Use the long division method to find the result when 3, x, cubed, plus, 5, x, squared, plus, 3, x, plus, 13x 3 +5x 2 +3x+1 is divided by x, plus, 1x+1.
Question
Use the long division method to find the result when 3, x, cubed, plus, 5, x, squared, plus, 3, x, plus, 13x 3 +5x 2 +3x+1 is divided by x, plus, 1x+1.
Solution
Sure, let's use long division to divide the polynomial 3x^3 + 5x^2 + 3x + 1 by x + 1.
Step 1: Divide the first term of the numerator (3x^3) by the first term of the denominator (x). This gives us 3x^2.
Step 2: Multiply the entire denominator (x + 1) by the result from step 1 (3x^2) and subtract this from the original polynomial. This gives us:
3x^3 + 5x^2 + 3x + 1 - (3x^3 + 3x^2) = 2x^2 + 3x + 1
Step 3: Repeat the process. Divide the first term of the new polynomial (2x^2) by the first term of the denominator (x). This gives us 2x.
Step 4: Multiply the entire denominator (x + 1) by the result from step 3 (2x) and subtract this from the polynomial we had after step 2. This gives us:
2x^2 + 3x + 1 - (2x^2 + 2x) = x + 1
Step 5: Repeat the process one more time. Divide the first term of the new polynomial (x) by the first term of the denominator (x). This gives us 1.
Step 6: Multiply the entire denominator (x + 1) by the result from step 5 (1) and subtract this from the polynomial we had after step 4. This gives us:
x + 1 - (x + 1) = 0
So, the result of the division is 3x^2 + 2x + 1.
Similar Questions
Use the long division method to find the result when 8, x, cubed, plus, 26, x, squared, plus, 25, x, plus, 68x 3 +26x 2 +25x+6 is divided by 2, x, plus, 32x+3.
Use the long division method to find the result when x, cubed, plus, 9, x, squared, plus, 21, x, plus, 9x 3 +9x 2 +21x+9 is divided by x, plus, 3x+3.
Use the long division method to find the result when 4, x, cubed, minus, 4, x, squared, plus, 13, x, minus, 64x 3 −4x 2 +13x−6 is divided by 2, x, minus, 12x−1. If there is a remainder, express the result in the form q, left parenthesis, x, right parenthesis, plus, start fraction, r, left parenthesis, x, right parenthesis, divided by, b, left parenthesis, x, right parenthesis, end fractionq(x)+ b(x)r(x) .
Use the long division method to find the result when 2, x, cubed, minus, 8, x, squared, plus, x, plus, 12x 3 −8x 2 +x+1 is divided by x, minus, 4x−4.
Use synthetic division to find the result when 4, x, to the power 4 , minus, 7, x, cubed, plus, 7, x, squared, minus, 12, x, plus, 154x 4 −7x 3 +7x 2 −12x+15 is divided by x, minus, 1x−1. If there is a remainder, express the result in the form q, left parenthesis, x, right parenthesis, plus, start fraction, r, left parenthesis, x, right parenthesis, divided by, b, left parenthesis, x, right parenthesis, end fractionq(x)+ b(x)r(x) .
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.