Solve each problem.
Find the quotient and remainder when
x^2 – 5x + 9 is divided by x – 3.
I don't understand how to divide and solve this problem. Can someone help me understand the steps on how to do it. Thanks.
The method you need to learn and use is called polynomial long division.
It is explained at:
http://www.sosmath.com/algebra/factor/fac01/fac01.html
and at other websites easily found with a Google search. Learn and practice the method.
To solve this problem, you can use polynomial long division method. Here are the steps:
1. Start by writing the dividend, which is x^2 - 5x + 9, and the divisor, which is x - 3.
2. Divide the first term of the dividend (x^2) by the first term of the divisor (x). This gives you x, which is the first term of the quotient.
3. Multiply the divisor (x - 3) by the quotient term (x) and write the result below the dividend.
- This step would give you x(x - 3) = x^2 - 3x.
4. Subtract the result obtained in step 3 from the dividend.
- Subtracting x^2 - 3x from x^2 - 5x gives you 5x.
5. Bring down the next term from the dividend, which is 9.
6. Divide the new dividend term (5x) by the first term of the divisor (x). This gives you 5, which is the second term of the quotient.
7. Multiply the divisor (x - 3) by the new quotient term (5) and write the result below the previous subtraction.
- This step would give you 5(x - 3) = 5x - 15.
8. Subtract the result obtained in step 7 from the new dividend (5x).
- Subtracting 5x - 15 from 5x gives you 15.
9. Since there are no more terms in the dividend, the process is complete.
The quotient is found by combining the quotient terms from steps 2 and 6, which gives you the final quotient of x + 5. The remainder is the last value obtained in step 8, which is 15.
Therefore, the quotient when x^2 - 5x + 9 is divided by x - 3 is x + 5 with a remainder of 15.