How is this problem solved?
x^3 + 7x^2 - 49
_______________
x + 5
You did not say exactly what you need done.
I assume you are trying to divide, right?
Divide the trinomial by the binomial.
You can use synthetic division to solve this question more easily.
If you get stuck, let me know.
but guido, if that is your real name, wait a sec how do u divide a trinomial by a binomial
To solve this problem, you need to perform polynomial long division. Here's how you can do it step by step:
Step 1: Write the dividend and divisor in the proper format.
The dividend is x^3 + 7x^2 - 49, and the divisor is x + 5. Write them as a division problem, placing the dividend inside the long division symbol and the divisor to the left.
-------------
x + 5 | x^3 + 7x^2 - 49
Step 2: Divide the first term of the dividend by the first term of the divisor.
Divide x^3 by x to get x^2, and write it above the long division symbol.
x^2
-------------
x + 5 | x^3 + 7x^2 - 49
Step 3: Multiply the divisor by the quotient term (x^2).
Multiply (x + 5) by x^2 to get x^3 + 5x^2, and write it below the dividend.
x^2
-------------
x + 5 | x^3 + 7x^2 - 49
- (x^3 + 5x^2)
Step 4: Subtract the product from the dividend.
Subtract (x^3 + 5x^2) from (x^3 + 7x^2) to get 2x^2, and write it below the line.
x^2
-------------
x + 5 | x^3 + 7x^2 - 49
- (x^3 + 5x^2)
2x^2
Step 5: Bring down the next term.
Bring down the -49 from the dividend.
x^2
-------------
x + 5 | x^3 + 7x^2 - 49
- (x^3 + 5x^2)
2x^2
------
- 49
Step 6: Repeat the process until the dividend is fully divided.
Divide 2x^2 by x to get 2x, and write it above the line. Multiply (x + 5) by 2x, subtract the product from the remaining terms, and bring down the next term -49.
x^2 + 2x - 10
---------------------
x + 5 | x^3 + 7x^2 - 49
- (x^3 + 5x^2)
2x^2
------
- 49
- (2x^2 + 10x)
- 49
------
- 49
Step 7: Write the final answer.
The quotient is x^2 + 2x - 10, and the remainder is -49.
Therefore, the solution to the problem is (x^2 + 2x - 10) with a remainder of -49.