How would I simplify this and then write it in standard form
(2x^2 -3x+2)/(x-3)
simplified, it is in the form you started out with:
2x+3 + 11/(x-3)
That's about as standard as it gets -- a polynomial and a remainder in simplest form.
So I can’t write it in standard form?
To simplify and write the expression (2x^2 - 3x + 2)/(x - 3) in standard form, follow these steps:
Step 1: Perform the division by using long division or synthetic division.
2x + 3
--------------
x - 3 | 2x^2 - 3x + 2
In the above division, the result is 2x + 3, which represents the quotient.
Step 2: Rewrite the original expression using the quotient and the divisor:
2x + 3 + remainder/(x - 3)
Step 3: Simplify the remainder to express the expression as a sum:
2x + 3 + (remainder)/(x - 3)
The remainder cannot be further simplified, so the expression in simplified form is:
2x + 3 + remainder/(x - 3)
The quotient is 2x + 3, and the remainder is (2x + 9)/(x - 3). To write the expression in standard form, combine like terms:
2x + 3 + (2x + 9)/(x - 3)
This is the expression simplified and written in standard form.
To simplify and write the expression in standard form, you'll need to perform polynomial division. This involves dividing the polynomial (2x^2 - 3x + 2) by the divisor (x - 3). Here's how you can do it step by step:
Step 1: Set up the polynomial division, placing the dividend (2x^2 - 3x + 2) inside the long division symbol and the divisor (x - 3) outside of it:
________________________
x - 3 | 2x^2 - 3x + 2
Step 2: Divide the first term of the dividend (2x^2) by the first term of the divisor (x). The result is 2x:
2x
________________________
x - 3 | 2x^2 - 3x + 2
Step 3: Multiply the divisor (x - 3) by the quotient (2x) obtained in the previous step. The result is 2x^2 - 6x.
2x
________________________
x - 3 | 2x^2 - 3x + 2
- (2x^2 - 6x)
Step 4: Subtract the product obtained in the previous step (2x^2 - 6x) from the dividend (2x^2 - 3x + 2) to get the new dividend:
2x
________________________
x - 3 | 2x^2 - 3x + 2
- (2x^2 - 6x)
_______________
3x + 2
Step 5: Now, divide the first term of the new dividend (3x) by the first term of the divisor (x). The result is 3:
2x + 3
________________________
x - 3 | 2x^2 - 3x + 2
- (2x^2 - 6x)
_______________
3x + 2
- (3x + 9)
Step 6: Multiply the divisor (x - 3) by the new quotient (3) obtained in the previous step. The result is 3x - 9.
2x + 3
________________________
x - 3 | 2x^2 - 3x + 2
- (2x^2 - 6x)
_______________
3x + 2
- (3x - 9)
Step 7: Subtract the product obtained in the previous step (3x - 9) from the new dividend (3x + 2) to get the remainder, which is 11:
2x + 3
________________________
x - 3 | 2x^2 - 3x + 2
- (2x^2 - 6x)
_______________
3x + 2
- (3x - 9)
_______________
11
Step 8: The quotient is the result obtained by adding up the quotients from all the divisions above:
Quotient: 2x + 3
Step 9: Finally, express the simplified polynomial in standard form by combining the quotient and the remainder:
(2x^2 - 3x + 2)/(x - 3) = 2x + 3 + 11/(x - 3)
Therefore, the simplified expression written in standard form is:
2x + 3 + 11/(x - 3)