Please check.
1. (5x^3+x^2-7)/(x+1)= ?
My answer: 5x^2-4x+4-11/x+1
2 (9x^3+5x-8)/(3x-2)= ?
My answer: 3x^2+2x+3-2/3x-2
1. yes 5 x^2 - 4 x + 4
R = -11
2. yes 3 x^2 + 2 x + 3
R = -2
To check if your answers are correct, we can simplify the expressions on the right side and see if they match the original expressions on the left side when simplified.
1. (5x^3 + x^2 - 7) / (x + 1)
To simplify this expression, we can use polynomial long division. Here are the steps:
Step 1: Divide the first term of the numerator (5x^3) by the first term of the denominator (x). This gives us 5x^2.
Step 2: Multiply the entire denominator (x + 1) by the quotient from step 1 (5x^2). This gives us 5x^3 + 5x^2.
Step 3: Subtract the result from step 2 from the numerator (5x^3 + x^2 - 7). This gives us: (5x^3 + x^2 - 7) - (5x^3 + 5x^2) = -4x^2 - 7.
Step 4: Bring down the next term from the numerator (-4x^2): -4x^2 + x^2 = -3x^2.
Step 5: Divide the first term of the result obtained in step 4 (-3x^2) by the first term of the denominator (x). This gives us -3x.
Step 6: Multiply the entire denominator (x + 1) by the quotient from step 5 (-3x). This gives us -3x^2 - 3x.
Step 7: Subtract the result from step 6 from the result obtained in step 4 (-3x^2 - 3x). This gives us: (-3x^2 - 3x) - (-3x^2 - 3x) = 0.
Step 8: Since the subtraction gives us zero, the division can be considered complete.
The simplified expression is 5x^2 - 3x.
Your answer: 5x^2 - 4x + 4 - (11/x + 1).
As we can see, your answer does not match the simplified expression. The correct simplified expression is 5x^2 - 3x.
2. (9x^3 + 5x - 8) / (3x - 2)
To simplify this expression, we can also use polynomial long division. Here are the steps:
Step 1: Divide the first term of the numerator (9x^3) by the first term of the denominator (3x). This gives us 3x^2.
Step 2: Multiply the entire denominator (3x - 2) by the quotient from step 1 (3x^2). This gives us 9x^3 - 6x^2.
Step 3: Subtract the result from step 2 from the numerator (9x^3 + 5x - 8). This gives us: (9x^3 + 5x - 8) - (9x^3 - 6x^2) = 6x^2 + 5x - 8.
Step 4: Bring down the next term from the numerator (6x^2): 6x^2 + 5x - 8.
Step 5: Divide the first term of the result obtained in step 4 (6x^2) by the first term of the denominator (3x). This gives us 2x.
Step 6: Multiply the entire denominator (3x - 2) by the quotient from step 5 (2x). This gives us 6x^2 - 4x.
Step 7: Subtract the result from step 6 from the result obtained in step 4 (6x^2 - 4x). This gives us: (6x^2 - 4x) - (6x^2 - 4x) = 0.
Step 8: Since the subtraction gives us zero, the division can be considered complete.
The simplified expression is 3x^2 + 2x.
Your answer: 3x^2 + 2x + 3 - (2/3x - 2).
Similar to the first question, your answer does not match the simplified expression. The correct simplified expression is 3x^2 + 2x.
It's important to be careful when simplifying expressions and performing calculations to avoid errors.