Divide (3x^3-x^2+8x-9) by (x-1)
Please help!
I'll show you how this works out:
3x^2 + 2x + 10
x - 1 | 3x^3 - x^2 + 8x - 9
3x^3 - 3x^2
2x^2 + 8x
2x^2 - 2x
10x - 9
10x - 10
1
Remember when you subtract, you change the signs. This did not divide evenly, so you will have a remainder of 1.
I hope this helps.
The answer is 3x^2 + 2x + 10 with a remainder of 1.
To divide the polynomial (3x^3 - x^2 + 8x - 9) by (x - 1), you can follow these steps:
Step 1: Write the dividend (3x^3 - x^2 + 8x - 9) and divisor (x - 1) side by side, placing a line between them.
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x - 1 | 3x^3 - x^2 + 8x - 9
Step 2: Start by dividing the first term of the dividend by the first term of the divisor, which gives you 3x^2 as the quotient.
3x^2
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x - 1 | 3x^3 - x^2 + 8x - 9
Step 3: Multiply the divisor (x - 1) by the quotient 3x^2.
3x^2 (x - 1) = 3x^3 - 3x^2
Step 4: Subtract the result from step 3 from the original dividend.
3x^3 - x^2 + 8x - 9 - (3x^3 - 3x^2) = 2x^2 + 8x - 9
Step 5: Bring down the next term from the dividend, which is 8x.
2x^2 + 8x - 9
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x - 1 | 3x^3 - x^2 + 8x - 9
Step 6: Divide the first term of the new polynomial (2x^2 + 8x) by the first term of the divisor (x), which gives you 2x as the next term of the quotient.
3x^2 + 2x
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x - 1 | 3x^3 - x^2 + 8x - 9
Step 7: Multiply the divisor (x - 1) by the new quotient term 2x.
2x (x - 1) = 2x^2 - 2x
Step 8: Subtract the result from step 7 from the polynomial obtained in step 6.
2x^2 + 8x - 9 - (2x^2 - 2x) = 10x - 9
Step 9: Bring down the last term from the dividend, which is -9.
10x - 9
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x - 1 | 3x^3 - x^2 + 8x - 9
Step 10: Divide the new polynomial (10x - 9) by the divisor (x - 1), which gives you 10 as the next term of the quotient.
3x^2 + 2x + 10
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x - 1 | 3x^3 - x^2 + 8x - 9
Step 11: Multiply the divisor (x - 1) by the new quotient term 10.
10(x - 1) = 10x - 10
Step 12: Subtract the result from step 11 from the polynomial obtained in step 10.
10x - 9 - (10x - 10) = 1
Step 13: Since there are no more terms left in the dividend, we have successfully divided the polynomial.
Therefore, the result of dividing (3x^3 - x^2 + 8x - 9) by (x - 1) is:
Quotient: 3x^2 + 2x + 10
Remainder: 1
To divide (3x^3 - x^2 + 8x - 9) by (x - 1), follow these steps:
Step 1: Divide the first term of the numerator (3x^3) by the first term of the denominator (x).
This gives you the first term of the quotient: 3x^2.
Step 2: Multiply the denominator (x - 1) by the first term of the quotient (3x^2).
This gives you 3x^3 - 3x^2.
Step 3: Subtract the result from step 2 from the numerator (3x^3 - x^2 + 8x - 9).
This gives you -3x^2 + 8x - 9.
Step 4: Bring down the next term from the numerator (-3x^2).
The expression becomes -3x^2 + 8x - 9.
Step 5: Divide the first term of the resulting expression (-3x^2) by the first term of the denominator (x).
This gives you -3x.
Step 6: Multiply the denominator (x - 1) by the new term of the quotient (-3x).
This gives you -3x^2 + 3x.
Step 7: Subtract the result from step 6 from the resulting expression (-3x^2 + 8x - 9).
This gives you 5x - 9.
Step 8: Bring down the next term from the numerator (5x).
The expression becomes 5x - 9.
Step 9: Divide the first term of the resulting expression (5x) by the first term of the denominator (x).
This gives you 5.
Step 10: Multiply the denominator (x - 1) by the new term of the quotient (5).
This gives you 5x - 5.
Step 11: Subtract the result from step 10 from the resulting expression (5x - 9).
This gives you -4.
Step 12: Since there are no more terms in the numerator, the remainder is -4.
Therefore, the quotient is 3x^2 - 3x + 5 with a remainder of -4.