To find the quotient of the expression 3x² + 17x + 10 divided by x + 5, we need to use polynomial long division.
Firstly, we arrange the polynomial division:
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x + 5 | 3x² + 17x + 10
1. Divide the first term of the dividend, 3x², by the first term of the divisor, x, to get 3x.
2. Multiply 3x by the entire divisor (x + 5):
3x * (x + 5) = 3x² + 15x.
3. Subtract this result from the original polynomial:
3x
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x + 5 | 3x² + 17x + 10
- (3x² + 15x)
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2x + 10
4. Now, bring down the next term (if there was one), but in this case, we can proceed directly as we have 2x + 10.
5. Now, divide 2x by x to get 2.
6. Multiply 2 by the entire divisor:
2 * (x + 5) = 2x + 10.
7. Subtract this from 2x + 10:
3x + 2
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x + 5 | 3x² + 17x + 10
- (3x² + 15x)
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2x + 10
- (2x + 10)
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0
Since the remainder is 0, we find that:
The quotient of 3x² + 17x + 10 divided by x + 5 is: 3x + 2.
This means that you can express the original polynomial as:
3x² + 17x + 10 = (x + 5)(3x + 2).