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dimaraw [331]
3 years ago
5

Divide: (-7x+x^2+15)÷(-3+x)

Mathematics
1 answer:
kakasveta [241]3 years ago
3 0
Since the divisor is in the form (x + #) or (x - #), This can be done by synthetic division.
First put the polynomial ion descending order: x^2 - 7x + 15
Take the coefficients of the terms and follow these steps:

3 |  1 -7  15
         3  -12
___________  Bring down the 1, multiply the 3 by the 1 and place under the
     1  -4    3       -7, then add.
                         Multiply 3 by -4, place under the 15, then add.
       The bottom row is our answer. Since the problem started with a second power, the answer will start with a first power.
The bottom row are the coefficients of the terms and the last number is the remainder.
x - 4 remainder 3 ALSO WRITTEN   x - 4 + 3/(x -3)
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On solving (a) and (b),  we get k=-7 and p=1.

Put h=-2, k=-7 and p=1 in equation (1).

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y=\frac{1}{4}(x+2)^2-7

Therefore option A is correct.

2 The directrix of a parabola is the line y=5 . The focus of the parabola is (2,1) .

k-p=5                   ...(c)

(h,k+p)=(2,1)

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Put h=2, k=3 and p=-2 in equation (1).

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Therefore option D is correct.

3. The focus of a parabola is (0,−2) . The directrix of the parabola is the line y=−3 .

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(h,k+p)=(0,-2)

k+p=-2            .... (f)

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On solving (e) and (f),  we get k=-2.5 and p=0.5.

Put h=0, k=-2.5 and p=0.5 in equation (1).

y=\frac{1}{4(0.5)}(x-(0))^2+(-2.5)

y=\frac{1}{2}(x)^2-2.5

y=\frac{1}{2}(x)^2-\frac{5}{2}

Therefore option D is correct.

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