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12345 [234]
3 years ago
7

Use polynomial long division to rewrite the following fraction in the form q(x)+r(x)d(x), where d(x) is the denominator of the o

riginal fraction, q(x) is the quotient, and r(x) is the remainder.
2x^2+8x-12/x+1
Mathematics
1 answer:
SOVA2 [1]3 years ago
6 0

Step-by-step explanation:

p(x) = 2x^2+8x-12

d(x) = x + 1

r(x) = -13

q(x) = 2x + 6

\\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  2x +6 \\ x  + 1 \sqrt{ {2x}^{2}  + 8x - 12}  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  {2x}^{2}  + 2x \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \frac{  \: -  \:  \:  \:  \:  \:  \:  -  \:  \:  \:  \:  \: }{}  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  6x - 12 \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: 6x + 1 \\   \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \frac{ -  \:  \:    -  \:  \:  \:  \:  \: }{}  \\  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \: \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:  \:   \:  - 13

q(x)+r(x)d(x)

= 2x + 6 + (-13) * x + 1

= 2x + 6 -13 * x + 1

= 2x + 6 - 13x + 1

= (- 11x + 7)

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