Question

P(2)=4 и P(x+2) при делении на x+5 даёт остаток равный -11 чему равен будет остаток при делении P(x) на x^2+x-6

Answer 1

Ответ:скинь фото и решу

Пошаговое объяснение:

Answer 2

We can start by using the information given to find the polynomial P(x). Since we know that P(2) = 4, we can substitute x = 2 into the polynomial P(x) and solve for the constant term:

P(2) = a(2)^2 + b(2) + c = 4 4a + 2b + c = 4

We also know that when P(x+2) is divided by x+5, the remainder is -11. This means that:

P(x+2) = (x+5)Q(x) - 11

where Q(x) is the quotient polynomial. We can substitute x = -3 into this equation to eliminate Q(x) and solve for the coefficients of P(x):

P(-1) = 2a - b + c = -11

Now we have two equations with three unknowns:

4a + 2b + c = 4 2a - b + c = -11

We can solve for the coefficients using elimination or substitution, and we find that:

a = 2 b = -8 c = 15

Therefore, the polynomial P(x) is:

P(x) = 2x^2 - 8x + 15

To find the remainder when P(x) is divided by x^2 + x - 6, we can use polynomial long division or synthetic division. Here is the polynomial long division:

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     2x - 10

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x^2 + x - 6 | 2x^2 - 8x + 15

• (2x^2 + 2x - 12) -10x + 27 -(-10x - 10) 37

Therefore, the remainder is 37 when P(x) is divided by x^2 + x - 6.