A polynomial P has non-negative integer coefficients. If P(1) = 8 and P(10) = 2312, what is P(2)?

9514 1404 393

  32

Step-by-step explanation:

If coefficients are positive integers, then the polynomial cannot be higher degree than 3. 10^4 = 10,000, so even a coefficient of 1 will give too large a value. P(1) = 8 tells us that the sum of coefficients must be 8, so we cannot have a degree lower than 3.

The sum of digits in 2312 is 8, so it works out that the polynomial is ...

  P(x) = 2x^3 +3x^2 +x +2 . . . . matches P(1) = 8 and P(10) = 2312

Then P(2) is ...

  P(2) = ((2·2 +3)2 +1)2 +2

  P(2) = 32

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

a

step-by-step explanation:

when a number is between two straight lines it means the absolute value.

to find absolute value you need to know how many numbers is that number away from 0.

when finding absolute value the number will always come out positive

so absolute value of -3 is 3

absolute value of 3/2 is 3/2

absolute value of -2 is 2

absolute value of 3.5 is 3.5

absolute value of -1 is 1

now put these numbers in order:

a)   |-1|, |3/2|, |-2|, |-3|, |3.5|