Pre Calculus

Write f(x) =x^3-11x^2+18x+32 in the form f(x)= (x-k) q (x) +r when k=6 + (square root)6, and demonstrate that f(k)=r

1. 👍
2. 👎
3. 👁
1. A little synthetic division shows that

f(x) = (x-(6+√6))(x^2+(√6-5)x+(√6-6))+2

I leave it to you to verify that
f(6+√6) = 2

1. 👍
2. 👎
2. I will try to show my synthetic division, the .... are spaces:

6+√6 | 1 ........ -11 ........ 18 ........ 32
.................... 6+√6 .... √6-24 .... -30
............ 1 ..... √6-5 ..... √6-6 ........ 2

showing that:
x^3-11x^2+18x+32 = (x-6-√6)(x^2 + (√6-5)x + √6-6) + 2

that is, r = 2

now find f(6+√6)
= (6+√6)^3 - 11(√6+6)^2 + 18(√6+6) + 32
= 324+114√6 - 462 - 132√6 + 18√6 + 108 + 32
= 2 + 0√6
= 2

whewwwhh!

1. 👍
2. 👎
3. Good job with the formatting!!

Did you post somewhere in the past as a scratchpad?

1. 👍
2. 👎

Similar Questions

1. What is the simplified form of squared root 140? A.) 4 to the square root of 35 B.) 10 to the square root of 14 C.) 2 to the square root of 70 D.) 2 to the square root of 35 Please show me how to do this Thank You

2. ALGEBRA

1, Factor each expression x^2 - 10x - 24 A. (x + 4)(x - 6) B. (x + 6)(x - 4) C. (x + 2)(x - 12) D. (x + 12)(x - 2) 2, x^2 - 36 = 0 A. (1 + square root of 3, 1 - square root of 3) B. (-6,6) C. No solution D. None of these 3, Factor

3. MAth 109

The formula d= square root of 3h/2 models the distance, d, in miles, that a person h feet high can see to the horizon. If the pool deck on a cruise ship is 80' above the water, how far can passengers on the pool deck see? Write

4. math

1. Which of the following numbers is a rational? A. 4/5 B. square root of 27 C. 4.02002000200002... D. Square root of 31 2. Which type of number is shown below? 0.313311333111... A. repeating decimal B. rational C. irrational D.

1. help riemann sums

the expression 1/50 (1/50 +2/50+ 3/50+ .....50/50)is a Reimann sum approximation for (everything in the parantheses is square root except the 1/50 outside the paratheses) the answer has to me the integral form so from looking at

1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers? a. Square root 120 , n , Square root 3

3. Algebra

Use the quadratic formula to solve the equation. Give exact answers: 2x^2 -1 = 6x. The choices are: a) -3 + square root(7)/2, -3 - square root(7)/2 b) 3 + square root(11)/2, 3 - square root(11)/2 c) 3 + square root(7)/2, 3 -

Which radical expression is in simplified form? A.) 11y/3 square root *B.) square root of 6/5y C.) square root of 17/square root of 4 D.) square root of 25/81 Thank You

1. Tirginometry

the expression 4ab(square root of)2b-3a(square root of)18b^3+7ab(square root of)6b is equivalent to... (a)2ab(square root of)6b (b)16ab(square root of)2b (c)-5ab+7ab(square root of)6b (d)-5ab(square root of)2b+7ab(square root

2. math

Say if these numbers make a right triangle and a Pythagorean triple: 2, 2 square root 2, and 2 square root 3. I am confident that the answer for both parts of the question is no, because when 2 is squared and when 2 square root 2

3. Calculus

A rectangle is bounded by the x axis and the semicircle = square root 25-x^2. What length and width should the rectangle have so that its area is a maximum? When I worked the problem out(which is a bit detailed). I started with y

4. Math

1. Which of the following numbers is a rational? A. 4/5 B. square root of 27 C. 4.02002000200002... **** D. Square root of 31 2. Which type of number is shown below? 0.313311333111... A. repeating decimal B. rational C. irrational