
Question 3 4 pts Find the second derivative of the following function: x3-6x2+1 (a)3x+12 (b)3x-12 (c)6x-12 (d)6x+12 (e) 0 (a) (b) O (c) O (d) (e)
please answer questions 1-4
Divide using long division. (Show all work!) x2-x+3 6x2 +7x+5 3x-1 X+1 z! 15y3+y2–217 5y-3 2x3-29x+ x+4
Divide using long division. State the quotient, q(x), and the remainder, r(x). (6x2 + 6x² – 2x – 10) = (2x - 2) (6x2 + 6x2 - 2x – 10) = (2x - 2) = (+24 2x-2 (Simplify your answers. Do not factor. Use integers or fractions for any numbers in the expressions.)
If f(x) = 6x2 - 6x² + 7x-9 and g(x)= 0, find (fog)(x) and (gof)(x). What is (fog)(x)? (fog)(x) = What is (gof)(x)? (gof)(x) =
f(x+h)-f(x) Find if f(x)=3x2 + 5x-18 h O A. 6x+5-3h 0 B. 6x +5+h 0 C. 6x+5 O D. 6x + 5+ 3h
Determine whether the following polynomials are irreducible in Q[x]. (i) f(x) = 3x2 – 7x – 5 (ii) f(x) = 2x3 – x – 6 (iii)f(x) = x3 + 6x2 + 5x + 25
4. (a) Prove that if f(x) E Q[x] is irreducible in R[x], then it is irreducible in Q[x]. Is the converse of this statement true? Explain why or why not. (b) Prove that if f(x) E Q[x] is reducible in Q[x], then it is reducible in R[x]. Is the converse of this statement true? Explain why or why not.
5 4 3 + - + 6x - 4x + 8)e to Find the derivative of the function. y= (2x3 – 2x2 + 8x - 6)e ** O B. (6x5 - 6x4 + 24x3 – 12x2 - 4x + 8)e O C. (6x5 - 6x4 + 24x3 – 1872)e ** OD. (6x2 - 4x+8)e ** to
MATEMATIK MATHEMATICS 5 Polinomlar Polynomials 1. P(x)-(a-b-4)/x+(a+b-12)x1+6x+4 5. 2 Yant/ Answer 32 2. Px)-(a-2(a+b-8)x2+4x-7 6. Yanit / Answer: 12 12 7
MATEMATIK MATHEMATICS 5 Polinomlar Polynomials 1. P(x)-(a-b-4)/x+(a+b-12)x1+6x+4 5. 2 Yant/ Answer 32 2. Px)-(a-2(a+b-8)x2+4x-7 6. Yanit / Answer: 12 12 7
Write the polynomial f(x) as a product of irreducible polynomials in the given ring. Explain in each case how you know the factors are irreducible. 1) f(x) -x* + 2x2 +2x 2 in Z3[x]. 2) f(x)4 + 2x3 + 2x2 +x + 1 in Z3[x]. 3) f(x) 2x3-x2 + 3x + 2 in Q[x] 4) f(x) = 5x4-21x2 + 6x-12 in Q[x)