Given that p(x) is a polynomial of odd degree, which polynomial has the same end behavior as p(x)? O =(x) = p(x) (x³-1) Ow(x) = p(x)(x²-1) O g(x) = p(x)(x-1)

Q: 10. Given the polynomial function f(x) = 5x(x² - 4)²(x+3)³ (a) (6 points) Find the zeros of f(x).…

A: (a) Finding the Zeros: 𝑓(𝑥)=05𝑥(𝑥2−4)2(𝑥+3)3=0For 𝑥, we have three factors: 𝑥,(𝑥2−4)2, and…

Q: Now let f(x) be a polynomial of order n, i.e. one whose highest non-zero coeffi- cient is c,. For…

A: We will use repeated differentiation to prove this

Q: Consider the polynomial equation of P(r) = 0 where P(x) = #* – a* – ² – a – - 2. - T (a) What are…

A: The given polynomial is Px=x4-x3-x2-x-2.

Q: If f(x) is a polynomial of degree less than 3, then prove that f(a) (x-a) |1 f(b) (x-b) f(c) (x-c) 1…

A:

Q: Find a function f(x) so that h(x) = (gof)(x) given that -2x³ – 6x² 6x² + 5x+1 and g(x): = h(x) =…

A: (g∘f)(x) = g(f(x))

Q: A quadratic polynomial y = 4x² + 7x – 3 has roots p and q. Find a quadratic g(x) = x² + ax + ß with…

A:

Q: 9. For the polynomial f(x) = x(3x + 1)(x – 2)², determine the leading coefficient, leading term,…

A: Given: fx=x3x+1x-22 Now solve the parenthesis we get, ⇒fx=3x4-11x3+8x2+4x                    ...(1)…

Q: 4 Let p(x) be a degree 3 polynomial with a negative leading coefficient. Which of the functions…

A: p(x) be a polynomial of 3 degree with negative leading coefficient.

Q: loes it follow that P(3) = 0 as well? Why

A: We have to explain the given condition

Q: Let f(x) = 4+ (5x +9)³. Find f¹(x) = (1) · (√(x − 4) – 9) Find (ƒ(2)) -¹ = (¹) · (√(x-4) – 9)

A:

Q: Graph the polynomial function f(x)--(x + 1)(x - 1) (x - 3)²

A: Given: polynomial function f(x)=-(x+1)(x-1)2(x-3)2. To be find: graph the polynomial function.…

Q: Which equation matches the graph of the piecewise function f(x) below?

A: Given,

Q: If f(x) is a polynomial function satisfying f(x) ·ƒ ( ² ) = f(x) + f ( ² ) a and f(4) = 65, then…

A:

Q: Show that f (x) = x2 + 3x−1 and g(x) = 3x3 − 9x + x−2 are rational functions—that is, quotients of…

A: To show: That the functions are rational function: Given: The functions are fx=x2+3x-1 and…

Q: If f(x) is a polynomial of the first degree and a is not equal to B, show that f(x)= f(B)(x-a) -…

A:

Q: Which polynomial function in standard form has a root of multiplicity 1 at x= 3, and a root of…

A: A polynomial function has a root of multiplicity 1 at x=3, and a root of multiplicity 2 at x=4

Q: Let P(x) be a polynomial of degree 5 with roots 2, – 5 and (3 + i). Write P(x) as a product of…

A: It is given that the roots of 5 degree polynomial are 2,-5,3+i

Q: For the polynomials p(x)=4x* – 3x² +x -1 and d(x) =x² – 1, write in the form p(x)= d(x)q(x)+r(x).

A:

Q: Write a polynomial p(x) whose roots are 1 + √2 and 1-√3 such that p(2) = 5.

A: The given roots are, 1+2, 1-3 Since the given roots are irrational and as they exist in pairs we…

Q: Which function is a polynomial with roots x = 3, x = – 4, x = 1 ? A f(x) = (x + 3)(x +4)(x+ 1) f(x)…

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Q: The function, y = -x + 6 is shown on the graph below. Use the graph to select all correct…

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Q: Consider the functions: f(x) = X-4 x+5 * and g(x) = . Find the expression for the composition of…

A: