Question

let p(x) and Q(x) be two polynomials and consider the following two cases: case1:p(x) x Q(x)...

let p(x) and Q(x) be two polynomials and consider the following two cases:

case1:p(x) x Q(x)

case2: 3 Q (x)

for each case, find the following:

a) the number of terms

b) the degree

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let P and Q be polynomials of degree at least one and let a be the...
Let P and Q be polynomials of degree at least one and let a be the lead coefficient of P and b be the lead coefficient of Q. Prove that lim as n approaches infinity of P(n)/Q(n) = 0 deg Q > deg P a/b deg Q = deg P infinity deg Q < deg P
If p(x) and q(x) are arbitrary polynomials of degree at most 2, then the mapping =p(−1)q(−1)+p(0)q(0)+p(2)q(2)...
If p(x) and q(x) are arbitrary polynomials of degree at most 2, then the mapping =p(−1)q(−1)+p(0)q(0)+p(2)q(2) defines an inner product in P3. Use this inner product to find , ||p||, ||q||, and the angle θ between p(x) and q(x) for p(x)=2x^2+3 and q(x)=2x^2−6x.
Question 4. Consider the following subsets of the vector space P3 of polynomials of degree 3...
Question 4. Consider the following subsets of the vector space P3 of polynomials of degree 3 or less: S = {p(x) : p(1) = 0} and T = {q(x) : q(0) = 1} Determine if these subsets are vectors spaces with the standard operations for polynomials
5. Let S be the set of all polynomials p(x) of degree ≤ 4 such that...
5. Let S be the set of all polynomials p(x) of degree ≤ 4 such that p(-1)=0. (a) Prove that S is a subspace of the vector space of all polynomials. (b) Find a basis for S. (c) What is the dimension of S? 6. Let ? ⊆ R! be the span of ?1 = (2,1,0,-1), ?2 =(1,2,-6,1), ?3 = (1,0,2,-1) and ? ⊆ R! be the span of ?1 =(1,1,-2,0), ?2 =(3,1,2,-2). Prove that V=W.
Let p(x) = a0 + a1x + a2x2 and q(x) = b0 + b1x + b2x2...
Let p(x) = a0 + a1x + a2x2 and q(x) = b0 + b1x + b2x2 be vectors in P2 with p, q = a0b0 + a1b1 + a2b2. Determine whether the given second-degree polynomials form an orthonormal set, and if not, then apply the Gram-Schmidt orthonormalization process to form an orthonormal set. (If the set is orthonormal, enter ORTHONORMAL in both answer blanks.) { 3 (x2−1), 3 (x2 + x + 2)} u1 = u2 =
1 Approximation of functions by polynomials Let the function f(x) be given by the following: f(x)...
1 Approximation of functions by polynomials Let the function f(x) be given by the following: f(x) = 1/ 1 + x^2 Use polyfit to approximate f(x) by polynomials of degree k = 2, 4, and 6. Plot the approximating polynomials and f(x) on the same plot over an appropriate domain. Also, plot the approximation error for each case. Note that you also will need polyval to evaluate the approximating polynomial. Submit your code and both plots. Make sure each of...
Let Poly3(x) = polynomials in x of degree at most 2. They form a 3- dimensional...
Let Poly3(x) = polynomials in x of degree at most 2. They form a 3- dimensional space. Express the operator Q(p) = xp' + p'' . as a matrix (i) in basis {1, x, x^2 }, (ii) in basis {1, x, 1+x^2 } . Here, where p(x) represents a polynomial, p’ is its derivative, and p’’ its second derivative.
Let p(x) = a0 + a1x + a2x2 and q(x) = b0 + b1x + b2x2...
Let p(x) = a0 + a1x + a2x2 and q(x) = b0 + b1x + b2x2 be vectors in P2 with p, q = a0b0 + a1b1 + a2b2. Determine whether the given second-degree polynomials form an orthonormal set, and if not, then apply the Gram-Schmidt orthonormalization process to form an orthonormal set. (If the set is orthonormal, enter ORTHONORMAL in both answer blanks.) { square root 3 (x2−1), square root 3 (x2 + x + 2)} u1 = u2...
Let A be a nonempty set and let P(x) and Q(x) be open statements. Consider the...
Let A be a nonempty set and let P(x) and Q(x) be open statements. Consider the two statements (i) ∀x ∈ A, [P(x)∨Q(x)] and (ii) [∀x ∈ A, P(x)]∨[∀x ∈ A, Q(x)]. Argue whether (i) and (ii) are (logically) equivalent or not. (Can you explain your answer mathematically and by giving examples in plain language ? In the latter, for example, A = {all the CU students}, P(x) : x has last name starting with a, b, ..., or h,...
Let F be a field and let a(x), b(x) be polynomials in F[x]. Let S be...
Let F be a field and let a(x), b(x) be polynomials in F[x]. Let S be the set of all linear combinations of a(x) and b(x). Let d(x) be the monic polynomial of smallest degree in S. Prove that d(x) divides a(x).