Given the following set S of polynomials, find a polynomial p(x) in P₂ so that SU {p(x)} spans P2 and a non-zero polynomial q(x) in P2 so that SU {q(x)} does not span P2. Use the '^' character to indicate an exponent, e.g. 5x^2-2x+1. S={−5x²+4x−9, −8x²−6x+8| p(x) = 0 q(x) = 0

Q: Let f(x) = x³ - 2x² - 5x + 6. If x = 1 is a zero of f(x), use the Factor Theorem and synthetic…

A:

Q: Write the cubic polynomial function f(x)in expanded form with zeros −6,−4, and 1,,given that…

A:

Q: K degree and the leading coefficient. a) f(x) = 2x² 3x + 5 b) f(x) -3x³ + 2x² + 5x + 1 c) f(x) 5x3…

A:

Q: Write g(x) = x² + x³ + 2x²+x+2 as a product of irreducible polynomials over 2.₂. за

A: Write as a product of irreducible polynomials over .

Q: If p(x) is a polynomial in Zp[x] with no multiplezeros, show that p(x) divides xp^n-x for some n.

A: Px is a polynomial  Px=x-ax-bx-c...x-ux-vx-w where   a,b,c...∈Zp but u,v,w∉Zp Let Rx=x-ux-vx-w has…

Q: 4. Describe the end behaviour of each polynomial function using the K degree and the leading…

A: As you asked for multiple subpart according to our guideline we give only first three of them.…

Q: Write a polynomial f(x) of degree 3 that has the zeros 1/3, √3, and -√3

A:

Q: 3. Determine whether the polynomial function t's g(x) = -4x²³²+ d x² even godd or reiter

A: The polynomial function is:gx=-4x5+2x2 To Do:We have to determine whether the given function is odd…

Q: Find a polynomial that interpolates (−1,0), (0, 2), (1, 1), (2, 2) using the Newton form.

A: x-1012f(x) 0212We have to find a polynomial using the newton form.