Use the division algorithm to find q (x) and r(x) such that a(x) = q (x) b(x) +r (x) with degr(x) deg b (x) for a(x) = 5x³ + 6x²-3x+4 by b(x) = x-2 in Z7[x]x Hint: use long division.

Q: Two polynomials P and D are given. use  either synthetic division or long division to divide P(x) by…

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Q: Verify the factorization by using synthetic division 3x3 - 5a2-4x + 4 = 3(x+ 1)(x– 2)(x –) Verify…

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Q: Find 2) (x) using long division for f(x) = x? + 8x + 16 g(x) = x + 3 The quotient is The remainder…

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Q: Let P(x)=-x²³+2x2-6x'-5x'-1 and D(x)=x+1 Determine the remainder when P(x) is divided by D(x)

A: The given polynomial is:Px=-x23+2x12-6x7-5x4-1Dx=x+1To find the remainder.

Q: Let f(x) = 3x4 +4x3 −6x2 +21x−7. Let g(x) = x2 −x+2. Since the degree of g is 2, the basic fact…

A: Given: The given expression is:

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: F(x)=x3+8x2-8x-15 Use synthetic division to test several possible rational zeros in order to…

A: By useing the synthetic division to test several possible rational zeros in order to identify one…

Q: Find the remainder when f(x) is divided by g(x), without using long division f(x)=x²-9 g(x)=x+3

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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: Use the x-intercepts (don't forget the multiplicity), the end behavior, or any other properties of…

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…