Using the inner product (,): P2(R) x P2(R) → R, (p, q) = p(0)q(0) +p(1)q(1) +p(2)q(2) + p(3)q(3) find the distance between -3x + 8x² and 5 + 4x + 4x².

Q: Consider the points (x₁, y₁) (-1,6), (x2, 12) (0, -2), (x3, 13) (1,4), (X4, Y4) = (2,4). + = x + =…

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Q: 3r²-7r-6 lim r2 - 9 6.

A: We have to evaluate the limit 11) limx→33x2-7x-6x2-9 12) limx→25x-25x-5

Q: f(x)=-6x2-6x3+x4             find the degree of the polynominal

A: Since, we have been given f(x)=x4-6x3-6x2 -(i)Our aim is to find the degree of polynomial given by…

Q: =x2+10x+24 Express the quadtractic function in standard form

A: First  make perfect square and then put constant

Q: Find all the zeros given that z 2 and z=-7 are zeros: j (z) = 4x + 19z - 64z2 -I+ 42 %3D %3D %3D O x…

A: Answer

Q: (2x)(x-y+5)(5y)

A: Firstly, we multiply 2x by each term of x-y+5

Q: What is the quotient when f(x) = 6x¹ − 2x³ + x² − 3x + 1 is divided by g(x) = x² + x -2 in Z₂[x]?

A:

Q: Evalvade- (3-2i)(X+y) =2(X-2ly)+2i-!

A: 3 - 2ix + iy = 2x-2iy + 2i - 1x = ?y = ?

Q: Find the remainder when f(x) = x7 + 3x5 + x - 1 is divided by x2 +1 in Z5[x].

A:

Q: factorise (c) x - - 3x - 4x + 12 (f) x'y – 4xy

A:

Q: Find the coefficients a,b in the function f(x)=ax+b so that (f(x1)-y1)^2+(f(x2)-y2)^2+(f(x3)-y3)^2…

A: Given data: Function fx=ax+b so that fx1-y12+fx2-y22+fx3-y32 is as small as possible. Given table of…

Q: Identify the x-intercepts for: f(x)=x²+x-12 O (0, -4) (3,0) O (-4,0) (3,0) O (0, -4) (0, 3) O(-4,0)…

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Q: Evaluate f(x+h)-f(x) h , given f (x) = 5 x+2 Use a / to represent a fraction line. Do not include…

A: The function is given byTo determine: The expression of .

Q: Given m (x) = 3x - 9 and n(x) = - 4 +2x, find 2(x) – m (x). Do not include spaces in your answer.

A: By using direct subtraction rules we can   find n(x)-m(x)

Q: h = (-6x³ + 9xª + 5x7) (7 + 5x – 4x?). Then h= fgwhere %3D f = and g = Using the product rule h'(x)…

A: differentiate this with product rule.

Q: The Range of the quadratic function f(x) = -x² + 24x + 48 is, O [-48, 12]| о (), 12] O [48, 0) O…

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Q: h(z)=-z5+8z3-5z2-7z+35      differentiate

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Q: 1. Differentiate. Do not simplify. I b) g(x) = (7x3 – 3x² + x)(1+ 4x²) a) y = Vx4 -5x+1 d) g(x) =…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: The Range of the quadratic function f(x) =-² +24r + 55 is O (-55, 12] O (-00, 55] O [55, 00) О (),…

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Q: Given a rectangular box. Lengths are in cm 2x X X

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Q: > For y, polynomial x = y₁ 1 D²-2 [x²] y, = [-1-D² +...]. [2x+3]

A:

Q: Explain how the domain of g1x2 = 2x compares to thedomain of g1x - k2, where k Ú 0.

A: Given, gx=2x

Q: In Exercises 10-11, add the polynomials. 10. (-8r³ + 5x² – 7x + 4) + (9x³ – 11x² + 6x – 13) 11.…

A: since you have asked multiple questions in single request so we will be answering only first…

Q: A variable circle passes through the point A(a, b) and touches the x-axis. Show that the locus o the…

A:

Q: Find the constants c0, c1, and x1 so that the quadrature formula Z 1 0 f(x)dx = c0f(0) + c1f(x1),…

A: Consider the given quadrature formula, ∫01fxdx=c0f0+c1fx1 here we need to determine the constants…

Q: Use the graph to guess possible linear factors of f(x). Then completely factor f(x) with the aid of…

A: For a function f(x), the root of f(x) is the points at which the graph of f(x) intersects x-axis.If…

Q: Which function is not quadratic? (O Ax) = (6x+ 9) -9 ()-x(x-9)(6x + 8) U Ax) = 7x + 8 Ax) = 6(x- 9)2

A: We have to check