The polynomial p(x) = 2-(x+1)+x(x+1)- 2x(x+1)(x–1) interpolates the first four points in the table: -1 1 2 3 y 2 -7 10

Q: Find all zeros of the polynomial. P(x) = x5 - 3x4 + 12x3 - 28x2 + 27x - 9

A: Zeroes of the polynomial are the values which return zero value for the polynomial. Highest power of…

Q: Q1-Using the nodes (x, =2, x-=2.5 and x; =4), to find the second interpolation polynomial for flx) =

A: Given nodes are x0=2, x1=2.5, x2=4 and function is f(x)=1x Now table is x 2 2.5 4 f(x) 0.5 0.4…

Q: 2. Find algebraically the zeros for 3 p(x) = x +x – 4x - 4

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Q: What will be the difference of the two polynomial function p(x) and q(x) at x= 9 where p(x)=6x2…

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Q: Find the value of c so that (x - 3) is a factor of the polynomial p(x).p(x) = x4 - 3x2 + - 2x + c

A: Consider the given polynomial.The given polynomial is p(x) = x4– 3x2– 2x +c.It is known that if x–a…

Q: Which is the graph of the polynomial function p(x) = (x-1)(x+1)(x-4)? 241r 24fr y p(x) 16 16 8 8- -6…

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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: A polynomial function P is given. P(x) = −x3 + 5x2 + 14x (a) Express the function P in factored…

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Q: Find a polynomial P(x)=x3+ax2+bx+c satisfying ALL of the following properties:

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Q: If the sum of the zeroes of the polynomial p(x) = (k2 -14) x2 - 2x -12 is 1 . Then find the value of…

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

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Q: Use the graph of the polynomial function f(x) (a) to solve f(x) = 0, and (b) find the factorization…

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Q: Find k so that f(x)=2x² +12x + k has one root.

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Q: Given f(x)=3x^3-8x+kf(x)=3x3−8x+k, and x-1x−1 is a factor of f(x)f(x), then what is the value of k?

A: We have to find out k

Q: , (-1, 13), and (2, -2).

A: To find the value of a, b and c in the polynomial ax2+bx+c passes through the point (1,1) , (-1,13)…

Q: 2. Consider the polynomial function f(x) =x* + 6r²-3x²-96x – 208. a. How many linear factors does…

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Q: Find the condition which must be satisfied by the coefficients of the polynomial p(x)=x3-px2+qx-r,…

A: we know for cubic equation,  ax^3+bx^2+cx + d having roots α,β and γ  Sum of roots,α+β+γ=−b/a, Sum…

Q: 6. Find the zeroes of the polynomial function P(x) = (x - 7) (x + 1), and state the multiplicity of…

A: Finding zero of the polynomial function

Q: 4. Find all the zeros of: P(x) = x* + x³ + 7x² + 9x- 18

A: To Determine: find all the zeros of                          P(x)=x4+x3+7x2+9x-18 Given: we have a…

Q: Given p(x)=(x-4)^5 (x+1)(x-2)^3State the zeros and their multiplicities. What is the degreeof the…

A: Given:The function is, p(x) = (x−4)5(x+1)(x−2)3.

Q: Find thezeroes of the polynomial p(x)=(x-2)2-(x+2)2

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Q: Find the graph of the polynomial function P(x) = x² + 2. -20 -16 -3 -12 -8 M 4 3 N -1 2 دی T in 20…

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Q: 1 is a zero of the polynomial P(x)= x³ – 3x* + 7x³ – 13x² + 12x – 4 of multiplicity (а) 3 (b) 5 (c)…

A: Let's find x value.

Q: A polynomialf(x) and 6) f(x) =x4 - 2x3 A) ±3, ±1 + 4,

A: In this we have to find the factors of the polynomial then after roots so I'm providing hand written…

Q: Find m so that x– 5 is a factor of f (x)= 4x² – 21x² +mx–15.

A: Consider the given polynomial fx=4x3-21x2+mx-15

Q: Find all zeros of the polynomial. P(x) = x2 + 2x2 + 4x + 8

A: Given: px=x2+2x2+4x+8 We know that zeros of quadratic equationax2+bx+c=0 is given by x=-b±b2-4ac2a…

Q: (b) Find the nested form Q(x) of the polynomial /(x) = x³ + 2x2-5x + 3 and hence evaluate Q(2.6)…

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Q: f(x)=(-6x-6)^(7)(-14x-14)^(4) Identify the Zeros and Their Multiplicities

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Q: find the zeros and multiplicities of the polynomial f(x)=x^3-x^2-x+1

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Q: 8) A soft-drink vendor at a popular beach analyzes his sale records and finds that if he sells x…

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Q: If x^3=3x^2, then what is x using the Zero-Product rule?

A: Given that x3 = 3x2.

Q: Find the value of k such that the remainder when f(x) = 2x3 + kx2− 3kx + 2 is divided by x − 3 is…

A: Find the value of k such that the remainder when f(x) = 2x3 + kx2− 3kx + 2 is dividedby x − 3 is 5.

Q: 4. How should the polynomial function f(x) = -x + 2x³ + 3x5 – 6 be written in standard form? A. f(x)…

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Q: Find all zeros of the polynomial. P(x) = x3 -x - 6

A: Given P(x)=x3-x-6 Let x=2, P(2)=23-2-6        =8-8        =0 Hence 2  is a zero of P(x). So, x-2 is…

Q: Find all zeros of the polynomial. P(x) = x3 - 7x2 + 17x - 15

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Q: Using the nodes (xo=2, x;=2.5 and x; =4), to find the second interpolation polynomial for f(x) =

A: According to the given information, it is required to find the second interpolation polynomial for…

Q: Find the value of c so that x+2 is a factor of the polynomial p(x). p(x)=4x3+cx2+x+2

A: Here we find the value of c so that x+2 is a factor of the polynomial p(x)where p(x)=4x3+cx2+x+2

Q: Find the critical points, A and B, of the following polynomial (with A < B). f(x) = 2x³ + 3x² 336х —…

A: Given polynomial function

Q: Find a zero of f(x)=9x3 - 10x +1 by finding a fixed point of x=g(x)=0.9x³+0.1. %D

A: see  below the calculation and answer

Q: If 1 is  a zero of the polynomial  p(x) = ax2 - 3 (a - 1 )x - 1 , then Find the value of a

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Q: Find algebraically the zeros for .3 p(x) = x³ + x² – 4x – 4 %3D -

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Q: Use the Factor Theorem to show that the statement in the exercise is true.

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Q: Find all zeros of the polynomial. P(x) = x3 - 2x2 + 2x - 1

A: Given: P(x)=x3-2x2+2x-1

Q: The polynomial function q(x) = 3x + 11x2 - 14x- 40 has a known factor of (3x+5). Rewrite g(x) as the…

A: Given, polynomial function qx=3x3+11x2−14x−40 and known factor 3x+5 To write: qx as the product of…

Q: Consider the polynomial function P(x) = x* – 3x³ + ax² – 6x + 14, where a is an unknown real number.…

A: Given, Px = x4-3x3+ax2-6x+14    a is an unknown real number . x-2 is a factor of the polynomial. We…

Q: Find the critical points, A and B, of the following polynomial (with A<B) f(x) = 6x3 - 45x2 - 432x…

A: A = -3.04 B = 8.04

Q: Consider the polynomial p (x) = 2 (x + 1) (x – 3)² (A) As х — —о y →? (B) As y →? (C) Find the zeros…

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Q: f(x) = x° – 32x2 + 256x Determine the zero(s), if they exist.

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