Use all available methods to factor each of the following polynomials completely, and then sketch the graph of each one. See Example 1. 9. f(x)= x° +4x +x' - 10x² – 4x+8 10. p(x)= 2x' -x² - 8x-5 %3D %3D 11. s(x) = -x* +2x° +8x² – 10x – 15 12. f(x)=-x' +6x² – 12x +8 13. H(x)= x* - x' - 5x² +3x+6 14. h(x)=x -11x* +46x³ – 90x² +81x– 27 %3D 15. f(x)= 2x³ +11x² + 20x+ 12 16. g(x)= x* + 3x° – 5x² -21x-14 %3D Use all available methods to solve each polynomial equation. Use the Linear Factors Theorem to make sure you find the appropriate number of solutions, counting multiplicity. 17. x +4x* +x³ = 10x² +4x-8 18. x* +15 = 2x³ +8x² – 10x %3D %3D 19. x* +x +3x² +5x-10 = 0 20. x -9x2 = 30– 28x %3D %3D 21. x +x* - x³ +7x² - 20x+12 = 0 22. 2x* - 5x3 – 2x² +15x = 0 %3D 23. x +15x +16 = x* + 15x²+16x 24. x - 5 = 5x² - 9x %3D Use all available methods (in particular, the Conjugate Roots Theorem, if applicable) to factor each of the following polynomials completely, making use of the given zero if one is given. See Example 2. 25. f(x)= x*-9x +27x2 -15x-52; 3-2i is a zero. |3D 26. g(x)= x² -(1-i)x² -(8-i)x+(12-6i); 2-i is a zero. %3D%X= 27. f(x)= x' -(2+3i)x² -(1-3i)x+(2+6i); 2 is a zero. 28. p(x)= x* - 2x+14x²-8x+40; 2i is a zero. %3D 29. n(x)= x*-4x +6x² +28x-91; 2+3i is a zero. %3D 30. G(x)= x*-14x +98x² - 686x+240o1; 7i is a zero. 31. f(x)= x* - 3x +5x-x-10 25r4 40r3 402 33r+16

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: Find the nth Maclaurin polynomial for the function. 4x - 1 f(x) n = 4 x + 1 P4(x) = %3D

A:

Q: Graph one of the following polynomials, showing the end behaviors, x-intercepts, behavior at…

A: fx=x3+4x2-3x-18 The graph is,

Q: Vhích polynomial would produce the following grap 5 4 3 2 -5 -4 -3 5 -2 -3 -4 -5 y= - x( x - 1)( x -…

A: Given the figure,

Q: If a third degree polynomial has a lone x-intercept at x a , discuss what this implies about the…

A:

Q: Consider the following polynomial function. f(x) = 2x³ – 7x² + 4x + • | Step 1 of 4: Factor the…

A: We can factorise it s below

Q: What is the degree and lead coefficient of the following polynomial? f(z) =−+52 = −x + 5x² − 6x³ +…

A: We have fx=-x+5x2-6x3+10 This can be written as: fx=-6x3+5x2-x+10 The degree is the highest power…

Q: 4) For the function 16 u y=-0.0519x+1.0777x-7.4569x+ 20.247x - 12.333 R=0.6113 12 10 4. time 10…

A:

Q: Consider the following polynomial. q(x) = 7x² – 8x Step 2 of 2: Describe the behavior of the graph…

A:

Q: Find the nth Maclaurin polynomial for the function. 2x - 5 f(x) n = 4 %D x + 1

A:

Q: 10) Find the cost of evaluating p2(x), for a specific x, where p2(x) is the Lagrange interpolating…

A: The cost of p2 (x) for a specific value of x will be given by following formula-

Q: Consider the Lagrange polynomial that passes through the 3 data points given by -1 3 |f(x) | -3 9 17…

A: the given table is ;       X      f(x) -1 -3 2 9 3 17 the value of the table for x and y…

Q: 4) For the function 16 4 y=-0.0519x+1.0777x-7.4569x +20.247x- 12.333 P=0.6113 12 10 4. 2. 4. time 10…

A:

Q: Suppose T4(x) = 2 – 4(x – 2) + 5(x – 2)² - 8(x – 2)3 + 5(x – 2)4 is the degree 4 Taylor polynomial…

A: We use Taylor's formula

Q: Which of the following is a factor of the polynomial function P (x) = x – x4 – 50x3 – 49x2 + 36?…

A: We need to find factor of given polynomial.

Q: 1. Identify which of the following are polynomial functions and, for those that are, specify the…

A:

Q: Consider the following polynomial. h(x) —D 7x3 — 9х2 — х — 15 Step 2 of 2: Describe the behavior of…

A: Given polynomial is- h(x)=7x3-9x2-x-15 To describe the behavior of the graph of h(x) as x→±∞

Q: Find Ao, A1, and A2 in rewriting the function of f(x)={* x20 in terms of Lagure polynomial, 00 S(x)…

A:

Q: Find the cubic polynomial which takes the following values : x: 1 3. f (x): 1 1 10 Hence or…

A:

Q: Suppose that P2(x) = a + bx + ca? is the second degree Taylor polynomial for the function f about æ…

A: Given : P2(x) = a + bx + cx2 is the second degree Taylor Polynomial for the function f about x = 0.…

Q: Q4) Fit a second order polynomial to the following data i 1 2 3 4 5 6. X 0.4 0.8 1.2 1.6 y 00.25 1…

A: In the given question we have to define a second order polynomial to a givendata  i 1 2 3 4 5 6…

Q: 1. Find the polynomial of degree three for the following data. Also find P(-2). X0 1 4 6 -1 1|-1 y 1

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Answer the questions about the following polynomial. 1+ 5x?

A: The given polynomial is 1+5x2 Standard form of the polynomial : 5x2+1

Q: This piecewise polynomial is NOT a cubic spline: if 0sx<1 if 1sx<2 %3D S(x) = So(x) = 6 S, (x) = 6+…

A:

Q: Find the Taylor polynomial p1 (x) for f(x) = 8x2 at x = 5. %3D Provide your answer below: P,(x) = O

A: To find the taylor polynomial p1(x) .

Q: The following table presents the temperature in different minutes that were taken from'a cup of…

A:

Q: Find the nth Maclaurin polynomial for the function. 4x - 5 f(x) = n = 4 x + 1 P4(x) =

A: A Maclaurin polynomial of nth order  for the function f(x) is               f(x) = ∑n=0∞fn(0)n!xn,…

Q: Find the zero/s of the given polynomial function f(x) = x* + x³ – 29x2 – 9x + 180

A: The factors of a quadratic form of equation ax2+bx+c can be calculated using integer factorization .…

Q: Find the second-degree Taylor polynomial for f(x) = 4x² – 8x + 8 about æ = 0. %3D P2(x) = What do…

A:

Q: Evaluate the following polynomial functions given its certain conditions. P(x) = 6x3 - 2x² + 11x-6,…

A: Given: Px=6x3-2x2+11x-6 To Find:  To determine the value of P2.

Q: 1. Fill in the table below with information about each of the following polynomials. Polynomial…

A: We have to find the degree and the end behaviour of the polynomial.

Q: find the nth Maclaurian polynomial for the function f(x)=(5x-3)/(x+1), n=4

A:

Q: Produce the quadratic polynomial interpolating the data {(-2, –15), (–1, –8), (0, –3)}. Find the…

A: We will find out the required equation of quadratic polynomial.

Q: (1) As x→ t0, the end behavior of the polynomial p(x) = 3x°(1 – 2x + x°) can be resembled as (A)…

A:

Q: Question 6 Determine the Charactaristic polynomial of x?y" + x?y" - 2xy' + 2y 0 OA None of the…

A:

Q: Q4) Fit a second order polynomial to the following data i 1 2 3 4 5 0.4 0.8 1.2 1.6 2 Ly 0 0.25 1…

A:

Q: Find the nth Maclaurin polynomial for the function. 3x - 1 F(x) = n = 4 x + 1

A:

Q: Given that the interpolation error is E, (x – x1)(x – x2) ...· (x – xn). (n+1)! Why is the error…

A: We have the interpolation error is En=fn+1ξ(n+1)!x-x1x-x2...x-xn Now, the roots of the Chebyshev…

Q: Find a polynomialf (x) of degree 3 that has the following zeros. 6 (multiplicity 2), –1 Leave your…

A: Given; 6(multiplicity 2),-1.

Q: #7: For what value of k will the polynomial function f(x)=x'+6x² +kx=4 have the same remainder when…

A: The Polynomial Remainder theorem states that if x-b divides the polynomial, Qx, then the remainder…

Q: 2. Which polynomial function would have the end behaviour of as, x → Ax) = 7x - 8x* - 2x +x + 3x - 2…

A: topic - polynomials The end behavior of a polynomial function is the behavior of the graph of…

Q: Find a polynomial with integer coefficients that satisfies the given conditions. P has degree 3 and…

A:

Q: Find the fifth Taylor polynomial of x3 - 7x2 + 8 at x = 0.

A: Given: fx=x3-7x2+8

Q: Consider the polynomial g(x) (x - 1)(2x + 1)(3z –1)(5x + 1). A. What are the roots of g? B. Suppose…

A:

Q: Suppose that P2(æ) = a + bx + ca² is the second degree Taylor polynomial for the function f about æ…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Find the nth Maclaurin polynomial for the function. 5x - 4 f(x): n = 4 x +1 P4(x) =

A:

Q: Q4) Fit a second order polynomial to the following data 1 2 3 4 5 X 0.4 0.8 1.2 1.6 Ly 0 0.25 1 2.25…

A: Equation of 2nd degree polynomial

Q: Consider the following polynomial. h(x) = -4x²(x + 8)(x + 2) %3D Step 2 of 2: Describe the behavior…

A: We will determine the behaviour of the graph of h(x) as x approaches + infinity as following.

Q: Find the nth Maclaurin polynomial for the function. 4x - 5 f(x) n = 4 x + 1 P4(x) = =

A: The function is  f(x)=4x-5x+1

Q: Fit a second order polynomial to the following data i 1 2 0 0.4 0.8 0 0.25 1 5 6 1.6 2 4 6.25 3 4 X…

A: Let a second degree polynomial that needed to be fitted to the given data be a0+a1x+a2x2=y-----(1)…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.