3. Write the polynomial f(x) = x − 11x³ + 40x² − 55x + 25 in the form f(x) = (x−a)Q(x) + f(a) for some polynomial Q(x) for the following values of a. (a) a=0 (b) a=1 (c) a=2 (d) a=3

Q: If f is a polynomial function, and x − 6 is a factor of f ( x ), what is the value of f ( 6 ) ?

A: Answer is 0 Explanation is given below..

Q: 1.Simplify: -2xy[6x² + {-6x³y – 2x²y – 2[2xy – x(3x²y– 3x – 2y) - 3x²] + 2x(xy)}– 3x²] a.

A: Topic:- Algebra

Q: Consider two polynomials P (x)=4x-5 and Q(x)=3x2+7x-2 (a.) P(x) times Q(x)= (b.) P(-5)+Q(-3)=…

A:

Q: What are all the zeros of the polynomial function f(x) = 3x³ – 5.x² - 10x – 62 A x=±3 only B x = 3,…

A:

Q: Given f(x) = (x−2)^3(−x+ 1)^7(2x+ 6)^2(x+ 4) determine the following: (a) What is the leading (or…

A: The given function is- f(x) = (x−2)3(−x+ 1)7(2x+ 6)2(x+ 4) (a) The leading term of the polynomial is…

Q: 2. Write the polynomial f(x) = 5x-4 in the form f(x) = (x−2)Q(x) + f(2) for some polynomial Q(x).

A:

Q: find the real polynomial f(x) which has zeros x=1 (multiplicity 2) and x=2+i (multiplicity 1). you…

A: We have given the zeros x = 1 with multiplicity 2 and x = 2+i with multiplicity 1.

Q: Which of the following equations is a polynomial in standard form? O f(x) = 4x - r +3VT %3D O f (r)…

A: Yes, you are correct.

Q: Forp(x)=a0+a1x+a2x2 andq(x)=b0+b1x+b2x2 fromP2,define ⟨p,q⟩=a0b0 +a1b1 +a2b2. Find the distance and…

A: Given for px=a0+a1x+a2x2 and qx=b0+b1x+b2x2 in ℙ2, define  p,q=a0b0+a1b1+a2b2

Q: (4r2 – 6x + 3) + (2x² + x – 8)

A: Let us consider an expression, (ax²+bx+c)+(-dx²-ex+f) = (a-d)x²+(b-e)x+(c+f)  This is the required…

Q: Which of the following polynomial functions has a graph that crosses the x- axis at (-4,0)? A. f(x)…

A: Let's find.

Q: 1. Sketch the polynomial /(x) = (2-x)²(x+1)(x-4)³

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Graph the polynomial function f(x)--(x + 1)(x - 1) (x - 3)²

A: Given: polynomial function f(x)=-(x+1)(x-1)2(x-3)2. To be find: graph the polynomial function.…

Q: Write ((x−1)/(x+3))−3x+2 on common fractional line. Answer in the form p(x)/q(x) , where p(x) and…

A: Step 1: Given, (x+3)(x−1)​−3x+2, the common fractional line means combining the terms into a single…

Q: Which of the following expressions are polynomials? (a) 2x- x + V3 (b) x? -- 3Vx 1 (c) x + 4x + 7…

A: Which of the following expressions are polynomials? a) 2x3-12x+3The powers of the variables are 3, 1…

Q: 1) Determine whether the following functions are polynomial functions. If they are, state the…

A:

Q: Solve the polynomials 3y-{[-4(x-y)+(2x - y)]-3x -[(5y-3(x-2y)]-2(-6x + y)}

A: Given polynomial,  3y-{[-4(x-y)+(2x - y)]-3x -[(5y-3(x-2y)]-2(-6x + y)}

Q: Determine whether the following polynomials are even, odd, or neither. (A) f (x) = 5a – 2a- 4x + 1…

A:

Q: - Express P(x) = xª +.2x³ + 2x² - x - 3 in terms of Legendre's polynomials

A: In this problem, we use Rodrigue's formula to express Legendre's polynomials.