6.Do the polynomials P1 = 1 – x + 2x², p2 = 3 + x, p3 = 5 – x + 4x², p4 = -2 – 2x + 2x² span P2 ? %3D

Q: Show that xଶ − 4 is a factor of x4− 5x3 + 2x2 + 20x − 24.

A: Let f(x) and g(x) be two functions  then g(x) will be the factor of f(x) if remainder(f(x) / g(x))…

Q: Show that x2 − 4 is a factor of x4 − 5x3 + 2x2 + 20x − 24.

A:

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: What is the value of f(2) for the polynomial x ^ 3 + 3x ^ 2 - x + 1 ? What does this mean about the…

A: Here, fx=x3+3x2-x+1

Q: Show that x² − 4 is a factor of x4 − 5x³+ 2x² + 20x − 24

A:

Q: Use the elimination method to find all soluti { % 4x - Зу 3-24 -7x + 6y = { By = 45

A: Given,             The system of equations are                4x-3y=-24                -7x+6y=45

Q: Show that x2 + 3x + 2 has four zeros in Z6.

A:

Q: Do the polynomials x? + 2,2x2 – x + 1,x + 2, and x² + x + 4 span P2?

A: Let u1 = x2+2, u2 = 2x2-x+1, u3 = x+2, and u4 = x2+x+4. Notice that u1 + u3 = u4. So, u1, u2, u3,…

Q: Find the sum of the polynomials -3x +7x - 8 and 5x -7x+2.

A: As per the company guidelines given to us  I am allowed to  solve first question. I hope that the…

Q: 3. Divide x+4x-3x-2 by X-2) then divide if CX-2) isa factor of x² t4x-3y-2 why?

A: We have to divide (x3 + 4x2 - 3x - 2) by (x - 2)  Then ,

Q: Show that (x-y) is a factor of (x2-7x2+14x-8) ,ccplete factors od expression

A:

Q: The number of polynomials having zeroes as -2 and 5 is

A:

Q: 10. Determine whether the first polynomial in P3(R) can be expressed as a linear combination of the…

A:

Q: Find the polynomials connecting the points (0,1), (1,3), and (2,13) ​​by quadratic interpolation.

A:

Q: Find the total ancd neguon between x-axis and the gruph of y==X2 - 3X, -7sx52

A:

Q: Express as a polynomial.

A: We know the identity that, a-ba+b=a2-b2                  ⋯⋯1a-b2=a2+b2-2ab       ⋯⋯2 We have the…

Q: verify that 6A = 3(2A)

A: Here given  Thus

Q: 18. Express the polynomial 6x -x +2x-4 in standard form. 6x'-2x-4 7 +2x-4 -4+2x-5x 5x +2x-4

A: standard form is the form in which polynomial is written decreasing power of x and all different…

Q: 3. Write down the polynomial having coordinates in B and the one with the same coordinates in B'.

A:

Q: Do the polynomials x³ + 2x – 4, x³ + x² – 3x + 1, and æ³ + 5 generate P3(R)? Explain. - -

A: Here generate means span.  The span of a set of vectors is the set of all linear combinations of the…

Q: determine the degree of the given polynomials. 5x3y2 - 6x3y3

A: The given polynomial is 5x3y2-6x3y3. Recall, "The degree of a polynomial is the degree of its terms…

Q: 23 – 522 – 9z + 45

A: Given: z3-5z2-9z+45

Q: Find the sum of the polynomials -3x +7x-8 and 5x-7x+2. Subtract -x +5x-3 from 6x2-3x-7. Express the…

A: We can find the answers as below

Q: Show that x2 − 4  is a factor of  x4− 5x3+ 2x2 + 20x − 24.

A:

Q: Show that x2 + 3x + 2 has four zeros in Z6

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: What is the coefficient of the term containing x^2*y^3 in the expansion of (2x-3y)^5?

A: In order to find the coefficient use binomial theorem, which is given below.

Q: What is the sum of the polynomials? (8x² - 9y² -4x] + (x²_3y² - 7x) 2-3y2-7x 8x -9y2 -4x +

A:

Q: Express as a polynomial. (2u +3)(u - 4) ( 4u+u ) 2

A: Given: y=22u+3u-44u+u For expressing given expression as a polynomial, we simplify given expression…

Q: 1. Find the sum of the polynomials: (5x°-2x+x)+(4x° – 3xª +2x³-5x) O x5 +3x4-4x3+6x O 9x5+3x4-4x³+6x…

A:

Q: Find the sum of the polynomials: 8x3 - 2x2 + 6x - 2 and 3x4 - 2x3 + x2 + x

A: To find the sum of polynomials: 8x3-2x2+6x-2 and 3x4-2x3+x2+x Solution: (8x3-2x2+6x-2 )+…

Q: Consider 2a – 3y² = 8

A: Differentiate wrt x

Q: Express as a polynomial. (5x + 7y)(3x - 2y)

A: Given that, the polynomial   (5x + 7y)(3x - 2y)   We need to  simplify the given polynomial.

Q: Show that x2− 4 is a factor of x4 − 5x3 + 2x2 + 20x − 24.

A:

Q: Express as a polynomial. (3u - 1)(u + 2) + 7u(u + 1)

A: Given expression: 3u-1u+2+7uu+1

Q: Which polynomial would have the following end behavior? x+ -00, f(x) - -00 x+ 0o, f(x) → -00 A y =…

A:

Q: Write x3 + 3x² + 3x + 4 in Zs[x] as a product of irreducible polynomials.

A:

Q: If f1x2 = 2x3 + Ax2 + 4x - 5 and f122 = 5, what is thevalue of A?

A: The given function is: f(x)=2x3+Ax2+4x-5

Q: 5lim V3+x-J3 8→0

A:

Q: how many polynomials are in this equation x^5-2x+x^9-9x^6

A: This is single polynomial of degree 9

Q: What is the sum of the polynomials 1 - 2x + 3x^2 and 8x^2 + 30x - 6

A: sum of the polynomials 1 - 2x + 3x^2 and 8x^2 + 30x - 6 = 1 - 2x + 3x^2 + 8x^2 + 30x - 6

Q: what is the multiplicity of -1 in x^4-2x^3-3x^2+4x+4

A:

Q: verify that 5A = 3A + 2A

A: Given that A=341127. Compute 3A+2A as follows.

Q: 2. Find the difference of the polynomials: (5x°-2x'+x)-(4x°- 3x+2x³-5x) O 9x° +3x-4x O…

A: Given,  ( 5x5 - 2x3 + x ) - (4x5 - 3x4 + 2x3 - 5x )

Q: x2 - 4 is a factor of x4 - 5x3 + 2x2 + 20x - 24

A:

Q: Do the polynomials x² + 2, 2x² – x + 1,x + 2, and x² + x + 4 span P2?

A: Solve the problem as shown below see if they are linear combination of each other and then verify,

Q: Show that x2 − 4 is a factor of x4− 5x3 + 2x2 + 20x − 24

A:

Q: subtract the polynomials using the horizontal format. -4a - 5 from 6a + 2

A: The given polynomials are: ( -4a - 5) and (6a + 2) We have to subtract the polynomial ( -4a - 5)…

Q: 1. Show that x + 4 is a factor of x* – x3 + 3x² – 3x + 356. -

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.