9. The polynomial 12 + kv -6 has 2x I as one of its factors. Determine the value of k.

Q: 6. Find the value of k if (x + 2) is a factor of x + 4x2 + x + k

A:

Q: How many inflection points can a: (a) quadratic polynomial have? (b) cubic polynomial have? (c)…

A: fx be a qudratic polynomial .⇒f''x=constant xtherefore a quadratic polynomial never has any…

Q: 3. If p = 4x3 + x² + 2x + 5 and %3D q = 6x3 + 3x² + x + 2 Find the product in p and q, ||p|| and…

A:

Q: For what value of a will five of the six real roots of 6xº + 7x3 – 43.r – 153 + 4922 + ax polynomial…

A: suppose

Q: When dividing x^3+2x+4 by 3x+2 in Z11[x], the remainder is

A: 1)  The statement is true  Now to see  ho the given polynomial is irreducible or not

Q: For which n E N is the polynomial f(x) = x^(2n) + x^n + 1 divisible by g(x) = x^2 + x + 1?​

A: To find the value of n ∈ ℕ for which the polynomial f(x) = x2n + xn + 1 is divisible by g(x) = x2 +…

Q: 29. Select the quadratic polynomial with roots -1 and 4. 22 + 3x – 4 O a3 – 2a? – 7æ – 4 O 4x2 + 8x…

A: It is given that the equation is in quadratic And the two roots of the equations are -1 , 4    This…

Q: ,37 19 Polynomial P(x)=6x200+7x-2x19+10 is divided by (x+1). Find the remainder. |

A: P(x)=6x200+7x37-2x19+10 Divisor =x-1

Q: The interpolating polynomial p(x) of degree 2 of f(x) = 6xª – 2x³ + x² + 9 is p(x) = x² + 9. %3D…

A:

Q: When dividing x^3+2x+4 by 3x+2 in Z5[x], the remainder is None of the choices 2

A:

Q: When p (x)=2x+kx +1 is divided by x+1, the remainder is the same as when q (x)=3x4+ kx² +2 is…

A: After calculating the division of two function, we will equate the remainder values to Find k valye

Q: 2. Prove: If ax? + bx + c factors nicely (i.e. the roots are fractions without square roots…

A:

Q: 9. When the polynomial mx' – 3x² + nx +4 is divided by x - 3, the remainder is 16. When it is…

A:

Q: 5. For how many different integers bis the polynomial x² + bx + 16 factorable over the integers?

A: From the given data

Q: The remainder upon the division of x 98 + 4 by x - 2 in z, is: 1 6. None

A:

Q: Upon factoring L(x)=(x^4)−16 as far as possible, which one is true?   A. L(x) has three linear…

A: Question is solved.

Q: When dividing x^3+2x+4 by 3x+2 in Z11[x], the remainder is O 5 4 O 2 None of the choices о

A:

Q: 1. Is x³ - 2√5x + x a polynomial? If not, state a reason. 2. Is -2020x a polynomial? If not,…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: What is the largest number k for which 2x+3y=20 and 3x+4y=k have the same number if positive integer…

A: Given that, there are two equations following, 2x + 3y = 20…

Q: 6. Determine the constant term of the polynomial with integer coefficients of lowest degree with…

A:

Q: Find the term of (a-2b)^13 that has b^3 in it.

A:

Q: For the remainder of the division of x-2x²+3kx+18 by x-6 to be equal to zero, k must be equal to?

A:

Q: 32. If p(x) is a polynomial in Z,[x] with no multiple zeros, show that p(x) divides xP" . x for some…

A: Let F be a field, and suppose p(x) ∈ F[x]. hp(x)i is the set of all multiples (by polynomials) of…

Q: 9. Find the quotient and the remainder of x³ + 2x² – 1 divided by 3x2 +1 in Z7[x].

A: Note that for Z_7  Any number is equal to the remainder when it is divided by 7.

Q: 1. It is known that the polynomial p(x) = 2 – (x + 1) + x(x + 1) – 2æ(x + 1)(x – 1) interpolates the…

A: Solution by using Newton's forward difference interpolation method .

Q: When dividing x^3+2x+4 by 3x+2 in Z7[x], the remainder is * O 4 O None of the choices 2.

A:

Q: 3. Suppose f(x) =. ) dr=AV 5x-4 +C, for constants. %3D If 5x-4 A and C, what is the value of A?…

A:

Q: 4. When the polynomial P(x) is divided by (x-2)2 the remainder is 3x - 3. What is the remainder when…

A:

Q: Lawrence will divide an 8th degree polynomial in x by (x – 10) using synthetic division. How many…

A:

Q: 2) Show that a3 + b³ = (a + b)(a² – ab + b²) is a polynomial identity. %3D |

A: Start with Right hand side as follows.

Q: Lawrence will divide an 10th degree polynomial in x by (x – 2) using synthetic division. How many…

A: Answer is 11. Because constant term is consider as zero degree.therefore there are 11 term in 10…

Q: The remainder upon the division of x75+ 6 by x- 3 in z, is: 1 5 6.

A: I am solving it in step 2

Q: 47. a) If (x – 2) is a factor of 2x – 3x + k, find k. - b) When ax – 4x² + 5x – 3 is divided by (x +…

A:

Q: 2) If a + bi is the remainder when P(x)=x²1 - 8x5 + x is divided by x +i, then a + b = A) -8 B) 6.…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 10.10) What is the least common denominator of (1 Point) 3 and 1 ? 3x3 6r2 9x O A.9x B. 18x O C.27x…

A:

Q: 8. (S.15). Write P20 = x2 +2x – 1 as a linear combination of the polynomials P31 = x2 – x – 2, P22 =…

A:

Q: 1(d) Show that x − 4 is a factor of x − 5x + 2x + 20x − 24

A:

Q: The remainder upon the division of x 98 + 4 by x - 4 in Z, is: None

A: We find remainder in Z_7 of function f(x)=x^98 + 4 when divide by g(x)= x - 4

Q: 2) When a polynomial, ax-3x² - bx - 5 is divided by the binomial (x-3), the remainder is 10. When…

A:

Q: The remainder upon the division of x75 + 6 by x-3 in z, is: 1.

A: concept : when f(x) is divided by x-a then  Remainder is f(a).

Q: 1 1 1 1 2 1 of finding the coefficients are equivalent

A:

Q: The remainder upon the division of x + 4 by x – 4 in Z, is: 1. None

A:

Q: What does it mean to say that c is a zero of P? Give two equivalent conditions that tell us that c…

A: If c is a zero of a polynomial P, then c is the point where the function crosses the x-axis.

Q: When dividing x^3+2x+4 by 3x+2 in Z5[x], the remainder is * O 5 O 4 O 2 O None of the choices

A: Just use long division and keep in mind that we are doing operations modulo 5.

Q: 1. What must be multiplied to (x2 + 2x + 1) to get (x + x + x2 + 3x + 2)? С. -ха- х - 2 D. x2 - x +…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 11 If P(x) 2x* + 6x3 + kx² – 45, find k for which P(-3) = 9.

A:

Q: 17. Find the solution to the interpolation problem of finding a polynomial q(x) with deg(q) < 2 and…

A:

Q: Prove that 2r +1 is not a factor of 4r +r - 1.

A: We have to prove that  2x+1 is not a factor of  4x3+x-1.

Q: A project management consultant estimated that if a particular project was completed, t years after…

A:

Q: 17. Find the solution to the interpolation problem of finding a polynomial q (x) with deg(q) < 2 and…

A: