15) Find the remainder of the polynomial 5x4 – 3x3 + 9x – 1 when divided by x + 3

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

A:

Q: 2. If the result of a polynomial division is 2x – 4x? – 5x + x+2 23 ,make at least three definitive…

A: Consider the given: If the result of the polynomial division is-2x3−4x2−5x+23x+2It means , The…

Q: Is x+2 a factor of x^5+8x^4−6x^3−3x^2−7x−146

A: To prove that x+2 is factor of given equation.

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

A:

Q: find the degree of the polynomial. 5xy3 + 2x2y2 - 3x3y2

A: The degree of a polynomial is equal to the highest degree of any individual term within the…

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

A:

Q: xpress the polynomial in factored form p(x)=x^3-x^2-8x+12

A:

Q: 2. If the result of a polynomial division is 2x³ – 4x² – 5x + 23 make at least three x + 2'…

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

Q: Show that (2x+7) is a factor 2x2+5x2-11x-14.Hence factories the given expression completly ,by using…

A:

Q: Express the polynomial x5 + 3x3 + x2 + 2x as a product of its irreducible factors in Z5[x].

A: Given: [May be the question is wrong, otherwise the given solution is correct.] The given polynomial…

Q: 1. Use long division to find each quotient. Divide the first polynomial by the second. 6x + 11x2-…

A:

Q: Test the polynomial x – 2x3 + 6x – 3 for irreducibility over Q.

A: We have to check whether the polynomial x4-2x3+6x-3 is irreducible over the set of rational numbers…

Q: Use synthetic division to find the result when 3x + 19x2 + x -21 is divided by x + 6. If there is a…

A: Polynomial is written in asked format using synthetic division.

Q: A. Determine the factors of the given polynomial. 1. х3 + 2х2 -5х-6 2. х3 + x2- х-1 3. x3- x2- 10x-8

A:

Q: 4. Find the factors of the following polynomials with complete solution using synthetic division.

A:

Q: The number of zeros of the polynomial x² + 3x +2 in Z, is: O 1 O None O 2

A:

Q: The polynomial -6x + 50x+ ax+ 24 has factors x-1 and 2x + 1. Determine the value of a.

A: Suppose px be the given polynomial such that px=-6x3+50x2+ax+24 And the factors of the polynomial…

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

A:

Q: Find the polynomial to represent (3x-7)2. O 9r2 - 21x + 49 O 9x2 + 21x + 49 9z2 – 42x + 49 9x2 + 42x…

A: We have to find the polynomial which represents the given expression: 3x-72 We know the algebraic…

Q: When a polynomial x4+x3-10x2-1 is divided by another polynomial, the quotient is x3-3x2+2x-8 and the…

A: See the details solution below

Q: 2. For what values of b will the polynomial ƒ (x) =-2x + bx² – 5x +2 have the same remainder when…

A:

Q: What is the result when 6x- 15x +4x? + 8x – 4 is divided by 3x2 – 3x – 1? If there is a remainder,…

A: Consider the equation

Q: what is the remainder in the polynomial 2x^4-5x^3+12x-7 divided by x-1

A: Perform the division:

Q: 5) If the leading term of a polynomial is -2x18, what do you know about the end behavior? As x → 0…

A: We will find the end behavior of the polynomial when Leading term is given.

Q: The number of zeros of the polynomial x² + 3x + 2 in Zg is: None O 2

A:

Q: What is the coefficient of x^7 in the polynomial (1+x+2x^2)^12

A:

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: The number of zeros of the polynomial x² + 2x + 3 in Z, is: O 2 None

A: Number of zeros in the polynomial equation is termed as the whole polynomial equation is zero for…

Q: 5. Determine whether 3x 4 is a factor for each polynomial. Show all your work! 3 a. 6x 6x³ - 26x²…

A: Solution is given below:

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

A:

Q: The number of zeros of the polynomial x² + 2x + 3 in Z, is: O None O 1 O 2 4

A:

Q: 9. Use the Factor Theorem to explain if x + 3 is a factor of x³ + 2x² – 3x + 5.

A: To use the factor theorem to explain if x+3 is a factor of x^3+2x^2-3x+5

Q: 1. Is (x – 3) a factor of the polynomial p(x) = x' – 11x + 6? Why or why not? 2. What is the…

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: find the quotient and remainder 3x^3-12x^2-9x+2 over x+3

A: Given query is to find quotient and remaineder using synthetic division.

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

A:

Q: I. Use the Factor Theorem to determine whether the given binomial of the form x - c is a factor of…

A:

Q: The problem involve the Remainder Theorem.

A: Given, P(x)=x500+6x101-x2-2x+4 We know by remainder theorem ,if a Polynomial function P(x) is…

Q: 4. Use what you have learned about the Remainder Theorem to show that X +1 is a factor of 19x42 +…

A: We will use the remainder theorem that states that the remainder is zero when we decide the function…

Q: By what polynomial must x3-4 x2y+5xy2-2y3 be divided to obtain a quotient of x-y?

A:

Q: 2. If the result of a polynomial division is 2x3 – 4x? – 5x + 23 ,make at least three x+ 2…

A: The given result of a polynomial division is 2x3-4x2-5x+23x+2. Observe the following. Quotient,…

Q: 2. Use long division to determine if (x- 8) Is a factor of P(x) = x -7x- 11. 3. What is the quotient…

A:

Q: Consider the polynomial Division (x³ + 5x2 - 7x - 4) ÷ (x – 2) The correct Answer is: • Remainder…

A: NOTE: Refresh your page if you can't see any equations. . take synthetic division using x=2

Q: We can apply Eisenstein criterion for irreducibility of the polynomial 4x10−9x3+24x−18 over Q. true…

A: Using Eisenstein Criterion for irreducibility of f(x) over Q,

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

A:

Q: In the polynomial P(x)=(x-1)4(x+3)(2x+3)3(x-6)2 the multiplicity of the zero 6 is?

A: Given:

Q: Find the remainder when the polynomial 2x* – 5x² + 12x – 7 is divided by (x – 1).

A:

Polynomials

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