1. When the polynomial 6x -ar' + bx² +3x+4 is divided by x+1 the remainder is 10. When it's divided by x-2 The remainder is 106. Determine the values of a and b. Provide an algebraic solution, showing all work.

Q: If x4 −2x3 −12x2 +10x+ 3 = 0 has the roots 1 and −3,

A:

Q: How do I complete the square on thsi following polynomial: x2-6x+12-y=0 To end up with:…

A: x2-6x+12-y=0 cannot be expressed as (x-3)2+4-y=0 because (x-3)2+4-y=0 when expanded will give…

Q: Show that (x- 3) is a factor of 2.x3 - 2x2 - 17x + 15. Hence express 2x³ – 2.x² – 17x + 15 in the…

A:

Q: To divide x^3+5x^2-2x+8 by x-5 using synthetic division,the first step is to write

A: According to question we have to calculate x3+5x2-2x+8x-5 By synthetic division

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: Choose the division problem that cannot be done using synthetic division. (a) 2x – 4x? + 6x – 8 is…

A: To choose which of the given division problems cannot be done using synthetic division. Synthetic…

Q: Determine all the roots the following polynomial 24 – 2z3 + 10z² – 18z + 9 if one of the root is -j3

A:

Q: The polynomial 2x^3 + ax^2 - 10x + b has a factor of ( x-1 ) and has a remainder of 15 when divided…

A:

Q: Suppose you were asked to solve the following two problems on a test. (a) Find the remainder when…

A:

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

A:

Q: A student is working on the rational equation + = 7, æ # –1.After multiplying both sides of this…

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

A:

Q: If the result of a polynomial division is 2x 3 − 4x 2 − 5x + 23 x + 2 , make at least three…

A:

Q: If the remainder on dividing the polynomial 2x* – kx +5x-3k+3 by (x + 2) is 4, then find the value…

A: Use the given information.

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: 7. What is the constant term of the polynomial expression: x* – 2x + x² – 5x + 6? А. 1 8. Express:…

A: Let's find.

Q: What is the equation whose roots are reciprocal of the roots of the equation of 2x2 + 5x + 2 = 0?

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: for (x)=15x^4+10x^3-6x^2+14 show that (3) is equal to the remainder when you divide(x) by (x-3)

A:

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: A polynomial P ( x ) with real coefficients has 5 + 9 i as a zero. What other number must be a zero…

A: Comples zeroes of polynomial always come with conjugate pair. For example if a + b i is zero then a-…

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: 11. If f(x) = -3x2 - 4x + 1, use synthetic division to evaluate f(4)

A: You have asked multiple unrelated questions in the same post. I have addressed the first one. Please…

Q: 4. Match the rational expression on the left with the extraneous solution(s) on the right. 8x2+2x-16…

A:

Q: For what value of a will five of the six real roots of 6x6 + 7x5 _ 43z4 - 153 + 49z2 + ax polynomial…

A: For what value of a will five of the six roots of polynomial P(x) be shared by the polynomial Q(x)

Q: Suppose a polynomial of degree 4 with rational coefficients has the given numbers as zeros. Find the…

A: Surd zeros are always in pairs. That is a+b is zero then a-b is also a zero of the polynomial.…

Q: The remainder upon the division of x98 +4 by x - 2 in z, is:

A: We have to use remainder theorem.

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: 10) If x = 1 is a zero, what are the other zeros for x3 - 3x2 + x + 1 = 0 ?

A:

Q: If the result of a polynomial division is  2x^3-4x^2-5x+23/X+2 make at least three definitive…

A: Given result of the polynomial is- 2x3-4x2-5x+23x+2 Here, Quotient = 2x3-4x2-5x Remainder = 23…

Q: The polynomial p(x) has the rest (x+2) when dividing it by (x^2+2x-3) and the rest 1 when dividing…

A: We have given that  p(x) leaves the remainder (x+2) when divided by x2+2x-3 and  p(x) leaves the…

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: 19. The polynomial f(x) = (x – 2)3 = (x – 2)(x – 2)(x – 2) has æ = 2 as a zero four times. True…

A:

Q: While reducing the fraction 200..0z 300...0y (x, y + 0) in which between 2 and a and between 3 and y…

A:

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: When px3 3 32x 2 − 10x + r is divided by (x x 2), the remainder is exactly the same as when it is…

A:

Q: Mr. Bean has a 5th degree polynomial using only the variable x. Mr. Kelly has a different 5th degree…

A: Mr. Bean has a 5th-degree polynomial using only the variable x. Mr. Kelly has a different 5th-degree…

Q: 8) If x = 2 is a zero, what are the other zeros for x3 – x2 - x- 2 = 0 ?

A:

Q: If x = -1 is a root of the polynomial 0 = æ³ + 2x2 – 5z – 6. what are the other roots? Ox =-3, x = 2…

A: see next step

Q: 3. If x=-2 is one of the roots of 6x'+11x - 4x -4 = 0, find the other two roots of the polynomial…

A:

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: 1. Create two different rational polynomial expressions with the following constraints: • one…

A: An expression is undefined when x=4 is given by  px=1xx2-16 An expression is undefined when x=-2 or…

Q: A polynomial f(x) = x³ + ax² – 3x + b when divided by 91 (x) = x – 2 gives a remainder of 6 and f(x)…

A: Given:             fx=x3+ax2-3x+b using remainder theorem: fx=x3+ax2-3x+b is divisible by g1x=x-2…

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

A: The result of the polynomial division is, 2x3-4x2-5x+23x+2 Let, f(x)=2x3-4x2-5x+23x+2…

Q: I am asking this question again, because the last response I was given just gave that the the other…

A: To invert the given polynomial in the polynomial ring over Z8.

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.