use the fator theerem to determine if X+3 is a x³-8x²+ZIx+18 factor of 3. C. =

Q: 2. Decide if the following polynomials are reducible in Q[x]. (a) 2x3 – 3x + 3; (b) 4x3 — 5х + 2.

A:

Q: Which of the following is the correct complete factorization of x4 - 1?…

A: To find the complete factorization of x4-1. Solution: We know that, a2-b2=a+ba-b Factorizing the…

Q: Which of the following represents a factor of 6x² + 10x 16 - O (2x +8) O (3x -2) O (6x -8) O (3x+ 8)

A: Simply Factories the quadratic equation and match the each factor with given options.

Q: Use the Factor Theorem to show that x - c is a factor of P(x) for the given value(s) of c. P(x) = x4…

A: We have given polynomial  Px=x4+3x3-16x2-27x+63 and c=3,-3 Then,…

Q: Show that the square of any integer is of the form 3m or 3m+1 but not of form 3m+2.

A: Proof :-

Q: Find all other zeros of P(x)=x²³ - 7x² + 19x - 13, given that 3 - 27 is a zero. (If there is more…

A: NOTE: Refresh your page if you can't see any equations. . the given zero is so other zero must be

Q: Show that the roots of px2 + (p - q)x - q = 0 are real for all real values of p and q.

A:

Q: The product rule for square roots states that if a and b are nonnegative, then Vab =

A: Product rule for simplifying square root: If a and b are non negative then  ab=ab

Q: Is there a real number whose square is –1? a. Is there a real number x such that _? such that x =…

A: In general, there does not exist any such real number whose square is a negative real number. Hence,…

Q: Use the Factor Theorem to show that x - c is a factor of P(x) for the given value(s) of c. P(x) =…

A:

Q: 1. Use the Factor Theorem, find all the real roots of x- 2x-9x+18=0.

A:

Q: Find a QR-factorisation of 1 1 -1 1 | 1 1 1 1 0 -

A: The given question is solved below.

Q: Complete the following tabel by stating whether the polynomial is a monomial, binomial, or…

A: Type: A monomial has just one term. Given term is , 12x7 .Remember that a term contains both the…

Q: Find all other zeros of p(x) = x3 – 7x2 + 20x – 24, given that 2 + 2i is a zero. If there is more…

A: Here we have to find the zeroes of the given polynomial. Here one of the zeroes of polynomial is…

Q: Use the remainder theorem to find which of the following is not a factor of x – 4x² – 4x + 16. Ox+ 2…

A: To factor x3-4x2-4x+16

Q: iven P(x)= 6x^5 + 49x^4 +122x^3 +33x^2 -234x-216, find the zeros and write P in factored

A: Given Data :  function p(x)=6x5+49x4+122x3+33x2-234x-216                                   (1) To…

Q: 3. Verify x + 2 and x – 4 are factors of P(x) = 8x* – 14x³ – 71x² – 10x + 24. %3D

A: Explanation of the answer is as follows

Q: 4. Determine the sum and the product of the roots of 3x2 11x – 6. %3D

A: Sum of roots = 11/3 Product of roots = 2

Q: If a and ß are the zeros of the quadratic polynom ial f (x)= 3x² – 4x+1, find a quadratic polynom…

A:

Q: 6. Factor each polynomial using the factor theorem.1 3- 3x2. 10x + 24 d) 4x* + 7x e) x - 5x – 7x³ +…

A: We find out the factors of the given polynomials.

Q: Use the Remainder Theorem to Evaluate P(c).  P(x)=3x3 +4x2-8x+7, c=3

A: Given that,

Q: Factor the following perfect square trinor 49x2 + 14x + 1 O 7(x + 1)2 O (7x - 1) O (x + 7)? (7x +…

A:

Q: Use the Factor Theorem to prove that x - c is a factor of xn - cn for any positive integer n.

A: Divide xn-cn by x-c using long division method.

Q: Let P(x)=x³-2x²-11x+12 Show that x-c is a factor of P(x) if c=-3 of P(x) if c=-3- Use this fact to…

A:

Q: The number of zeros of the polymomial x? + 2x + 3 in Z, is: None 4 1

A: Number of roots of a polynomial

Q: Show that if p is a positive integer, then the binomialseries for f(x) = (1 + x) p is a polynomial.

A: The binomial expansion is given as 1+xn=1+nC1x+nC2x2+nC3x3+.....nCnxn

Q: Use the Factor Theorem to determine whether x+3 is a factor of P (x) = -2x* - 5x'+ 4x-9.…

A:

Q: Use the Factor Theorem to determine whether x+3 is a factor of P (x) = x° + 2x² – 2x + 3.…

A: Given factor: x + 3   Given Polynomial: P(x)=x3+2x2-2x+3

Q: the possible zeros of x³+3x²-4x-12 are the divisors of

A:

Q: Find the highest common factor of 702 and 572 and express this in the form 702v+572w where v and w…

A:

Q: Use the Factor Theorem to determine whether x-3 is a factor of P(x) =-2x+5x+5. Specifically,…

A:

Q: In the polynomial x^6 − 3x^5 − 5x^4 + 22x^3 − 39x^2 − 39x + 135, it is known that 1 + 2i and √3 are…

A:

Q: Use the Factor Theorem to determine if x+3 is a factor of: x3+8x2+21x+18

A:

Q: 1. Which of these polynomials could have (x - 2) as a factor? Select all that apply. *

A: We have to find which polynomial has a factor (x-2).

Q: Show that the polynomial p(x) = -x^3+x^2+1 has a root in [1,2]

A: We can check for the values of p(x) :

Q: Given that x = 2 is one root of g(x) = 2x* + 4x – 9x² – 11x – 6 = 0, use factorisation to determine…

A:

Q: Assume that the polynomial 7? + bx +c = 0 in which b, cE Z, has two integer solutions. Which one of…

A: We have to equation as - x2 + bx + c = 0.......(1) The above equation (1) is a quadratic equation…

Q: Use the Factor Theorem to determine whether x+2 is a factor of P (x)=x'+4x-8. Specifically, evaluate…

A: We have to determine whether (x+2) is a factor of p(x)=x3+4x2-8.

Q: Factor T623000 Compretely. Wrie,o0suwer in canonical form.

A:

Q: Which polynomials have been factored correctly? Ox+ 9x*+ 8x - 60 (x+ 5)(x- 2)(x+ 6) 3 120x'+ 164x*+…

A:

Q: Use the Factor Theorem to determine whether x-2 is a factor of P(x) = 2x-3x-4. %3D

A:

Q: Which of the following is a factor of 500x3 + 108y18?  6  5x + 3y6  25x2 + 15xy6 + 9y2  All of…

A: The solution for the above question is as shown below.

Q: 11 Which of the following is a factor of 2x3 + x2 - 2x – 1. x + 2 2 x – 1 x – 2 2 x + 1

A:

Q: Find the greatest common divisor of p(x) = x^3 + x^2 − 4x + 4 and q(x) = x^3 + 3x − 2 in Z5[x].

A:

Q: Use the given zero to write P(x) as a product of linear and irreducible quadratic factors. P(x) =x…

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: Determine the definiteness of the quadratic form q(x) = xỉ + 2V6x,X2 + 2x3

A:

Q: the following polynomial irreducible over Q? (Prove your statement)! 14x6 – 18x3 + 9x² + 6x – 60 - -

A: The polynomial is irreducible over Q by using Eisenstein's Criterion for irreducibility test.

Q: Find all other zeros of p(x) = x3 + 2x2 – 14x – 40, given that -3 + i is a zero. (If there is more…

A: The polynomial p(x)=x3+2x2-14x-40 has zero -3+i.

Q: Consider the polynomial P(x) = x³ + 3x² + 4x + 12. %3D Given is that 2i is a root of P(x) = 0. Find…

A: we can solve the problem by obtaining the conjugate root.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.