iii. Find all three)factors of the following polynomial expression: ... 3 2 x - 5x- 2x + 24 X - 3

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 polynomials have a zero of 2? Choose ALL that are correct. O k(z) = (z² – 2) (z + 1) %3D O…

A: Polynomials are given, we have to find a polynomial that has zero of 2.

Q: 6. Use the factor theorem to determine if r – 1 is a factor of f(r) = 2x* + 3x2 – 5x + 7.

A: Given- fx=2x4+3x2-5x+7 To determine- x-1 is a factor of function fx or not. Concept used- In factor…

Q: 4. In each part, determine whether the polynomial is a linear combination of P, = 2+x+x², P, = 1-x²,…

A: We have to determine whether the polynomial is a linear combination of given polynomials.

Q: Select ALL the factors of the following polynomial: 2.x – 3r – 12? + 7x +6

A:

Q: The polynomial p(x) = -2x°+ 3x +4 is given. Which conclusion is valid if p(1)

A:

Q: 3. P(x) = x + x'-14x- 24

A:

Q: Which of the following factors produce the following polynomial expression: x+ 5x +4x-47 I. (x + 2)…

A:

Q: Find m so that x + 5 is a factor of - 3x - 10x + 20x - 22x + m.

A: Given: x+5 is a factor of   -3x4-10x3+20x2-22x+m. To find: The value of m.

Q: a. Given the set {-3x3 + 2x2 + x – 2, –3 z3 + 2x² + x – 2,2 a3 – 2 22 + 1, x³ + 3x² – 3x + 2} write…

A:

Q: Q4: Determine whether each of the following is polynomial or not and if it is a polynomial write the…

A: Option (B) and (C) are polynomial Where as option (A) is not a polynomial

Q: 3) Show that (a + b +c)² = a² + b² + c² + 2ab + 2ac + 2bc is a polynomial identity.

A: To show: a+b+c2=a2+b2+c2+2ab+2ac+2bc

Q: Consider polynomial P(x) = x³ +x² – 10x – 10. 1. Is x+1 one of the factors of P? Explain.

A:

Q: The number of zeros of the polynomial x? + 4x +1 in z, is: 4 None 1

A: solution of the given problem is below...

Q: 10. Use the appropriate method to solve the following polynomials. a. y = x* + 35x² – 36 - b. y =…

A:

Q: Consider polynomial P(x) = x³ + x² – 10x – 10. 1. Is x + 1 one of the factors of P? Explain.

A:

Q: 1. The number of courses that Felix takes in this cycle is numerically equal to the number of prime…

A:

Q: 3. P(x) = x + x? - 14x- 24

A:

Q: Consider the polynomial p(x) = 45x³ + 69x? – 24 – 48 What are the zeros of 3p (x + 1)? O-, -2, - ,…

A: Given the polynomial,

Q: Let q represent the degree of the following polynomial 5xym -43y'z'+21. Find the value of q- 2. 19…

A: If a polynomial contains more than one variables then we must add the powers of each variables of…

Q: the factorization for the following polynomial 2x2 - 2x - 24 = 2(x ____) (x______)

A:

Q: 28. Give the formula, in factored form, of the polynomial p(x) whose graph is shown below (2,0) Нх…

A: Given graph of P(x),From the graph, we can say that it is a cubic polynomial.

Q: The following polynomial has factors (x + 8) and (3x + 2). Determine the value of k. -6x³-55x² + kx…

A: We have a polynomial -6x3-55x2+kx-16 Now, x+8and 3x+2 are the factors. So,  x+8=0 ⇒x=-83x+2=0 ⇒x=-23…

Q: Which of the following polynomial expressions factors to x'(4x - 7)(4x + 7)? O 16x6 – 49x O 16x° +…

A:

Q: Find the zeroes of the given polynomials  p(x)=x4-16

A: The polynomial is given as, Px:x4-16 The degree of the given polynomial is four. Therefore, it will…

Q: Determine the standard form of the following polynomial: p(x) = (2x²+1)(x²-3)

A:

Q: Ise the definition to determine whether the polynomials x3 – 4x2 + 3x, x* + 6x2 + 1la+6, x² – 2, and…

A: True

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: The polynomial p(x) = - 2x ^ 3 + 3x + 4 is given. Which conclusion is valid if p(1) = 5

A: Given ,  The polynomial  p(x) = -2x3 + 3x + 4  We have to find valid conclusion if p(1) = 5

Q: Given (xi , xi2022 i ) ∀i = 0, ..., n, where x0 = −1, x1 = 0, x2 = 1, x3 = 2, ..., xn = n − 1. Write…

A: Given xi,xi2022∀i=0,1,2,...,n  Where x0=-1, x1=0, x2=1, x3=2,..., xn=n-1

Q: 29. Determine BER with the property that x+5 is a factor of the polynomial -3x- 10x + 20x2- 22x + B.

A:

Q: 32. If k is a constant, what is the value of k such that the polynomial k2x3 - 6kx +9 is divisible…

A: If the polynomial is divisible by -1 then the remainder will be 0.

Q: Select the polynomial that has exactly three zeros O - 111 O 4x + 11x O 22 - 3x? + 2x2 2 x² 2x 8 -…

A: we know that if polynomial has n degree then there are at most solutions. here in option A…

Q: The polynomial 3x^4-2x^3+x^2-k is divisible by x+1. Find k.

A: Given:- p(x)= 3x4-2x3+x2-k, given polynomial p(x) divisible by x+1 To find:- value of k

Q: 1. Determine for which polynomial(s) (x + 2) is a factor. Explain your answer. Р(x) — х4- Зх3 - 16х…

A: we have to show if (x+2) is a factor of the polynomials P(x)=x4-3x3-16x-12 and Q(x)=x3-3x2-16x-12 or…

Q: Given the polynomial P(z)=r7-935-3-222-9+18, determine whether x+3 or x-3 is one of its factors.

A: Please see the answer in step 2

Q: 21. Which of the following is a polynomial? ii. V5x + 3x d. i and i i. x3 + 2x2 + 5x + 2 ii. 5x³ +…

A: Given: (i) x-3+2x-2+5x+2 (ii) 5x3+3x2+x+2 (iii) 5x+3x To find: Which of the given expression is…

Q: 7) Using the fact that x = 1 is a zero of the polynomial P(x) = x³ - 4x² - 7x + 10, reduce P(x) to a…

A: Given polynomial is Since, x=1 is zero of P(x) , therefore (x-1) is factor of P(x) Dividing P(x) by…

Q: Q.18 If x– 1 and x + 2 are factors of x +10x + ax+b, then find the values of a and b. If x = 2 and x…

A:

Q: 15.) Use Descartes Rule of signs to determine how many positive and how many negative real zeros the…

A: Consider the given polynomial:

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: 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: 2. Find all the zeros of P(x)=x' +4x? -17x-60 if one is x = 4.

A:

Q: 9. State the leading coefficient of the polynomial. (Hint: Be sure it's in standard form first.) *…

A: 9. The polynomial is given by 36x3-8x4-32x5+9x2 To determine : The leading coefficient of the…

Q: Which polynomial is prime? O x + 3x2 + 2x + 6 O x + 3x2 - 2x-6 O 10x -4x + 3x + 6 O 10x2- 10x- 10x +…

A: Definition used -   Prime polynomial -  The polynomial that can not be factored in any way is…

Q: It can be proven that the expression (a +b) a - ab +b-) is equivalent to which of the following…

A: Given,            a + b a2 -ab + b2

Q: . (a) If a is a zero of the polynomial P, then mustbe a factor of P(x).(b) If a is a zero of…

A: let the polynomial function Px=x-ck where, c is constant and k is the power of the function. The…

Q: Find the value of c so that the polynomial p(r) is divisible by (r + 2). p(z) 4x + ca +a + 2 %3D %3=

A: According to the given information it is required to find value of c such that (x+2) divides…

Q: 1. Which of the following expressions are monomials with degree 2? i) 2x + 2x ii) 2x2 iii) x iv) 2x…

A:

Q: Which of the following expression is a non polynomial ? O 6xy° + 6 O 3x² + x +1 O 3x4 + 12xy O V6x –…

A: Polynomials are the expressions that consists of exponents, constants and variables connected by the…