6. Each of the following trinomials has a non-prime leading coefficient. Using a guess-and-check technique, write each trinomial in its factored form. Show each guess and its check. (a) 18x' – 25x+8 (b) 20.x² – 1 Lx –42

Q: Find the value of k such that x − 4 is a factor of x3 − kx2 + 2kx − 8.

A: Here we have to find the value of k,  It is given that,  x − 4 is a factor of f(x)= x3 − kx2 + 2kx −…

Q: 4n^12-32n^7+48n^2

A:

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

A:

Q: Which of the following is a perfect square trinomial? O 9x² – 12x + 4 O x2 – 12x + 4 O 9x? – 12x – 4…

A:

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: If  x3 + 7x - a has a remainder of 1 when divided by x+1 then a has a value of __?

A: Please refer the attached image for complete solution.

Q: B. Find the value of k that makes x2 + (k + 5)x + (5k + 1) a perfect square.

A:

Q: 4. If x=-4 and x=1 are the roots of x* + 3x' - 3x +3x – 4 = 0, find the other two roots of the…

A:

Q: 5. P(x) = x-x-19x2 + 49x-30 %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: 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: Which of the following is a factor of 6x² + 17x + 12? O 3x + 4 O 2x +4 O 3x + 3 O None of the above

A:

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: 4 of 4 9. Circle the letter of any trinomial with (x +3) as one of its factors. A B x2 - 11x + 24 x2…

A: Solution: The objective is to factor the given equations

Q: Suppose that the volume V of a cylindrical can is given by the polynomialV = nh3 + nh2+ 4nh, h is…

A: Given, Volume = πh3+πh2+4πh

Q: Find the value of k so that x-2 is a factor of P(x) = 2x3 – x2 + kx + 2

A:

Q: 3. If one of the factors of (x2 + 12x + 20)is (x + 10). Find the other factor

A:

Q: We begin the process of factoring a polynomial by first factoring out the assuming that there is one…

A: Consider the given statement. Let's explain it by an example. Example. 3x2+6x Now, find the factor…

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

A:

Q: What is the completely factored form of xy – xn

A: Given : xy3 - x3y

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: By what polynomial of lowest degree must (x2 – 64)(x² + 5x – 24) be multiplied to make it a perfect…

A: Givem polynomial is (x2-64)(x2+5x-24)To find lowest degree multiplier to make it perfect square.

Q: 5. Identify the Lead Coefficient (LC), Degree (D), and the name of polynomial. -2x + 4x a. LC=3,…

A: Note: As per company guidelines we are supposed to solve only one question. So, kindly repost other…

Q: 5. Given the polynomial P(x) = 3x + kx? + mx + 12 has a known factor of (x-3). When P(x) is divided…

A:

Q: 11. Express the following as a trinomial in simplest form in terms of the variable z. (z + n)" n=0…

A:

Q: 3. Determine the value of K so that x+3x +kx - 24 has x +2 as a factor.

A: Solving the problem by putting the the value of zeros in given equation.

Q: 16. Find the smallest root of x - 3x +2x2 - 3x – 1.6 = 0.

A:

Q: Is 5 a root of x* 5x' + 8x– 40? Is (x + 1) a factor of x- 1?

A:

Q: 9. Find values of the 800k of polynomial 1- 42+9x +b b. -9 and if 3-42²+9x +6. a and ane

A: Given the polynomial  x3−4x2+ax+b

Q: 11. Factor the polynomial completely. 2x (3x+6) (x + 2) 6x (x + 2) (x+3) O6x (2x+3)(x+2) 3x (x + 3)…

A:

Q: (d) Show that x^2 − 4 is a factor of x^4 − 5x^3 + 2x^2 + 20x − 24.

A:

Q: Show that If 2 is a root of  kx4 - 11x3 + kx2 + 13x + 2 Then K = 3

A: Given,          2 is a root of kx4-11x3+kx2+13x+2 then k=3.

Q: Find the specific solution. Hint: factor by grouping in pairs first. x" + 2x" - 9x'- 18x = 0,…

A:

Q: 1. Write the complete factored form of f(x). y 8. y = f(x) 4 -2 2 3 -8

A: Note  Factor form of a function is given by  f(x) =(x-a)(x-b)(x-c)....... and so on Where  a,b,c are…

Q: 2. Determine whether x + 1 is a factor of x27 + 4x20 – 3x15 – 6. -

A: We have to solve

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

A:

Q: 19. What is the largest value of the quadratic form 5(x,)? - 3(x2)² if x²x = 1. 20. What is the…

A:

Q: y4- 3y2-28

A: The given polynomial is: y4-3y2-28 To factorize the polynomial.

Q: 9. What is the possible equation of the following polynomial in factored form?

A:

Q: Given the solution below, what is the polynomial in factored form? 3 T = -, x = -5 %3D 4 Factored…

A: Solution: Polynomial in factor form is a product of its factor.

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: 22. Find the quotient and the remainder for each of the followir x3-4x2+2x+5 1) x-2 4x3-2x2-3 2)…

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: To find the possible roots of the polynomial 2x³ + x4 - 7x² - 8x + 12 divide factors of + by factors…

A:

Q: 5. Given that (x – 2) is a factor of the polynomial (x3 – kx² – 24x + 28), find k and the roots of…

A:

Q: 10.Determine if the given binomial is a factor of the polynomial, yes or no P(x) = x 3 +8x² +11x -…

A: Consider a polynomial p(x). If, At x=a, value of p(x) =0, then (x-a) is a factor of polynomial p(x).

Q: 1 (i) Show that 2x-1 is a factor of 2x³-5x2 + 10x -4.

A:

Q: 8. Find the zeros of each of the following by factoring: (a) 8x +12x = 0 (b) 2x -12x-54 =0 (c) x'+2x…

A: The factorisation method factorises an equation by splitting the middle term. The middle term is…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.