Title: Polynomial Factoring Exercises Exercise 9: - **Task:** Factor the polynomial \( 27x^2 + 36xz + 12z \) completely. Exercise 11: - **Task:** Factor \( 8x^3 + 125 \). Exercise (Additional): - **Task:** Factor the polynomial \( 30x^3 + 2 \). **Instructions:** To solve these factoring exercises, apply techniques such as identifying common factors, using special polynomial identities (like the difference of squares or sum/difference of cubes), and recognizing patterns within the polynomials. Test your solutions by expanding your factored forms to ensure they match the original polynomials.

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: Use the remainder thereom to find the remainder when x^4+2x^3+x^2-22x+12 is divided by x-2

A: To find the remainder

Q: Factor and then simply  csc^2 x-1/csc x-1

A:

Q: The area of a rectangle is given by (8x^(2)y+12xy^(3)+4xyz) sq. units. Its length and width have no…

A:

Q: Factor and then simplify  csc^3 x-csc^2 x-ccs x+1

A: Given,           csc3(x) - csc2(x) - csc(x) + 1

Q: Factor 8x^2+8x+2

A:

Q: Factor c^3 - 1/125

A: Factorization

Q: 1. Given the following polynomial, state a) the zeros (C_ R b) the multiplicity of each zero c) the…

A: Since you have posted more than one question we have solved the first question for you.  For solving…

Q: Use long divison to divide polynomial. 6x^4+3x^3-7x^2+6x-5/2x^2+x-3. According to my textbook the…

A:

Q: Is x+1 a factor of 5x^4+2x^3−2x^2+3x+1​?

A:

Q: factorize -x^3+3x^2-3x+1 by getting the common factor out every time

A: The objective of this question is to factorize the given polynomial -x^3 + 3x^2 - 3x + 1 by getting…

Q: Express as a polynomial.

A: Express as a polynomial.         9p4q3-6p2q4+5p3q23p2q2

Q: 5x^2 - x - 4 Factor completely Using ax^2 +bx+c form

A:

Q: 2 X²³² +8x²+12 Factor by grouping

A: Let P(x)=x2+8x+12

Q: rectangle with an area of (2x2-x2-30x+8) and width of (x-4)  finf the length?

A:

Q: Factor fully the polynomial 4x^4+4x^3-35x^2-36x-9

A:

Q: Factor x^11/3+3x^8/3-10^5/3 completely

A:

Q: Find the quotient for 6m^3-2m+7/2m-4 using long division. Clearly indicate your quotient with any…

A: we will find the required quotient.

Q: synthetic division to determine the quotient of (5x^4+2x^2-15x+10)/(x+2). Example of how to solve…

A: Given query is to perform synthetic division.

Q: factor 3x^3+18x^2+27x

A: We have