Why is a polynomial be thought as adding terms, even if some coefficients are negative

Q: Find the polynomial if the zeroes are -4,-1,3,4

A:

Q: Show all steps to subtract the two polynomials and simplify: (6x5 + 9x2 + 7x) - (-2x5 - 6x2 + 6) =

A: We distribute the negative sign

Q: Make up two polynomials, not of the same degree, with thefollowing characteristics: crosses the…

A: Here it is given that Polynomial  crosses the x-axis at - 2  touchesthe x-axis at 1, and is above…

Q: Which of the following polynomial expressions factors into 3x(y - 3z)(y+ 2z)?

A:

Q: 5. The revenue of a company that makes toy cars is modeled by 4x +5x -40. The cost for making the…

A: Given: The revenue of a company that makes toy cars is modeled by 4x2+5x-40. The cost for making the…

Q: What is the leading term of the polynomial (v2z – 3x

A: The given polynomial is:  2x2-3x+963x-1433

Q: Explain why x - 1 is NOT a factor of the polynomial 15 -2 + 3.

A: Let, f(x) = x¹⁵ - x² + 3 By FACTOR THEOREM, if (x-1) is a factor of f(x) then, 1 is a zero of f(x)…

Q: Explain how to subtract polynomials ?

A:

Q: Is the expression a polynomial?

A: Given problem is :

Q: Written as a simplified polynomial in standard form, what is the result when (2x + 4)² is subtracted…

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

Q: What polynomial is 8^2 +6x

A:

Q: If a sixth-degree polynomial is divided by a third-degree polynomial, what is the degree of the…

A: We have to find the degree of the quotient polynomial If a sixth degree polynomial is divide by a…

Q: Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 2x + 3x-1…

A: Inside a polynomial, we can not have a negative exponent of x.  In this expression, the second term…

Q: Is the expression 4x3 - 3.6x2 - 22 a polynomial? If so,what is its degree?

A: 4x3-3.6x2-22 is polynomial because the powers are positive.

Q: Explain why the degree of the product of two nonzero polynomials equals the sum of their degrees.

A: Let the two polynomials be of degree m & n respectively. Then, the highest power of x in the…

Q: Own

A: we have to find difference of the polynomial 8x3+6x2-7 and 4x3+2x2+5x+3 Difference is :…

Q: simplify the expression to a polynomial in standered form (4x+5)(x^2-x-4)

A: The given expression, (4x+5)(x2-x-4)

Q: According to Descartes' Rule of Signs, how many negative zeroS could the polynomial æ4 – 3x³ – 2x² +…

A: According to Descartes's rule of signs, maximum number of positive real root of a polynomial…

Q: 3. x – 6x² + x

A: We know that a polynomial with its highest degree 3 is known to be a Cubic polynomial. The general…

Q: what are polynomials?

A: A polynomial is an algebraic expression with 2 or more terms with non-negative integer powers and…

Q: According to Descartes' Rule of Signs, how many positive zeros could the polynomial 3x 4x4 + 2x2 + 9…

A: We have to find the number of positive zeroes of the polynomial.

Q: According to Descartes' Rule of Signs, how many negative zeros could the polynomial -3z + 2x® – 2x2…

A: The number of possible negative real zeros is equal to the number of changes in the sign of the…

Q: Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. [(2x +…

A: Here given expression as 2x+3x

Q: how would i subtract these polynomials? what do i have to do?

A:

Q: If a sixth degree polynomial is divided by a third degree polynomial, what is the degree of the…

A: Explained below

Q: If the area of a trapezoid, A=1/2h (b1 + b2 ), is 2x2+19x+45 sqaure meters and the two parallel…

A: Suppose the area of the trapezoid is 2x2+19x+45 square meters and two parallel sides are x meters…

Q: Explain how to find the degree of a polynomial in two variables.

A: We have to explain how to find the degree of a polynomial in two variables.

Q: Classify the polynomial  - 3 x^4 + 4 x^2 - 2

A: The given polynomial is,

Q: Express as a polynomial.

A: The given equation is 2a+b3 To express it as a polynomial Polynomial is collection of variables and…

Q: What is the relationship between the number of factors and the degree of the polynomial?

A: To explain: The relationship between the number of factors and degree of the polynomial. Concept…

Q: Is the algebraic expression a polynomial? If it is, write the polynomial in standard form. 2x + 3x2…

A:

Q: Express as a polynomial.

A: Here, both expression 3a-5b and 2a+7b are binomials. The product of two binomial can be computed…

Q: The length, width, and height of a rectangular box are represented by 2r, 3x + 1, and 5x - 6,…

A: Use the formula for volume of the rectangular box and than simplify.

Q: the zeros of polynomial are 5 multiple of 2, and -1. write in standard form

A:

Q: The process of writing a polynomial containing the sum of monomials as a product is called

A: The process of writing a polynomial containing sums of monomials as a product is called factoring.…

Q: A storage company is designing a new storage unit. Based on the dimensions shown, the volume of a…

A:

Q: Explain how to determine the leading coefficient of a polynomial.

A: The leading term is the term containing the highest power of the variable, or the term with the…

Q: what is the power of the polynomial (2x-1)¹⁰×(3x+3)⁹?

A: Let, f(x) and g(x) are linear functions of x .       The polynomial {f(x)}m.{g(x)}n   The power of…

Q: Express as a polynomial. (3x - 4)(2x + 9)

A: 3x-42x+9

Q: Is the algebraic expression a polynomial? If it is, write the polynomial in standard form : 2x + 3x2…

A: A polynomial is defined as an expression which is composed of variables, constants and exponents,…

Q: Explain why the degree of the sum of two polynomials of different degrees equals the larger of their…

A: If two polynomials are given then their sum is calculated by adding the coefficients of the…

Q: how many polynomials are in this equation x^5-2x+x^9-9x^6

A: This is single polynomial of degree 9

Q: Subtract 3x2 + 7x – 4 from 8x? – 6x + 2. Your answer should be a polynomial in standard form.

A: p(x) = 8x2-6x+2q(x) = 3x2+7x-4To find: p(x) - q(x).

Q: If a fifth degree polynomial is divided by a third degree polynomial, what is the degree of the…

A: Let there be two polynomials fx=ax5+bx4+cx3+dx2+ex+f and gx=mx3+nx2+px+q where a≠0, m≠0.

Q: Can I use a vertical format to subtract polynomials, like we did with addition?

A: Yes, we can use a verical format to subtract polynomials, like we did with addition.

Q: What is the degree of the polynomial  - 3 x^3 y^2 + 3x^2 y^4 + 3 x y^2

A: Rewrite the given polynomial in terms of decreasing powers.

Q: Explain how to determine the degree of each term of a polynomial.

A: Finding degree of a term: If the term has only one variable then degree of term is the exponent of…

Q: 2. Add one term to the polynomial expression 14x19 – 9x²5 + 11x* + 5x² +3 to make it into a 22nd…

A:

Q: Find the polynomials whose zeroes are (i)3,-4 and (ii)3, 3.

A: First I have written a short note about , how to a polynomial us given, when two of its zeros are…