What Is The Factored Form Of The Polynomial 27X2Y-43Xy2 (2024)

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What Is The Factored Form Of The Polynomial 27X2Y-43Xy2? ›

Summary: The factored form of the polynomial 27x²y - 43xy² is (x)(y)(27x - 43y).

If a polynomial of lowest degree p has zeros at x=x1,x2,…,xn x = x 1 , x 2 , … , x n , then the polynomial can be written in the factored form: f(x)=a(x−x1)p1(x−x2)p2⋯(x−xn)pn f ( x ) = a ( x − x 1 ) p 1 ( x − x 2 ) p 2 ⋯ ( x − x n ) p n where the powers pi on each factor can be determined by the behavior of the graph ...

Hence, the factorization of 81 x 4 − 16 y 4 is ( 9 x 2 + 4 y 2 ) ( 3 x + 2 y ) ( 3 x − 2 y ) .

An equation of a polynomial function is in factored form if it is written as f (x) = a(x - r1)(x - r2) ... (x - rn), where (x - rk ) is a factor corresponding to x-intercept rk . Note that it is not always possible to express a polynomial function using factored form.

You can check your factoring by multiplying them all out to see if you get the original expression. If you do, your factoring is correct; otherwise, you might want to try again.

Summary: The factored form of the polynomial 27x²y - 43xy² is (x)(y)(27x - 43y).

To write a polynomial in factored form, it must be expressed as a product of terms in its simplest form. The terms could be constant or linear or any polynomial form which is not further divisible.

What is the completely factored form of f(x) = 6x³ - 13x² - 4x + 15? Using the factor theorem, (x + 1) is a factor of the given polynomial. Therefore, the completely factored form is (x + 1)(2x - 3)(3x - 5).

Explanation: The factored form of x⁹ + 27 is (x³ + 3)(x⁶ - 3x³ + 9), which corresponds to option B. To factorize the given expression, we can use the formula for sum of cubes: a³ + b³ = (a + b)(a² - ab + b²). In this case, x⁹ + 27 can be written as x⁹ + 3³, where a = x³ and b = 3.

Summary: The completely factored form of f(x) = x³ - 2x² - 5x + 6 is (x - 1)(x + 2) and (x - 3).

What is completely factored form polynomial? ›

A polynomial is completely factored if it is written as a product of a real number (which will be the same number as the leading coefficient of the polynomial), and a collection of monic quadratic polynomials that do not have roots, and of monic linear polynomials.

Factoring a polynomial is the process of decomposing a polynomial into a product of two or more polynomials. For example, f ( x ) = x 2 + 5 x + 6 f(x) = x^2 + 5x + 6 f(x)=x2+5x+6 can be decomposed into. f(x) = (x+3)(x+2) .

Factored form refers to the form of a number or algebraic expression when it has been broken down into a product of its factors. Putting a number in factored form is simply a matter or rewriting that number as a product of its factors. For example, the number 6 can be written as the product of 2 and 3: 6 = 2 × 3.

Step 1: Group the first two terms together and then the last two terms together. Step 2: Factor out a GCF from each separate binomial. Step 3: Factor out the common binomial. Note that if we multiply our answer out, we do get the original polynomial.

To solve a polynomial equation, first write it in standard form. Once it is equal to zero, factor it and then set each variable factor equal to zero. The solutions to the resulting equations are the solutions to the original. Not all polynomial equations can be solved by factoring.

It is a polynomial with integer coefficients that cannot be factored into polynomials of lower degrees. x² + 7 can not be factorized with rational numbers. Therefore, it is a prime polynomial.

Factoring Polynomials using Identities. Factoring binomials of the form x 2 − y 2 = ( x − y ) ( x + y ) : x^2 - y^2= (x-y)(x+y): x2−y2=(x−y)(x+y): This approach applies the difference of two squares identity. Factor x 2 − 16 x^2 - 16 x2−16.

The factored form of the polynomial x² + 9x + 20 is (x + 5)(x + 4).