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? ›

27x²y – 43xy² = xy(27x – 43y). ∴27x²y – 43xy² can be factored as x × y × (27x – 43y) or we can also say that x, y and (27x – 43y) are the factors of 27x²y – 43xy².

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.

Answer and Explanation: The factored form of 3 x + 24 y is 3 ( x + 8 y ) .

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 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.

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.

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) .

What is the completely factored form of f x 6x 3 13x 2 4x 15? ›

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).

81 x 4 − y 4 = ( 9 x 2 + y 2 ) ( 3 x + y ) ( 3 x − y )

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.

Difference of Cubes: A difference of cubes is two perfect cube terms with subtraction in between. A perfect cube can be written as a term multiplied by itself a total of three times. Factoring: Factoring is the process of undoing distribution. Factoring is useful in finding the roots of equations.

Factorization depends on the base field. For example, the fundamental theorem of algebra, which states that every polynomial with complex coefficients has complex roots, implies that a polynomial with integer coefficients can be factored (with root-finding algorithms) into linear factors over the complex field C.

Summary: The fully factored form of the given algebraic expression is 4a²(8a + 3).

Summary: Isiah determined that 5a² is the GCF of the polynomial a³ - 25a²b⁵ - 35b⁴.

Expert-Verified Answer

An expression is defined as a set of numbers, variables, and mathematical operations. The factored form of the expression 16x²+8x+32 is 8(2x²+x+4).

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