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.

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 ...

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

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 ) .

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.

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) .

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.

How to factorise x2 9x 20? ›

∴ x 2 + 9 x + 20 = ( x + 4 ) ( x + 5 )

The factored form of 3 x + 24 y is 3 ( x + 8 y ) .

Answer: x² − y² can be factorised as ( x − y ) ( x + y ) We can proceed step by step to solve this problem.

Final answer:

The factored form of 1,458x³ − 2 is (9x − 2)(81x² + 18x + 4), by applying the difference of cubes factoring rule.

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.

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).

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

x2−16xy+64y2=x2−2⋅8xy+(8y)2=(x−8y)2.

Expert-Verified Answer

The statement is true about the factorization of 30x2 + 40xy + 51y2? is, The polynomial can be rewritten after factoring as 10(3x2 + 4xy + 5y2). Instead, the polynomial cannot be rewritten in the form of factors, as there are no common terms.

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.