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Answer: The factor form of the given polynomial  \(3x^5-7x^4+6x^2-14x\) is \(x(3x-7)(x^3+2)\)


Step-by-step explanation:

Given polynomial is \(3x^5-7x^4+6x^2-14x\)

To factorize the given polynomial take x as common from all the terms of the polynomial.

\(\Rightarrow\ x(3x^4-7x^3+6x-14)\\\text{[taking }x^3\text{ as common from first two terms, we get]}\\\\\Rightarrow\ x(x^3(3x-7)+2(3x-7))\\\text{[taking (3x-7) as common ,we get]}\\\Rightarrow\ x((3x-7)(x^3+2))=x(3x-7)(x^3+2)\)

Therefore, the factor form of the given polynomial  \(3x^5-7x^4+6x^2-14x\) is \(x(3x-7)(x^3+2)\)

Polynomial is an expression that consists of variables and coefficients.

The factors of the given polynomial 3x⁵ – 7x⁴ + 6x² – 14x is

x(3x-7)(x³+2).

What are polynomial?

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

Given to us

\(3x^5 - 7x^4 + 6x^2 - 14x\)

We can factorize the given polynomial in the following manner,

\(3x^5 - 7x^4 + 6x^2 - 14x\)

Take x common from the entire polynomial,

\(= x(3x^4 - 7x^3 + 6x - 14)\)

Further, take x³ as the common factor from the first two-term in the bracket,

\(= x[x^3(3x - 7) + 6x - 14]\)

Take 2 as the common factor from the last two terms,

\(= x[x^3(3x - 7) + 2(3x - 7)]\\\\=x[(3x-7)(x^3+2)]\\\\=x(3x-7)(x^3+2)\)

Hence, the factor of the given polynomial 3x⁵ – 7x⁴ + 6x² – 14x is

x(3x-7)(x³+2).

Learn more about Polynomials:

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