Answer :
Answer: The factor form of the given polynomial [tex]3x^5-7x^4+6x^2-14x[/tex] is [tex]x(3x-7)(x^3+2)[/tex]
Step-by-step explanation:
Given polynomial is [tex]3x^5-7x^4+6x^2-14x[/tex]
To factorize the given polynomial take x as common from all the terms of the polynomial.
[tex]\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)[/tex]
Therefore, the factor form of the given polynomial [tex]3x^5-7x^4+6x^2-14x[/tex] is [tex]x(3x-7)(x^3+2)[/tex]
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
[tex]3x^5 - 7x^4 + 6x^2 - 14x[/tex]
We can factorize the given polynomial in the following manner,
[tex]3x^5 - 7x^4 + 6x^2 - 14x[/tex]
Take x common from the entire polynomial,
[tex]= x(3x^4 - 7x^3 + 6x - 14)[/tex]
Further, take x³ as the common factor from the first two-term in the bracket,
[tex]= x[x^3(3x - 7) + 6x - 14][/tex]
Take 2 as the common factor from the last two terms,
[tex]= x[x^3(3x - 7) + 2(3x - 7)]\\\\=x[(3x-7)(x^3+2)]\\\\=x(3x-7)(x^3+2)[/tex]
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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