The greatest common factor of the terms of the given polynomial is 5x². So, option D is correct
How do find the GCF of a polynomial?
To find the GCF of a polynomial,
- find all the possible factors of each term in the polynomial
- pick out the common factors from all the terms ( the factor must be common for all the terms)
- multiply all the common factors to get the greatest common factor of the polynomial.
Calculation:
Given that,
the polynomial is [tex]20x^4-10x^3 + 15x^2[/tex]
Finding factors for all the terms:
[tex]20x^4[/tex] = 2 × 2 × 5 × x × x × x × x
[tex]10x^3[/tex] = 2 × 5 × x × x × x
[tex]15x^2[/tex] = 3 × 5 × x × x
So, from these three terms, the common factors are 5, x, x
On multiplying them,
⇒ 5 × x × x
∴ GCF = 5x²
Therefore, the greatest common factor of the given polynomial is 5x². So, option D is correct.
Learn more about the GCF of a polynomial here:
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