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texaschic101
12x^4 + 2x^3 - 30x^2

to find the GCF, lets first look at the coefficients.....the GCF of 12,2,and 30 is 2.

as for the variables....pick the one with the smallest exponent...and that would be x^2

so the GCF of this polynomial is 2x^2 <=

Answer:

Option (4) is correct.

Greatest common factor of the given polynomial [tex]12x^4+2x^3-30x^2[/tex]   is [tex]2x^2[/tex]

Step-by-step explanation:

given polynomial [tex]12x^4+2x^3-30x^2[/tex]

We have to find the greatest common factor of the terms in the given  polynomial.

Greatest common factor is the largest number that is a factor of the each given term.

Consider the given polynomial [tex]12x^4+2x^3-30x^2[/tex]

Here , the polynomial has three terms,

Prime factorization of given terms are,

[tex]12x^4=2\cdot 2 \cdot 3 \cdot x \cdot x \cdot x \cdot x\\\\2x^3=2 \cdot x\cdot x\cdot x\\\\\-30x^2=-2 \cdot 3\cdot 5\cdot x\cdot x[/tex]

Thus, Greatest common factor [tex]2x^2[/tex]

Thus, Greatest common factor of the given polynomial [tex]12x^4+2x^3-30x^2[/tex]   is [tex]2x^2[/tex]

Thus, option (4) is correct.

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