The given polynomial is prime, and the greatest common factor of the terms is 1.

Step-by-step explanation:

Given : Expression

We have to choose the correct option from the given options that correctly describe the correct statement about the factorization of

Consider the given expression

Greatest common factor is the highest factor that divide the each term of the polynomial.

You are watching: Which statement is true about the factorization of 30x2 + 40xy + 51y2?

For the given polynomial

There is no term which is common in each three terms.

Hence, The greatest common factor of the polynomial is 1.

So, The given polynomial is prime, and the greatest common factor of the terms is 1.

prime

not factorable over the reals

Step-by-step explanation:

30x^2+40xy+51y^2 is not factorable (also know as prime)

because the discriminant is negative.

That is when I computed b^2-4ac, in this case 40^2-4(30)(51)=-4520.

If the discriminant is negative, then it isn"t factorable over the reals.

The correct option is 4.

Step-by-step explanation:

The given expression is, The factors of the terms are,   We did not find any common factor among these three terms. So the GCF is 1.

The polynomial which is completely factored (can not be factored further) is called prime polynomial.

Since the common factor of the terms is 1, therefore the polynomial is prime.

Option 4 is correct.

we have Find the greatest common factor of the polynomial

Find the factors so

The greatest common factor of the polynomial is equal to

Statements

case a) The factorization of the polynomial is The statement is False-----> is not a common factor of the three terms

case b) The polynomial can be rewritten as the product of a trinomial and xy

The statement is False------> the original polynomial is already a trinomial

case c) The greatest common factor of the polynomial is

The statement is False------> the polynomial do not contain

case d) The polynomial is prime, and the greatest common factor of the terms is

The statement is True

Therefore

case d) The polynomial is prime, and the greatest common factor of the terms is

You are correct

Step-by-step explanation:

Option D. The polynomial is prime, and the greates common factor of the terms is 1.A is not right because 10 is not a common factor of the three terms.B is not right because the original polynomial is alrerady a trinomialD is not right because the terms do not contain 51x^2y^2
The answer is D. There is nothing that comes out because 51 is only divisible by 3 or 17 and neither go into 40.

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