Factoring Polynomials with Four Terms

What is the first step in factoring by grouping when given a polynomial with four terms?

• Divide the polynomial into two groups

• Identify the common factor in all terms

• Multiply all terms by the leading coefficient

• Calculate the coefficients' ratio of the first two and last two terms

What does having the same ratio of coefficients in the first two and last two terms indicate?

• A quadratic formula is needed to solve the polynomial

• Factoring by grouping is possible

• The polynomial is already in its simplest form

• The polynomial cannot be factored

After factoring out the greatest common factor (GCF) from both groups, what should you ideally find?

• Different terms in each group

• A common binomial factor in both groups

• No common factors at all

• A prime number as a factor

How do you verify the correctness of your factoring by grouping?

• By adding the factors

• By dividing the original polynomial by the factors

• By foiling the factors to see if they reproduce the original polynomial

• By graphing the polynomial

What is the significance of finding a common factor like 'x - 4' in the terms of a polynomial?

• It allows for further factoring by grouping

• It suggests the polynomial is prime

• It indicates a mistake in calculations

• It confirms the polynomial can be factored further

In the context of cubic polynomials, what does factoring out a GCF from the terms help reveal?

• The irreducibility of the polynomial

• The roots of the polynomial

• A simpler polynomial that might be factored further

• The degree of the polynomial

What technique is used to factor 'x squared minus 4'?

• Sum of squares

• Quadratic formula

• Difference of squares

• Factoring by grouping

What does the presence of a common binomial factor in grouped terms indicate about the polynomial?

• It is a cubic polynomial

• It can be factored further

• It is a prime polynomial

• It is non-factorable

When factoring a polynomial with mixed terms (variables and constants), what should you first look for?

• The highest degree of the polynomial

• The coefficients of the leading terms

• The GCF in each group of terms

• The variable with the highest exponent

How can you simplify the expression '3x squared minus 3' after factoring by grouping?

• By dividing each term by x

• By adding one to each term

• By factoring out a three from the expression

• By applying the quadratic formula