Factoring Polynomials: Greatest Common Factor Insights

What does GCF stand for in the context of polynomial factoring?

• Gradient Central Feature

• Geometric Configuration Form

• General Calculus Function

• Greatest Common Factor

What is the first step in factoring polynomials?

• Solving for x

• Applying the distributive property

• Finding the GCF

• Identifying the highest exponent

How do you find the GCF of a polynomial?

• By adding the coefficients

• By subtracting the exponents

• By dividing each term by the smallest coefficient

• By identifying common prime factors

What method is described as a 'surefire way' to always find the GCF?

• Quadratic formula

• Synthetic division

• Completing the square

• Prime factorization

In the context of GCF, what must a variable fulfill to be considered as part of the GCF?

• It must be an integer.

• It must be a prime number.

• It must be present in all terms with the smallest exponent.

• It must have the highest exponent in the term.

What is the result of factoring out the GCF in the expression '4a squared plus 8a'?

• 4a(2a + 1)

• 8a(a + 1)

• 2a(2a + 4)

• 4a(a + 2)

What does the term 'prime' refer to in polynomial factoring?

• The highest coefficient in the polynomial

• A polynomial that can be factored further

• The smallest exponent in the polynomial

• A polynomial that cannot be factored further

How is the GCF used once it is factored out from a polynomial?

• It is added to each term inside the parentheses.

• It is multiplied by the remaining terms inside the parentheses.

• It is subtracted from each term inside the parentheses.

• It is divided by each term inside the parentheses.

What should you do if you automatically recognize the GCF in an expression?

• Divide each term by the GCF and state the GCF explicitly.

• Multiply each term by the GCF.

• Add the GCF to each term.

• Ignore the GCF and factorize using a different method.

What is the factored form of '18a squared b squared - 48abc to the third'?

• 18ab(abc squared - 2c squared)

• 6abc squared(3a - 8c)

• 9ab(2a - 5bc)

• 6ab squared c(3a - 8c)