Question

1. factoring is the opposite of _______

1. what is the greatest common factor of these terms: \\(4xy^2, 10x^2y^2, 8xy^3\\)

• \\(40xy^2\\)
• \\(2xy^2\\)
• \\(2x^2y^3\\)
• \\(2xy\\)

1. factor the polynomial fully: \\(2x^2 + 26x + 60\\). explain your steps and how you found the factor pairs.

Explanation:

Define factoring as an operation

Factoring is the process of breaking down an expression into a product of simpler expressions.

Using the Factoring Definition knowledge point

$$ \text{Factoring is the opposite of multiplying (or expanding).} $$

Find the greatest common factor of the terms

Using the Greatest Common Factor knowledge point

$$
LATEXBLOCK0
$$

Factor out the greatest common factor

Using the Greatest Common Factor and Factoring Trinomials knowledge points

$$
LATEXBLOCK1
$$

Factor the remaining quadratic trinomial

Using the Factoring Trinomials knowledge point

$$
LATEXBLOCK2
$$

Answer:

Question 5

Factoring is the opposite of <blank>multiplying</blank> (or <blank>expanding</blank>).

Question 6

• (A) \(40xy^2\)
• (B) \(2xy^2\) (Correct answer)
• (C) \(2x^2y^3\)
• (D) \(2xy\)

Question 7

To factor the polynomial \(2x^2 + 26x + 60\) fully:

1. Factor out the GCF: The greatest common factor of the terms is \(2\). Factoring it out gives:

$$2(x^2 + 13x + 30)$$

1. Find the factor pairs: We need two numbers that multiply to \(30\) and add up to \(13\).

• The factors of \(30\) are: \((1, 30)\), \((2, 15)\), \((3, 10)\), and \((5, 6)\).
• The pair that adds up to \(13\) is \(3\) and \(10\) (since \(3 \times 10 = 30\) and \(3 + 10 = 13\)).

1. Write the factored form:

$$2(x + 3)(x + 10)$$