Common Factors and Trinomial Factoring

Oliver, Olivia, and Owen are trying to split a large number of candies evenly among themselves. What would you call a number that allows them to do this without any candies left over?

• A number that evenly divides into the total number of candies

• A number not divisible by any other number

• A number divisible only by 1 and the total number of candies

• A prime number

Charlotte, Mira, and Ellie are trying to split 12 apples and 18 oranges equally among themselves. What is the maximum number of fruits each person can get?

• 9

• 3

• 4

• 6

Oliver, Ishaan, and Harper are working on a math problem. They are trying to break down a trinomial equation into simpler parts. What is this process called?

• Multiplying three binomials

• Factoring a binomial into three trinomials

• Factoring a trinomial into two binomials

• Dividing a trinomial by a binomial

Harper is trying to solve a math problem. She needs to factorize the expression 2x^2 + 7x + 3. Can you help her?

• (2x + 3)(x + 1)

• (2x + 1)(x + 3)

• (2x + 2)(x + 1)

• (2x - 1)(x - 3)

Mia, Aarav, and Amelia are studying for a math test. Mia is confused about the difference between common factors and trinomial factoring. Can you help her understand?

• Common factors involve adding numbers, like when Mia adds up the cost of her school supplies, while trinomial factoring is like when Aarav multiplies a trinomial by a binomial to calculate the area of a complex shape.

• Common factors involve finding the greatest common factor, like when Amelia finds the greatest number of apples she and Aarav can equally share, while trinomial factoring is like factoring a trinomial into binomial factors to break down a complex problem into simpler parts.

• Common factors involve finding the smallest common factor, like when Mia finds the smallest number of candies she and Amelia can equally share, while trinomial factoring is like when Aarav factors a binomial into trinomial factors to solve a complex equation.

• Common factors involve dividing numbers, like when Aarav divides his candies equally among his friends, while trinomial factoring is like finding the square root of a trinomial, similar to when Amelia calculates the square root of a number.

Zoey, Anaya, and Isabella are trying to solve a math problem. They need to factorize the expression 3x^2 - 10x + 8. Can you help them?

• (3x-2)(x-4)

• (3x-4)(x-2)

• (3x+4)(x-2)

• (3x+2)(x-4)

Samuel and Isabella are trying to split a set of marbles evenly between them. They want to find the greatest number of marbles each can have without any left over. How should they find this number?

• List all possible numbers of marbles each could have (factors) and find the largest number that works for both.

• Divide the total number of marbles by two.

• Add the number of marbles each currently has.

• Multiply the number of marbles each currently has.

Priya was helping Emily with her math homework when they came across a problem: 'Factorize the expression representing the area of a rectangle, if the length is (4x - 3) and the width is (x - 3)'. The expression was 4x^2 - 12x + 9. How would you factorize this expression?

• (2x+3)^2

• (2x-3)(2x+3)

• (2x-3)^2

• (4x-3)(x-3)

Aarav, Henry, and Chloe are working on a math problem. They need to factor a trinomial where the leading coefficient is greater than 1. How should they approach this problem?

• They should divide the trinomial by the leading coefficient.

• They should use the FOIL method.

• They should subtract the constant term from the trinomial.

• They should use the AC method or trial and error.

Jacob, Emily, and Rohan are trying to build a structure using blocks. They have 24 blocks and 36 blocks respectively. They want to build the structure in such a way that each of them uses the same number of blocks. What are the possible numbers of blocks each of them can use?

• 5, 8, 10, 15, 20, 24

• 7, 14, 21, 28, 35, 42

• 9, 18, 27, 36, 45, 54

• 1, 2, 3, 4, 6, 12