Question 1: Monica wants to find the greatest common factor of the terms of the polynomial p(x)=12x3^y+6xy^2+18xy+24x. She sees that each term is divisible by 3x. She factors the polynomial as follows:

3x(4x^2y+2y^2+6y+8)

Did Monica correctly factor out the greatest common factor? Why or why not?

a. Monica is incorrect, the GCF should only include constants.
b. Monica is correct, 3x is the GCF and she factored it out correctly.
c. Monica is incorrect, the GCF should only include variables.
d. Monica is incorrect, there is a common factor larger than 3x.

Question 2: Lana uses factoring by grouping to factor the polynomial 8x^2y−10xy^2+12x−15y. Her work is shown below, but the last two lines of work are missing.

8x^2y−10xy^2+12x−15y
(8x^2y−10xy^2)+(12x−15y)
__[blank 1]__
__[blank 2]__

Select one statement for each blank to correctly complete Lana’s work.

a. blank 1: 2xy(4x−5y)+3(4x−5y)
a. blank 2: (2xy−3)(4x+5y)
b. blank 2: (2xy+3)(4x−5y)
b. blank 1: −2xy(4x+5y)−3(4x+5y)
c. blank 1: −4x(2xy+3)+5y(2xy+3)
c. blank 2: −(2xy+3)(4x−5y)

Question 1:  Option D, Monica is incorrect, there is a common factor larger than 3x.

Question 2:  

Option 1, a. blank 1: 2xy(4x−5y)+3(4x−5y)

Option 3, b. blank 2: (2xy+3)(4x−5y)

Step-by-step explanation:

Question 1

Step 1:  Find the greatest common factor

p(x) = 12x^3y + 6xy^2 + 18xy + 24x

p(x) = 3x(4x^2y + 2y^2 + 6y + 8)

 Option D, Monica is incorrect, there is a common factor larger than 3x.

Question 2

Step 1:  Factor

8x^2y − 10xy^2 + 12x − 15y

(8x^2y − 10xy^2) + (12x − 15y)

2xy(4x - 5y) + 3(4x - 5y)

(2xy + 3)(4x - 5y)

Option 1, a. blank 1: 2xy(4x−5y)+3(4x−5y)

Option 3, b. blank 2: (2xy+3)(4x−5y)

angle uzt is congruent to angle tzy. angle vzw is congruent to angle yzx.

(credits to leowren)

step-by-step explanation:

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.