Question

Choose two trinomials from the list below to factor. Using complete sentences, explain how to factor each one. Be sure that the final factorization (or "answer") is a part of your explanation.


2x2 + 13x + 15
2x2 + 27x + 13
5x2 − 2x − 7
10x2 − 7x − 3
8x2 − 11x + 3

Answer 1

Please help me

Answer 2

i would help but im not very smart lol

Answer 3

me neither thts y i need help :/ lol

Answer 4

2x² + 13x + 15 = ( x + 5)(2x + 3)

2x² +13x + 15 Look for a GCF None this time. If there was one, factor it out. Then temporarily start both parentheses
............................. with the first number and variable.
(2x.......)(2x..........) First sign goes in first parentheses.
(2x +....)(2x..........) Product of signs goes in 2nd parentheses.
(2x +....)(2x +.....) <== plus is because pos x pos = positive

Now multiply your first and third numbers together. Ignore their signs - you've already done them. 2 x 15 = 30 So, out to the side list pairs of factors of 30.

30
------
1, 30
2, 15
3, 10
5, 6

Now you want to pick which factors go in your parentheses, using these rules:

If the signs you put on your parentheses are the SAME, find the factors that ADD up to the middle number in the problem.
If the signs you put on your parentheses are the DIFFERENT, find the factors that SUBTRACT to the middle number in the problem. (Note you look at signs in the parentheses, not in the problem.)

(2x +....)(2x +.....) Your signs are the same, so you want to add factors to get 13. Those factors are 3 and 10. When you put the numbers in the parentheses, the bigger number is pushy - it always goes first. So your factors now are:
(2x + 10)(2x + 3)

Now you have to reduce either or both parentheses by dividing each parentheses' terms by the largest possible divisor. In our problem, the first parentheses is divisible by 2 but the second parentheses does not reduce.

(2x + 10)(2x + 3)
------------
.......2 This reduces to your final factors of

(x + 5)(2x + 3) <==ANSWER


2x² + 27x + 13 = (x + 13)(2x + 1)

2x² + 27x + 13 Look for a GCF None this time. If there was one, factor it out. Then temporarily start both parentheses
............................. with the first number and variable.
(2x.......)(2x..........) First sign goes in first parentheses.
(2x +....)(2x..........) Product of signs goes in 2nd parentheses.
(2x +....)(2x +.....) <== plus is because pos x pos = positive

Now multiply your first and third numbers together. Ignore their signs - you've already done them. 2 x 13 = 26 So, out to the side list pairs of factors of 26.

26
------
1, 26
2, 13

Now you want to pick which factors go in your parentheses, using these rules:

If the signs you put on your parentheses are the SAME, find the factors that ADD up to the middle number in the problem.
If the signs you put on your parentheses are the DIFFERENT, find the factors that SUBTRACT to the middle number in the problem. (Note you look at signs in the parentheses, not in the problem.)

(2x +....)(2x +.....) Your signs are the same, so you want to add factors to get 27. Those factors are 1 and 26. When you put the numbers in the parentheses, the bigger number is pushy - it always goes first. So your factors now are:
(2x + 26)(2x + 1)

Now you have to reduce either or both parentheses by dividing each parentheses' terms by the largest possible divisor. In our problem, the first parentheses is divisible by 2 but the second parentheses does not reduce.

(2x + 26)(2x + 1)
------------
.......2 This reduces to your final factors of

(x + 13)(2x + 1) <==ANSWER

5x² − 2x − 7 = (5x - 7)(x + 1)

5x² - 2x - 7 Look for a GCF. There is none this time. If there was one, factor it out. Then temporarily start both parentheses with the first number and variable.
(5x.......)(5x..........) First sign goes in first parentheses.
(5x -....)(5x.........) Product of signs goes in 2nd parentheses.
(5x -....)(5x +.....) <== pos is because neg x neg = positive

Now multiply your first and third numbers together. Ignore their signs - you've already done them. 5 x 7 = 35 So, out to the side list pairs of factors of 35.

35
------
1, 35
5, 7

Now you want to pick which factors go in your parentheses, using these rules:

If the signs you put on your parentheses are the SAME, find the factors that ADD up to the middle number in the problem.
If the signs you put on your parentheses are the DIFFERENT, find the factors that SUBTRACT to the middle number in the problem. (Note you look at signs in the parentheses, not in the problem.)

(5x -....)(5x +.....) Your signs are different, so you want to subtract factors to get 2. Those factors are 5 and 7. When you put the numbers in the parentheses, the bigger number is pushy - it always goes first. So your factors now are:
(5x - 7)(5x + 5)

Now you have to reduce either or both parentheses by dividing each parentheses' terms by the largest possible divisor. In our problem, the first parentheses does not reduce, but the second parentheses is divisible by 5.

(5x - 7)(5x + 5)
. . . . . . ----------
..... . . . . . . 5
This reduces to your final factors of

(5x - 7)(x + 1) <==This is the answer to your problem.


10x² − 7x − 3 = (x - 1)(10x + 3)

10x² - 7x - 3 Look for a GCF. There is none this time. If there was one, factor it out. Then temporarily start both parentheses with the first number and variable.
(10x.......)(10x..........) First sign goes in first parentheses.
(10x -....)(10x.........) Product of signs goes in 2nd parentheses.
(10x -....)(10x +.....) <== pos is because neg x neg = positive

Now multiply your first and third numbers together. Ignore their signs - you've already done them. 10 x 3 = 30 So, out to the side list pairs of factors of 30.

30
------
1, 30
2, 15
3, 10
5, 6

Now you want to pick which factors go in your parentheses, using these rules:

If the signs you put on your parentheses are the SAME, find the factors that ADD up to the middle number in the problem.
If the signs you put on your parentheses are the DIFFERENT, find the factors that SUBTRACT to the middle number in the problem. (Note you look at signs in the parentheses, not in the problem.)

(10x -....)(10x +.....) Your signs are different, so you want to subtract factors to get 7. Those factors are 3 and 10. When you put the numbers in the parentheses, the bigger number is pushy - it always goes first. So your factors now are:
(10x - 10)(10x + 3)

Now you have to reduce either or both parentheses by dividing each parentheses' terms by the largest possible divisor. In our problem, the first parentheses is divisible by 10, but the second parentheses does not reduce.

(10x - 10)(10x + 3)
.-----------
. . . . 10
This reduces to your final factors of

(x - 1)(10x + 3) <==This is the answer to your problem.



8x² − 11x + 3 = (x - 1)(8x - 3)

8x² - 11x + 3

Then temporarily start both parentheses with the first number and variable.
(8x.......)(8x.......) First sign goes in first parentheses.
(8x -....)(8x.......) Product of signs goes in 2nd parentheses.
(8x -....)(8x -....) <== neg is because neg x pos = negative

Now multiply your first and third numbers together. Ignore their signs - you've already done them. 8 x 3 = 24 So, out to the side list pairs of factors of 24.

24
------
1, 24
2, 12
3, 8
4, 6

Now you want to pick which factors go in your parentheses, using these rules:

If the signs you put on your parentheses are the SAME, find the factors that ADD up to the middle number in the problem.
If the signs you put on your parentheses are the DIFFERENT, find the factors that SUBTRACT to the middle number in the problem. (Note you look at signs in the parentheses, not in the problem.)

(8x -....)(8x -....) Your signs are the same, so you want to add factors to get 11. Those factors are 3 and 8. When you put the numbers in the parentheses, the bigger number is pushy - it always goes first. So your factors now are:
(8x - 8)(8x - 3)

Now you have to reduce either or both parentheses by dividing each parentheses' terms by the largest possible divisor. In our problem, the first parentheses is divisible by 8, but the second parentheses does not reduce.

(8x - 8)(8x - 3)
----------
. . . 8


(x - 1)(8x - 3)

Answer 5

thanks