Download Factor Diamond Practice Problems 1. x2 + 5x + 6 2. x2 +7x + 12 3

Factor Diamond Practice Problems
1. x2 + 5x + 6
2. x2 +7x + 12
3. x2 + 9x + 8
4. x2 + 9x +14
5. 2x2 – 7x – 4
6. 3x2 –x – 4
7. 5x2 + x -18
8. 2y2 – x – 1
9. 6 -13x + 6x2
10.
15 + x -2x2
Factor Diamond Practice Problems Walkthrough
1. x2 + 5x + 6
- Put the 6 on the top and the 5 on the bottom
Find 2 numbers that multiply to the top number and add to the bottom
Now put them in the equation
(x + 3)(x + 2) Now that you have the equation find the number which add or
subtracts to make a 0
Lets start with the first one, (x + 3) a -3 would make it 0, (-3 + 3) = 0
For (x + 2) it would be a -2, (-2 + 2) = 0
So your two answers are
2. x2 +7x + 12
-Put the 12 on top and the 7 on the bottom
Find 2 numbers that multiply to the top number and add to the bottom
Now put them in the equation
Now its (x + 3)(x + 4), make them 0
For (x + 3) it would be -3, (-3 + 3) = 0
For (x + 4) it would be -4 (-4 + 4) = 0
So your two answers would be
3.
3. x2 + 9x + 8 Put the 8 on top and the 9 on bottom
Find 2 numbers that multiply to the top number and add to the bottom
Now put them in the equation
Now its (x + 1)(x + 8)
For (x + 1) its -1, (-1 + 1) = 0
For (x + 8) its -8, (-8 + 8) = 0
So your two answers would be
4.
x2 + 9x +14 Put the 14 on top and the 9 on bottom
Find 2 numbers that multiply to the top number and add to the bottom
Now put them in the equation
Now its (x + 2)(x + 7)
For (x + 2) its -2, (-2 + 2) = 0
For (x + 7) its -7, (-7 + 7) = 0
So your two answers are
5. 2x2 – 7x – 4
Here you will be using the borrowing method, so multiply the
first and last numbers, so the equation turns into x2 – 7x -8
Now plug it into the diamond, the -8 on top and the -7 on bottom
Find 2 numbers that multiply to the top number and add to the bottom
- Now put them in the equation
- Now its (x - 8)(x + 1) But since you borrowed a 2 you have to give it back, so
divide both numbers by 2
- For (x - 8) it would turn into (x - 8/2)
- For (x + 1) it would turn into (x + ½) And reduce them both
- 8/2 reduces to 4, and ½ can’t reduce any further so the equations are (x – 4)(x + ½)
- To get rid of the denominator multiply by it, in this problem it is (x + ½) so when
multiplied by 2, it turns into (2x + 1)
- Our final two equations are (x – 4)(2x + 1) and make them both 0
- For (x – 4) it would be 4, (4 – 4) = 0
- For (2x + 1) it would be -½ , because 2 times -½ = -1, and (-1 + 1) = 0
- So your two final answers are
So your two answers are
6. 3x2 –x – 4
Multiply the first and last numbers, so the equation turns into
x2 – x -12
Now put it into the diamond, -12 on top and the -1 on bottom
- Find 2 numbers that multiply to the top number and add to the bottom
- Now put them in the equation
- Now its (x – 4)(x + 3) But you have to give back the 3 so (x – 4/3)(x + 3/3)
- Simplify them and if they cant be simplified anymore multiply by the denominator
So (x – 4/3) cant be simplified so you multiply by 3 which turns the problem into
(3x – 4)
-For (x + 3/3) simplifies to (x + 1)
- For (3x – 4) it would be 4/3, (4 -4) = 0
- For (x + 1) it would be -1, (-1 + 1) = 0
- So your two answers are
7. 5x2 + x -18 Multiply the first and last numbers, so the equation turns into
x2 + x - 90
Now put it into the diamond, -90 on top and 1 on bottom
- Find 2 numbers that multiply to the top number and add to the bottom
- Now put them in the equation
- Now its (x – 9)(x + 10) But you have to give back the 5 so (x – 9/5)(x + 10/5)
- Simplify them and if they can’t be simplified anymore multiply by the denominator
So (x – 9/5) cant be simplified so you multiply by 5 which turns the problem into
(5x – 9)
-For (x + 10/5) simplifies to (x + 2)
- For (5x – 9) it would be 9/5, (9 - 9) = 0
- For (x + 2) it would be -2, (-2 + 2) = 0
-So your final two answers are
8. 2y2 – y – 1 Multiply the first and last numbers, so the equation turns into y2 - y - 2
Now put it into the diamond, -2 on top and -1 on bottom
- Find 2 numbers that multiply to the top number and add to the bottom
- Now put them in the equation
- Now its (x – 2)(x + 1) But you have to give back the 2 so (x – 2/2)(x + 1/2)
- Simplify them and if they can’t be simplified anymore multiply by the denominator
So (x – 1/2) cant be simplified so you multiply by 2 which turns the problem into
(2x – 1)
-For (x + 2/2) simplifies to (x + 1)
- For (2x + 1) it would be -1/2, (-1 + 1) = 0
- For (x - 1) it would be 1, (1 – 1) = 0
So your two solutions are
9. 6 -13x + 6x2 First you have to put it in descending order which changed the
equation to 6x2 -13x + 6 and use the borrowing method
- This changed the problem to x2 -13x + 36
Now put it into the diamond, 36 on top and -13 on bottom
- Find 2 numbers that multiply to the top number and add to the bottom
- Now put them in the equation
- Now its (x – 9)(x - 4) But you have to give back the 6 so (x – 9/6)(x - 4/6)
- Simplify them and if they can’t be simplified anymore multiply by the denominator
So (x – 9/6) simplifies to 3/2 and it cant be simplified anymore so you multiply by 2
which turns the problem into (2x – 3)
-When simplifying (x - 4/6) turns to (x - 2/3) and now you multiply by 3. This turns
the problem into (3x - 2)
-For (2x - 3) it would be 3/2, (3 – 3) = 0
- For (3x - 2) it would be 2/3, (-2 + 2) = 0
The two final answers are
10. 15 + x -2x2 First you have to put it in descending order which changed the
equation to -2x2 + x + 15 and use the borrowing method
- This changed the problem to x2 + x - 30
Now put it into the diamond, -30 on top and 1 on bottom
- Find 2 numbers that multiply to the top number and add to the bottom
- Now put them in the equation
- Now its (x – 5)(x + 6) But you have to give back the 2 so (x – 5/2)(x + 6/2)
- Simplify them and if they can’t be simplified anymore multiply by the denominator
So (x – 6/2) simplifies to 3 which turns the problem into (x – 3)
-(x – 5/2) cannot be simplified anymore so you multiply it by 2 which turns it into
(2x - 5).
-For (x - 3) it would be 3, (3 – 3) = 0
- For (2x - 5) it would be 5/2, (5 - 5) = 0
The two final answers are