Factor ` x^2 -9x + 8` and `4x^2 -13x +9` .

(1) `x^2-9x +8`

To factor, let's use ac method.

Since a=1, b= -9 and c = 8, then ac= (1)(8)=8.

Then, determine the pair factor of 8 that would give us a sum of equal to b.

`(-1)(-8)=8 `

`(-1) + (-8)=-9`

Since the pair factor -1 and -8 satisfy the condition above, use them to re-write the middle term as sum of two terms.

So,

`x^2-9x +8`

`=x^2 -1x - 8x + 8`

`=x^2 -x - 8x+ 8`

Then, group the terms into two.

`=(x^2 - x) - (8x - 8)`

Factor out the GCF of each group.

`=x(x-1)-8(x-1)`

And factor out the GCF of the two groups.

`=(x-1)(x-8)`

**Thus, ` x^2-9x+8=(x-1)(x-8)` . **

(2) `4x^2-13x +9`

To factor this, use ac method too.

Since a=4, b=-13 and c=9, then ac=(4)(9)=36.

Then, determine the pair factor of 36 that would give us a sum equal to b.

`(-4)(-9)=36`

`(-4)+(-9)=-13`

So, use the pair factor -4 and -9 to express the middle term as sum of two terms.

`4x^2-13x+9`

`=4x^2-4x-9x+9`

Then, group the terms into two.

`=(4x^2-4x)-(9x-9)`

Factor out the GCF of each group.

`=4x(x-1)-9(x-1)`

And, factor out the GCF of the two groups.

`=(x-1)(4x-9).`

**Hence, `4x^2-13x+9=(x-1)(4x-9)` .**

Factor: `x^2-9x+8`

What 2 numbers multiply to give (+)8 and add to give (-)9?

Factors of 8 are: `+-` 1 and `+-` 8 or `+-` 2 and `+-` 4

Since we need a sum of -9, the only factors that work are -1 and -8.

Therefore: `x^2-9x+8 = (x-8)(x-1)`

`4x^2-13x+9 `

`(4x-9)( x-1)`

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**QUESTION:-**

**Factor x^2-9x+8 And 4x^2-13x+9**

- `x^2-9x+8=0`
- `4x^2-13x+9=0`

**SOLUTION:-**

1.

`x^2-9x+8=0`

The method that we have to use is factorization since it is required in the question:-

Divide the middle number in such a way that the same number comes and when taken common's then the bracket value must be same. Like this;

`x^2-9x+8=0`

`x^2-x-8x+8=0`

`x(x-1)-8(x-1)=0`

Separate the two solutions:-

`x-8=0,x-1=0`

`x=8,x=1`

Hence the solution set is: {8,1}.

2. `4x^2-13x+9=0`

According to the method of factorization we have to divide the equation:-

`4x^2-13x+9=0`

`4x^2-4x-9x+9=0`

`4x(x-1)-9(x-1)=0`

Hence separating values;

`4x-9=0,x-1=0`

`4x=9,x=1`

`x=9/4,x=1`

Hence the solution set: {9/4,1}

Hence Solved!

When it comes to factoring, there are several different ways, and it really depends on preference and the type of problem. I personally would use the box method here.

Basically, draw a box and draw 4 smaller boxes inside, like a 4-square court. Put the first term in the 1st box on the top left, and the last term on the bottom right. From there you find two numbers that will add to make your middle term but multiply to make your last. And just multiply all connecting columns and rows, add the diagonally when similar terms.

Factoring:

`x^2-9x+8`

` 4x^2-13x+9`

So for the first equation you decide what factors of eight make nine which are 1 and 8. so you break it down and end up with:

`(x-1) (x-8)`

For the second equation you decide what factors of nine give you thirteen with the 4x in mind. You should end up with:

`(4x-9)(x-1)`

Factor x^2-9x+8 And 4x^2-13x+9

To factor x^2 - 9x + 8 you have to find what 2 numbers multipled together equals 8 but when added equals -9

So when x^2-9x+8 is factored the answer is (x - 1)(x - 8)

To factor 4x^2-13x+9 you do the same thing

So the answer for the second one is ** **(4x-1)(x-1)

To factor the two given equations we would have to expand the middle term.

For the first equation, x^2 -9x +8 we need the factors of 8 that could be the sum or difference of 9. The factors of 8 are 8 and 1, and 4 and 2. It is logical to say that 8 and 1 are the probable factors to use. For the sign, think how we could get a positive 8 and a negative 9. Remember, two negatives have a positive product.

(x - 8) (x - 1) Using the FOIL method

= x^2 -8x - x + 8

= x^2 -9x +8

Therefore **the factors of x^2 - 9x + 8 are (x-8)(x-1)**

For the second equation, 4x^2 - 13x + 9, we are going to do the same thing but this is more complicated since there is a coefficient which is 4. Figure out factors of 9 that could give a sum or difference of 13, BUT considering that one x has a coefficient of four. The factors of 9 are 3 and 3, and 9 and 1. Logically, we should apply 9 and 1. But it is a matter of trial and error which one should go with 4 and which won't. The signs are also the same with the first equation.

(4x - 9)(x-1)

4x^2 - 4x - 9x + 9

= 4x^2 - 13x +9

Therefore **the factors of 4x^2 - 13x + 9 are (4x-1)(x-1)**

**A.** When you factor you have to think about each part individually. For x^2-9x+8 you must first think what two things will multiply to give you an x^2? x and x will multiply to give you x^2, so that would be the first part of both your factors. (x )(x )

Next, you must think what two numbers will give you an 8 but also, when added or subtracted, give you a 9 in the middle. The numbers 8 and 1 can be multiplied to get 8 but also added to get 9, so this would be the second parts. (x 8)(x 1)

Now you must figure out the signs which will create a negative 9x and a positive 8. Since two negatives make a positive, you can have a -8 and a -1 that can multiply to make a positive 8 and add to make a negative 9. So your factors are *(x - 8) and (x - 1)*.

**B.** For 4x^2-13x+9, to get a 4x^2 you'd multiple 4x and x. (4x )(x )

Now you have to find two numbers that will multiply to be a 9 and add/subtract to be 13. However, you must also account for the 4x because when multiplying, the 4x affects these numbers. The numbers 9 and 1 will multiply to get 9, and if you pair the 1 with the single x, you end up getting a 4x and 9x, which adds to 13. (4x 9)(x 1).

To get a negative 13 and a positive 9 you can use two negatives like in the previous problem. Your two factors are *(4x - 9) and (x - 1)*.

Factoring (a) `x^2 -9x+8` and (b) `4x^2 -13x+9`

For (a): First check whether the coefficient of `x^2 ` is one. If it is, proceed to find the numbers that when added gives -9 and when multiplied give 8.

Those numbers are -8 and -1

So `x^2 -9x + 8` will be `(x-1)(x-8)`

For (b): The coefficient for `x^2` for part (b) is 4 so you cannot simply find the values that add to form -13 and multiply to form 9. So you will need to do the following steps. Find the numbers that have the product of 4x9=36 and when added together give -13. These values are -4 and -9.For this equation you will need to split -13x to -4x and -9x. The equation will become `4x^2-4x-9x+9.` This will become `4x(x-1)-9(x-1)`

Factoring part (b) will give you `(4x-9)(x-1)` .

For both of these questions, the process is very similar. We know the equation is in the form ax^2+bx+c. So you'd solve this by asking yourself what two numbers m and n multiply to give ac and adds up to give b?

For `x^2-9x+8`

What two numbers have a product of 8 and a sum of -9?

The answer is** -1** and **-8**, so the factors are **(x-1)(x-8)**.

For `4x^2-13x+9`

Find two numbers that have a product of 4x9=36 and a sum of -13

In this case, the answer is **-4** and **-9**. Now, since a is not 1, you cannot simply put (x-4)(x-9), nor can you say it factors into (4x-4)(4x-9).

Instead, you split the -13x into two, into -4x-9x,

So the equation becomes `4x^2-4x-9x+9`

Then you can group them together resulting in **4x(x-1)-9(x-1)**** = (x-1)(4x-9)**