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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 `

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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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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)` .

Approved by eNotes Editorial Team