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what are the factors of x²-2x-24​

Sagot :

Ayvervillanuevaidn

✏️what are the factors of x²-2x-24​

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➡ Solution

STEP1: Trying to factor by splitting the middle term

1.1    Factoring  [tex]x^{2} -2x-24[/tex]

The first term is,  [tex]x^{2}[/tex]  its coefficient is  1 .

The middle term is,  -2x  its coefficient is  -2 .

The last term, "the constant", is  -24

Step-1 : Multiply the coefficient of the first term by the constant   1 • -24 = -24

Step-2 : Find two factors of  -24  whose sum equals the coefficient of the middle term, which is   -2 .

 -24    +    1    =    -23  

     -12    +    2    =    -10  

     -8    +    3    =    -5  

     -6    +    4    =    -2  

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  4

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-6)

Add up the last 2 terms, pulling out common factors :

                   4 • (x-6)

Step-5 : Add up the four terms of step 4 :

                   (x+4)  •  (x-6)

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Final result :

 (x + 4) • (x - 6)

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