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musiclover10045

When factoring find 2 numbers that when added together equal the middle value and when multiplied equal the last value.


min this problem the middle value is 7 and the last value is 10


5 + 2 = 7 and 5 x 2 = 10


The answer is: (x+2)(x+5)

Answer:

  • (x+2)(x+5)

Step-by-step explanation:

  • Factoring  x^2+7x+10
  • The first term is,  x^2  its coefficient is  1 .
  • The middle term is,  +7x  its coefficient is  7 .
  • The last term, "the constant", is  +10
  • Step-1 : Multiply the coefficient of the first term by the constant   1 * 10 = 10
  • Step-2 : Find two factors of  10  whose sum equals the coefficient of the middle term, which is   7 .
  •      -10    +    -1    =    -11
  •      -5    +    -2    =    -7
  •      -2    +    -5    =    -7
  •      -1    +    -10    =    -11
  •      1    +    10    =    11
  •      2    +    5    =    7    That's it
  • Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  5
  •                     x2 + 2x + 5x + 10
  • Step-4 : Add up the first 2 terms, pulling out like factors :
  •                    x * (x+2)
  •              Add up the last 2 terms, pulling out common factors :
  •                    5 * (x+2)
  • Step-5 : Add up the four terms of step 4 :
  •                    (x+5)  * (x+2)
  •             Which is the desired factorization

Solution:

  • (x+2) * (x+5)

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