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z^2 + 11z+ 28 find the factor of polynomial

Sagot :

rdesmangles

Answer:

(z+7)*(z+4)

Step-by-step explanation:

The first term is,  z2  its coefficient is  1 .

The middle term is,  +11z  its coefficient is  11 .

The last term, "the constant", is  +28

Step-1 : Multiply the coefficient of the first term by the constant   1 • 28 = 28

Step-2 : Find two factors of  28  whose sum equals the coefficient of the middle term, which is   11 .

     -28    +    -1    =    -29

     -14    +    -2    =    -16

     -7    +    -4    =    -11

     -4    +    -7    =    -11

     -2    +    -14    =    -16

     -1    +    -28    =    -29

     1    +    28    =    29

     2    +    14    =    16

     4    +    7    =    11    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  4  and  7

                    z2 + 4z + 7z + 28

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

                   z • (z+4)

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

                   7 • (z+4)

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

                   (z+7)  •  (z+4)

            Which is the desired factorization

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