What is the factor of k2 + k - 42

(k + 7) • (k - 6)

Step-by-step explanation:

Final result :

 (k + 7) • (k - 6)

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "k2"   was replaced by   "k^2".

Step by step solution :

Step  1  :

Trying to factor by splitting the middle term

1.1     Factoring  k2+k-42

The first term is,  k2  its coefficient is  1 .

The middle term is,  +k  its coefficient is  1 .

The last term, "the constant", is  -42

Step-1 : Multiply the coefficient of the first term by the constant   1 • -42 = -42

Step-2 : Find two factors of  -42  whose sum equals the coefficient of the middle term, which is   1 .

     -42    +    1    =    -41

     -21    +    2    =    -19

     -14    +    3    =    -11

     -7    +    6    =    -1

     -6    +    7    =    1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6  and  7

                    k2 - 6k + 7k - 42

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

                   k • (k-6)

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

                   7 • (k-6)

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

                   (k+7)  •  (k-6)

            Which is the desired factorization

Final result :

 (k + 7) • (k - 6)

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2

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step-by-step explanation: