Question

factorise the following equation :2k2-5k+3

Answer 1

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Step by step solution :

Step  1  :

Equation at the end of step  1  :

(2k2 - 5k) - 3

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  2k2-5k-3 

The first term is,  2k2  its coefficient is  2 .

The middle term is,  -5k  its coefficient is  -5 .

The last term, "the constant", is  -3 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -3 = -6 

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   -5 .

     -6   +   1   =   -5   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -6 and  1 

                     2k2 - 6k + 1k - 3

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

                    2k • (k-3)

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

                     1 • (k-3)

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

                    (2k+1)  •  (k-3)

             Which is the desired factorization

Final result :

(k - 3) • (2k + 1)

Answer 2

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(2k2 - 5k) - 3

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 2k2-5k-3

The first term is, 2k2 its coefficient is 2 .

The middle term is, -5k its coefficient is -5 .

The last term, "the constant", is -3

Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6

Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is -5 .

-6 + 1 = -5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 1

2k2 - 6k + 1k - 3

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

2k • (k-3)

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

1 • (k-3)

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

(2k+1) • (k-3)

Which is the desired factorization

Final result :

(k - 3) • (2k + 1)