Question

Factorise the following Expression using multiplication frame.
$30 + 14k - {4k}^{2}$
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Answer 1

Step-by-step explanation:

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Simplification or other simple results



Enter an equation or problem30+14k−4k2

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30+14k-4k2

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1 solution(s) found

−2⋅(k−5)⋅(2k+3)

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Step by Step Solution



Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "k2"   was replaced by   "k^2". 

STEP1:Equation at the end of step 1

(14k + 30) - 22k2

STEP2:

STEP3:Pulling out like terms

 3.1     Pull out like factors :

   -4k2 + 14k + 30  =   -2 • (2k2 - 7k - 15) 

Trying to factor by splitting the middle term

 3.2     Factoring  2k2 - 7k - 15 

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

The middle term is,  -7k  its coefficient is  -7 .

The last term, "the constant", is  -15 

Step-1 : Multiply the coefficient of the first term by the constant   2 • -15 = -30 

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   -7 .

     -30   +   1   =   -29     -15   +   2   =   -13     -10   +   3   =   -7   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  3 

                     2k2 - 10k + 3k - 15

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

                    2k • (k-5)

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

                    3 • (k-5)

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

                    (2k+3)  •  (k-5)

             Which is the desired factorization

Final result :

-2 • (k - 5) • (2k + 3)

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