Question

The common factor for the whole expression 14ksquare+49k+21 is

Answer 1

Answer:

Step by Step Solution

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STEP

1

:

Equation at the end of step 1

((2•7k2) + 49k) + 21

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

14k2 + 49k + 21 = 7 • (2k2 + 7k + 3)

Trying to factor by splitting the middle term

3.2 Factoring 2k2 + 7k + 3

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

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

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 7 .

-6 + -1 = -7

-3 + -2 = -5

-2 + -3 = -5

-1 + -6 = -7

1 + 6 = 7 That's it

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

2k2 + 1k + 6k + 3

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

k • (2k+1)

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

3 • (2k+1)

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

(k+3) • (2k+1)

Which is the desired factorization

Final result :

7 • (2k + 1) • (k + 3)

Step-by-step explanation:

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