Question

k² + 12k + 36 = 0
Answer please​

Answer 1

Answer:

Given

$k {}^{2} + 12k + 36 \\ = k {}^{2} + 6k + 6k + 36 \\ = k(k + 6) + 6(k + 6) \\k {}^{2} + 12k + 36 = (k + 6) {}^{2}$

Answer 2

Answer :

k^2 +12k + 36

• Step 1 -

trying to Factor by splitting the middle term method.

first term is k^2 it's coefficient is 1 .

the middle term is +12k it's coefficient is 12 and the last term is, ''the constant" is 36.

multiplying 1st term with last(constant) term

1×36 = 36

• Step-2 :

Find two factors of 36 whose sum equals the coefficient of the middle term, which is 12 .

(-36) +(-1) = -37

(-18) +(-2 ) = -20

(-12)+ (-3 ) = -15

(-9 )+ (-4 ) = -13

(-6 )+ (-6 ) = -12

(-4) + (-9 ) = -13

(-3) + (-12 )= -15

(-2) + (-18 ) = -20

(-1 ) + (-36)= -37

1 + 36 =37

2 +18=20

3+12= 15

4+9 = 13

6 +6 =12 ⎯ That's it.

• Step-3 :

Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 6 and 6 .

:. k^2 + 6k + 6k + 36

• 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 :

6 × (k+6)

•Step-5 :

Add up the four terms of step 4 :

(k+6) × (k+6)

Which is the desired factorization.

(k+6) 2 represents, in effect, a product of 2 terms which is equal to zero

For the product to be zero, at least one of these terms must be zero. Since all these terms are equal to each other, it actually means : k+6 = 0

k=0-6

:. k=-6