Question

h^2 + 11h +18. The factored expression is

Answer 1

Answer:

(h+9)⋅(h+2)

Step-by-step explanation:

1.1     Factoring  h2+11h+18  

The first term is,  h2  its coefficient is  1 .

The middle term is,  +11h  its coefficient is  11 .

The last term, "the constant", is  +18  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 18 = 18  

Step-2 : Find two factors of  18  whose sum equals the coefficient of the middle term, which is   11 . -18    +    -1    =    -19  

     -9    +    -2    =    -11  

     -6    +    -3    =    -9  

     -3    +    -6    =    -9  

     -2    +    -9    =    -11  

     -1    +    -18    =    -19  

     1    +    18    =    19  

     2    +    9    =    11    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  2  and  9  

                    h2 + 2h + 9h + 18

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

                   h • (h+2)

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

                   9 • (h+2)

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

                   (h+9)  •  (h+2)

            Which is the desired factorization

Answer 2

Answer:

$\boxed{ \bold{ \huge{ \boxed{ \sf{(h + 9)(h + 2)}}}}}$

Step-by-step explanation:

$\sf{ {h}^{2} + 11h + 18}$

Here, we have to find out two numbers that adds to 11 and multiplies to 18

$\dashrightarrow{ \sf{ {h}^{2} + (9 + 2)h + 18}}$

Distribute h through the parentheses

$\dashrightarrow{ \sf{ {h}^{2} + 9h + 2h + 18}}$

Take h as common. Similarly, take 2 as common

$\dashrightarrow{ \sf{h(h + 9) + 2(h + 9)}}$

$\dashrightarrow{ \sf{(h + 9)(h + 2)}}$

Hope I helped!

Best regards! :F