Question

(4a^2 +23a+15)÷(a+5)

Answer 1

Answer:

4a + 3

Step-by-step explanation:

The first term is,  4a2  its coefficient is  4 .

The middle term is,  +23a  its coefficient is  23 .

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

Step-1 : Multiply the coefficient of the first term by the constant   4 • 15 = 60  

Step-2 : Find two factors of  60  whose sum equals the coefficient of the middle term, which is   23 .

     -60    +    -1    =    -61  

     -30    +    -2    =    -32  

     -20    +    -3    =    -23  

     -15    +    -4    =    -19  

     -12    +    -5    =    -17  

     -10    +    -6    =    -16  

     -6    +    -10    =    -16  

     -5    +    -12    =    -17  

     -4    +    -15    =    -19  

     -3    +    -20    =    -23  

     -2    +    -30    =    -32  

     -1    +    -60    =    -61  

     1    +    60    =    61  

     2    +    30    =    32  

     3    +    20    =    23    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  3  and  20  

                    4a2 + 3a + 20a + 15

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

                   a • (4a+3)

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

                   5 • (4a+3)

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

                   (a+5)  •  (4a+3)

            Which is the desired factorization

4a + 3

Answer 2

Answer:

$4a + 3$

steps

$\frac{(4a+3)(a+5)}{a+5}$

= $4a+3$

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