Question

Divide: 9a²+12a +4 by (3a+2)​

Answer 1

Answer:

3a + 2

Step-by-step explanation:

9a^2 + 12a + 4

= 9a^2 + 6a + 6a + 4

= 3a ( 3a + 2 ) + 2 ( 3a + 2 )

= ( 3a + 2 ) ( 3a + 2 )

( 9a^2 + 12a + 4 ) / ( 3a + 2 )

= ( 3a + 2 ) ( 3a + 2 ) / ( 3a + 2 )

= 3a + 2

Answer 2

Answer:

STEP

1

:

Equation at the end of step 1

(32a2 + 12a) + 4

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 9a2+12a+4

The first term is, 9a2 its coefficient is 9 .

The middle term is, +12a its coefficient is 12 .

The last term, "the constant", is +4

Step-1 : Multiply the coefficient of the first term by the constant 9 • 4 = 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

9a2 + 6a + 6a + 4

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

3a • (3a+2)

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

2 • (3a+2)

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

(3a+2) • (3a+2)

Which is the desired factorization

Step-by-step explanation:

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