Question

4x^2-2x+12 divided by 8x solve the following​

Answer 1

Answer:

Step by Step Solution:

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STEP

1

:

Equation at the end of step

1

:

STEP

2

:

8x2 + 2x + 12

Simplify —————————————

4x - 1

STEP

3

:

Pulling out like terms :

3.1 Pull out like factors :

8x2 + 2x + 12 = 2 • (4x2 + x + 6)

Trying to factor by splitting the middle term

3.2 Factoring 4x2 + x + 6

The first term is, 4x2 its coefficient is 4 .

The middle term is, +x its coefficient is 1 .

The last term, "the constant", is +6

Step-1 : Multiply the coefficient of the first term by the constant 4 • 6 = 24

Step-2 : Find two factors of 24 whose sum equals the coefficient of the middle term, which is 1 .

-24 + -1 = -25

-12 + -2 = -14

-8 + -3 = -11

-6 + -4 = -10

-4 + -6 = -10

-3 + -8 = -11

-2 + -12 = -14

-1 + -24 = -25

1 + 24 = 25

2 + 12 = 14

3 + 8 = 11

4 + 6 = 10

6 + 4 = 10

8 + 3 = 11

12 + 2 = 14

24 + 1 = 25

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Polynomial Long Division :

3.3 Polynomial Long Division

Dividing : 4x2+x+6

("Dividend")

By : 4x-1 ("Divisor")

dividend 4x2 + x + 6

- divisor * x1 4x2 - x

remainder 2x + 6

- divisor * 0x0

remainder 2x + 6

Quotient : x

Remainder : 2x+6

Final result :

2 • (4x2 + x + 6)

—————————————————

4x - 1