Question

6x+2x²-8x³= (3+x-4x²)

Answer 1

GIVEN :

The equation is $6x+2x^2-8x^3=_(3+x-4x^2)$

TO FIND :

The missing term for the given equation

SOLUTION :

The equation is $6x+2x^2-8x^3=_(3+x-4x^2)$

Solving the given equation as below :

$6x+2x^2-8x^3=_(3+x-4x^2)$

Let the missing term be 'a'

$6x+2x^2-8x^3=a(3+x-4x^2)$

Taking the term 2x we get

$2x(3+x-4x^2)=a(3+x-4x^2)$

From the above equation we have that 2x=a

⇒ a=2x

The missing term a is the common factor of the given equation.

⇒ the missing term a is 2x.

The given equation becomes $6x+2x^2-8x^3=2x(3+x-4x^2)$

Answer 2

Solve :- 6x+2x²- 8x³ = (3+x-4x²)

Solution :-

→ 6x+2x²- 8x³ = (3+x-4x²)

→ 6x + 2x² - 8x³ = 3 + x - 4x²

→ 3 + x - 4x² + 8x³ - 2x² - 6x = 0

→ 8x³ - 6x² - 5x + 3 = 0

Now, Putting x = 1, we get,

→ f(1) = 8(1)³ - 6(1)² - 5*1 + 3

→ f(1) = 8 - 6 - 5 + 3

→ f(1) = 11 - 11

→ f(1) = 0.

Therefore, we can conclude that, (x - 1) is a factor of given polynomial .

Now, dividing f(x) = 8x³ - 6x² - 5x + 3 = 0 by (x - 1) we get,

x - 1) 8x³ - 6x² - 5x + 3 (8x² + 2x - 3

8x³ - 8x²

2x² - 5x

2x² - 2x

-3x + 3

-3x + 3

0.

Quotient = 8x² + 2x - 3

Remainder = 0

Therefore,

→ 8x³ - 6x² - 5x + 3 = 0

→ (x - 1)(8x² + 2x - 3) = 0

→ (x - 1)(8x² + 6x - 4x - 3) = 0

→ (x - 1)[2x(4x + 3) - 1(4x + 3)] = 0

→ (x - 1)(4x + 3)(2x - 1) = 0

Putting all equal to 0, we get,

→ x - 1 = 0

→ x = 0.

and,

→ 4x + 3 = 0

→ x = (-3/4).

and,

→ 2x - 1 = 0

→ x = (1/2).

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