Question

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SEE THE ATTACHMENT FOR THE QUESTION AND STEP BY STEP ANSWER NEEDED

Answer 1

$\textbf{\underline{\underline{Question :- }}}$

Add the sum of 4x² - 3x - 5 and 3x² + 5x+6 to the sum of 2x² - 6x + 8 and 3x² - 5x + 6

$\textbf{\underline{\underline{Answer :-}}}$

12x² - 9x + 15

$\textbf{\underline{\underline{Explanation :-}}}$

$\star$Sum of 4x² - 3x - 5 and 3x² + 5x + 6

$\tt{\Rightarrow}$ 4x² - 3x - 5 + (3x² + 5x + 6)

$\tt{\Rightarrow}$ 4x² + 3x² - 3x + 5x - 5 + 6

$\tt{\Rightarrow}$ 7x² + 2x + 1

$\boxed{\sf{7 {x}^{2} + 2x + 1 }}$

$\star$Sum of 2x² - 6x + 8 and 3x² - 5x + 6

$\tt{\Rightarrow}$ 2x² - 6x + 8 + (3x² - 5x + 6)

$\tt{\Rightarrow}$ 2x² + 3x² - 6x - 5x + 8 + 6

$\tt{\Rightarrow}$ 5x² - 11x + 14

$\boxed{\sf{5 {x}^{2} - 11x + 14}}$

$\star$The sum of 7x² + 2x + 1 and 5x² - 11x + 14

$\tt{\Rightarrow}$ 7x² + 2x + 1 + (5x² - 11x + 14)

$\tt{\Rightarrow}$ 7x² + 5x² + 2x - 11x + 1 + 14

$\tt{\Rightarrow}$ 12x² - 9x + 15

$\boxed{\boxed{\sf{\red{12 {x}^{2} - 9x + 15 }}}}$

$\therefore$ The addition of the sum of 4x² - 3x - 5 and 3x² + 5x+6 to the sum of 2x² - 6x + 8 and 3x² - 5x + 6 is 12x² - 9x + 15 .

Answer 2

Question :

Add the sum of 4x² - 3x - 5 and 3x² + 5x+6 to the sum of 2x² - 6x + 8 and 3x² - 5x + 6

Answer:

( 4 x² - 3 x - 5 ) + ( 3 x² + 5 x + 6 )

⇒ 4 x² + 3 x² - 3 x + 5 x - 5 + 6

⇒ 7 x² + 2 x + 1 -------(1)

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

⇒ 2 x² + 3 x² - 6 x - 5 x + 8 + 6

⇒ 5 x² - 11 x + 14 ------(2)

Adding 1 and 2 we get :

⇒ 7 x² + 2 x + 1 + 5 x² - 11 x + 14

⇒ 12 x² - 9 x + 15

The resultant equation is 12 x² - 9 x + 15 .

Step-by-step explanation:

A polynomial is an expression of the form $ax^n+bx^{n-1}+...$ .

Here n has to be non-zero . n cannot be zero.

We will first group the like terms so that we can easily add the given polynomial .

Then we can add by taking common which we may or may not show in our steps .

For example :

Take any integer a , b :

$ax^2+bx^2\\\\\rightarrow x^2(a+b)$

This called taking common and it helps in adding unknown variables and two or more polynomials .