Questions: عند اجراء عملية الجمع لكثيرتي الحدود (3x2+6x-4x+5)+ + 3 (4x2-5) فإن الناتج يكون : 7 × 2+x-2 7 × 2+11 x-1 7 × 2-1 7 × 2+x+1

Transcript text: عند اجراء عملية الجمع لكثيرتي الحدود (3x2+6x-4x+5)+ + 3 (4x2-5) فإن الناتج يكون : $7 \times 2+x-2$ $7 \times 2+11 x-1$ $7 \times 2-1$ $7 \times 2+x+1$

Solution

The question is asking for the result of adding two polynomials: $(3x^2 + 6x - 4x + 5) + 3(4x^2 - 5)$.

Let's break down the steps to solve this:

Simplify the first polynomial: \[ 3x^2 + 6x - 4x + 5 = 3x^2 + 2x + 5 \]
Distribute the 3 in the second polynomial: \[ 3(4x^2 - 5) = 12x^2 - 15 \]
Add the simplified first polynomial and the distributed second polynomial: \[ (3x^2 + 2x + 5) + (12x^2 - 15) = 3x^2 + 12x^2 + 2x + 5 - 15 \]
Combine like terms: \[ 15x^2 + 2x - 10 \]

Now, let's compare this result with the given options:

$7x^2 + x - 2$
$7x^2 + 11x - 1$
$7x^2 - 1$
$7x^2 + x + 1$

None of the options directly match our result of $15x^2 + 2x - 10$. It seems there might be a mistake in the provided options or the question itself. However, based on the closest match and the structure of the options, the correct answer should be:

The answer is none of the provided options directly match the correct result of $15x^2 + 2x - 10$.

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