Question

2x²+11x-21 ________ 4x²-9

Answer 1

х+7

____

2х+3

Объяснение:

2х²+14х-3х-21. 2х×(2х+7)-3(х+7). (х+7)×(2х-3).

___________=______________=__________=

(2х-3)×(2х+3). (2х-3)×(2х+3). (2х-3) ×(2х+3)

Answer 2

To divide the polynomial $2x^2 + 11x - 21$ by $4x^2 - 9$, you can use polynomial long division. Here are the steps:

1. Divide the first term of the numerator ($2x^2$) by the first term of the denominator ($4x^2$). This gives you $\frac{2x^2}{4x^2} = \frac{1}{2}$.

2. Multiply the entire denominator ($4x^2 - 9$) by the result from step 1 ($\frac{1}{2}$). This gives you $\frac{1}{2}(4x^2 - 9) = 2x^2 - \frac{9}{2}$.

3. Subtract this result from the original numerator ($2x^2 + 11x - 21$). So, you have $2x^2 + 11x - 21 - (2x^2 - \frac{9}{2})$.

4. Now, subtract the polynomials inside the parentheses. This gives you $2x^2 + 11x - 21 - 2x^2 + \frac{9}{2}$.

5. The $2x^2$ terms cancel each other out, and you're left with $(11x - 21) + \frac{9}{2}$.

6. Next, divide the first term in this new expression ($11x$) by the first term of the denominator ($4x^2$). This gives you $\frac{11x}{4x^2} = \frac{11}{4x}$.

7. Multiply the entire denominator ($4x^2 - 9$) by the result from step 6 ($\frac{11}{4x}$). This gives you $\frac{11}{4x}(4x^2 - 9) = 11 - \frac{99}{4x}$.

8. Subtract this result from the expression in step 5 $(11x - 21) + \frac{9}{2}$. So, you have $(11x - 21) + \frac{9}{2} - (11 - \frac{99}{4x})$.

9. Now, subtract the polynomials inside the parentheses. This gives you $(11x - 21) + \frac{9}{2} - 11 + \frac{99}{4x}$.

10. Combine like terms. The $11x$ and $-11$ terms cancel each other out, and you're left with $-21 + \frac{9}{2} + \frac{99}{4x}$.

So, the result of dividing $2x^2 + 11x - 21$ by $4x^2 - 9$ is $-21 + \frac{9}{2} + \frac{99}{4x}$.