Question

(6x2-7x-3):(2x+3) решите пожалуйста

Answer 1

(6x²-7x-3):(2x+3)=(3х+1)(2х-3)/(2х+3)
Квадратный трехчлен ах²+bx+c можно разложить на множители по формуле.
ах²+bx+c =a(x-x₁)·(x-x₂), где х₁; х₂- корни квадратного трехчлена.
Найдем корни квадратного трехчлена 6x²-7x-3
D=(-7)²-4·6·(-3)=49+72=121=11²
х₁=(7-11)/12=-1/3; х₂=(7+11)/12=3/2
 6x²-7x-3=6(x-(-1/3))·(x-(3/2))=3((x-(-1/3))·2(x-(3/2))=(3x+1)·(2x-3)

Answer 2

To solve the expression (6x^2 - 7x - 3) divided by (2x + 3), we can use polynomial long division. Here's how you can do it step by step:

Step 1: Divide the first term of the numerator by the first term of the denominator. In this case, divide 6x^2 by 2x. The result is 3x.

Step 2: Multiply the entire denominator (2x + 3) by the result from step 1 (3x). The result is 6x^2 + 9x.

Step 3: Subtract the result from step 2 from the numerator (6x^2 - 7x - 3). This can be done by changing the signs and adding. The subtraction gives us -16x - 3.

Step 4: Bring down the next term from the numerator, which is -16x. Now we have -16x - 3.

Step 5: Repeat steps 1 to 4 until there are no more terms left in the numerator.

Step 6: Divide -16x by 2x. The result is -8.

Step 7: Multiply the entire denominator (2x + 3) by the result from step 6 (-8). The result is -16x - 24.

Step 8: Subtract the result from step 7 from the numerator (-16x - 3). This gives us 21.

Step 9: Since there are no more terms left in the numerator, the division is complete.

The final result is 3x - 8 with a remainder of 21. Therefore, the expression (6x^2 - 7x - 3) divided by (2x + 3) is equal to 3x - 8 with a remainder of 21.

I hope this helps! Let me know if you have any further questions.