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mashteyman
Problem: 2x^2+3x-9
For a polynomial of the form, ax^2+bx+c rewrite the middle term as the sum of two terms whose product a·c=2·-9=-18 and whose sum is b=3.
Factor 3 out of 3x
2x^2+3(x)-9
Rewrite 3 as -3 plus 6.
2x^2+(-3+6)x-9
Apply the distributive property
2x^2(-3x+6x)-9
Remove the parentheses
2x^2-3x+6x-9
Factor out the greatest common factor from each group
Group the first two terms and the last two terms
(2x^2-3x) (6x-9)
Factor out the greatest common factor in each group.
x(2x-3)+3(2x-3)
Factor the polynomial by factoring out the greatest common factor, 2x-3
(x+3) (2x-3). So, the quotient is 2x-3

A quotient is a quantity that is obtained by dividing two integers. The quotient of the division (2x²+3x-9) ÷ (x+3) is (2x - 3).

What is a quotient?

A quotient is a quantity that is obtained by dividing two integers. The quotient is a term that is widely used in mathematics to refer to the integer component of a division, as well as a fraction or a ratio.

The quotient of the division (2x²+3x-9) ÷ (x+3) can be found as shown below,

[tex]\dfrac{2x^2+3x-9}{(x+3)}\\\\=\dfrac{2x^2+6x - 3x -9}{(x+3)}\\\\=\dfrac{2x(x+3)-3(x+3)}{(x+3)}\\\\=\dfrac{(2x-3)(x+3)}{(x+3)}\\\\[/tex]

= (2x - 3)

Hence, The quotient of the division (2x²+3x-9) ÷ (x+3) is (2x - 3).

Learn more about Quotient:

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