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2x(3x+5)+3(3x+5)=ax^(2)+bx+c In the eq...

`2x(3x+5)+3(3x+5)=ax^(2)+bx+c`
In the equation above, a, b, and c are constants. If the equation is true for all values of x, what is the value of b ?

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The correct answer is 19. Since `2x(3x + 5) + 3(3x + 5) = ax^(2) + bx + c` for all values of x, the two sides of the equation are equal, and the value of b can be determined by simplifying the left-hand side of the equation and writing it in the same form as the right-hand side. Using the distributive property, the equation becomes `(6x^(2) + 10x) + (9x + 15) = ax^(2) + bx + c`. Combining like terms gives `6x^(2) + 19x + 15 = ax^(2) + bx + c`. The value of b is the coefficient of x, which is 19.
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