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QuestionAnatomy and Physiology

Open parenthesis, a x plus 3, close parenthesis, times, open parenthesis, 5 x squared, minus b x, plus 4, close parenthesis, equals, 20 x cubed, minus 9 x squared, minus 2 x, plus 12 The equation above is true for all $x$, where $a$ and $b$ are constants. What is the value of $a b$ ? A. 18 B. 20 C. 24 D. 40
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Answer

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Step 1
: Compare the given equation to the general form of a quadratic equation.

(ax+3)(5x2−bx+4)=20x3−9x2−2x+12(ax+3)(5x^2-bx+4) = 20x^3-9x^2-2x+12
The given equation is in the form of a factored quadratic, which can be written as:

Step 2
: Expand the left side of the equation.

ax(5x2)+ax(−bx)+ax(4)+3(5x2)+3(−bx)+3(4)=20x3−9x2−2x+12ax(5x^2) + ax(-bx) + ax(4) + 3(5x^2) + 3(-bx) + 3(4) = 20x^3-9x^2-2x+12
Expand the product on the left side of the equation:

Final Answer

The value of $ab$ is 24, which corresponds to option C.

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