The expression 3 x - 23 19 x + 6 is equivalent to the expression a x 2 + b

Question

The expression 3 x - 23 19 x + 6 is equivalent to the expression a x 2 + b x + c , where a , b , and c are constants. What is the value of b ?

Accepted Answer

The correct answer is - 419 . It's given that the expression 3 x - 23 19 x + 6 is equivalent to the expression a x 2 + b x + c , where a , b , and c are constants. Applying the distributive property to the given expression, 3 x - 23 19 x + 6 , yields 3 x 19 x + 3 x 6 - 23 19 x - 23 6 , which can be rewritten as 57 x 2 + 18 x - 437 x - 138 . Combining like terms yields 57 x 2 - 419 x - 138 . Since this expression is equivalent to a x 2 + b x + c , it follows that the value of b is - 419 .

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