If the given expression is rewritten in the form , where k is a constant, what

Hard-difficulty · SAT Math · Equivalent Expressions — Simplifying polynomials. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

The correct answer is 4. It’s given that $2 x squared, plus 5 x, minus 12$ can be rewritten as $open parenthesis, 2 x minus 3, close parenthesis, times, open parenthesis, x plus k, close parenthesis$ ; it follows that $open parenthesis, 2 x minus 3, close parenthesis, times, open parenthesis, x plus k, close parenthesis, equals, 2 x squared, plus 5 x, minus 12$ . Expanding the left-hand side of this equation yields $2 x squared, plus 2 k x, minus 3 x, minus 3 k, equals, 2 x squared, plus 5 x, minus 12$ . Subtracting $2 x squared$ from both sides of this equation yields $2 k x minus 3 x, minus 3 k, equals, 5 x minus 12$ . Using properties of equality, $2 k x minus 3 x, equals 5 x$ and $negative 3 k, equals negative 12$ . Either equation can be solved for k. Dividing both sides of $negative 3 k, equals negative 12$ by $negative 3$ yields $k equals 4$ . The equation $2 k x minus 3 x, equals 5 x$ can be rewritten as $x times, open parenthesis, 2 k minus 3, close parenthesis, equals 5 x$ . It follows that $2 k minus 3, equals 5$ . Solving this equation for k also yields $k equals 4$ . Therefore, the value of k is 4.

Question if-the

If the given expression is rewritten in the form , where k is a constant, what

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