Question

If (x-2A)(2x+1) = 2x^2 - Bx + 10
A * B = ?

Answer 1

\[(x-2A)(2x+1) = 2x^2 - Bx + 10 \]
\[2x^2 + x -4Ax -2A = 2x^2 - Bx + 10 \]
\[2x^2 + (1-4A)x -2A = 2x^2 - Bx + 10 \]
\[\cancel{2x^2} + (1-4A)x -2A = \cancel{2x^2} - Bx + 10 \]
you can now see that:
\[-2A = 10\]
\[A = -\frac{10}{2}\]
\[A=-5\]
substitute into the equation for B:
\[B = 1-4A\]
\[B = 1-4(-5)\]
\[B = 20\]