To simplify the expression \(\left(4-2x\right)\left(\frac{-6x^2+10x+21}{4-2x}\right)\), we can cancel out the common factor \((4-2x)\) from the numerator and the denominator, as long as \(4-2x \neq 0\):
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Identify the factor that can be canceled: \[ 4 - 2x \neq 0 \Rightarrow x \neq 2 \]
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Cancel the common factor: \[ \left(4-2x\right) \left(\frac{-6x^2+10x+21}{4-2x}\right) = -6x^2 + 10x + 21 \quad \text{(for \(x \neq 2\))} \]
Thus, the simplified expression is: \[ -6x^2 + 10x + 21 \quad \text{(for \(4 - 2x \neq 0\))} \]
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