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The expression \(5h^{2}-40h+75\) factors to \(5(h-5)(h-3)\).
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The Deep Dive
To factor the expression \( 5 h^{2}-40 h+75 \) completely, first, we can factor out the greatest common factor, which is 5: \[ 5(h^{2} - 8h + 15) \] Next, we need to factor the quadratic \( h^{2} - 8h + 15 \). We look for two numbers that multiply to 15 and add to -8. Those numbers are -3 and -5. So we can rewrite the quadratic as: \[ 5(h - 3)(h - 5) \] The completely factored form of the expression is: \[ 5(h - 3)(h - 5) \]
