Factonie \( 5 x^{2}-21 x+18 \)

To factor the expression \( 5x^{2}-21x+18 \), we can look for two numbers that multiply to \( 5 \times 18 = 90 \) and add up to \(-21\). Those two numbers are \(-15\) and \(-6\). We then rewrite the middle term using these numbers: \( 5x^{2} - 15x - 6x + 18 \) Next, we group the terms: \( (5x^{2} - 15x) + (-6x + 18) \) Factoring out the common factors in each group gives us: \( 5x(x - 3) - 6(x - 3) \) Now, we can factor out the common binomial \( (x - 3) \): \( (5x - 6)(x - 3) \) So, the fully factored form of \( 5x^{2} - 21x + 18 \) is \( (5x - 6)(x - 3) \). Have fun playing with those factors! You can verify by expanding them back to check if you get back to the original expression. And remember, factoring is like solving a mystery: finding the right clues (factors) leads you back to the original equation!