Q. 3. Which expression is a factored form of 6x^2-17x+5 Do (3x-1)(2x-5) Do (3x+1)(2x-5) (3x-1)(2x+5) Do (3x+1)(2x+5)

To factor the quadratic expression $6x^2 - 17x + 5$, we need to find two binomials whose product gives us the original quadratic expression.<br /><br />Let's start by writing the quadratic expression in the form of $(ax + b)(cx + d)$, where $a$, $b$, $c$, and $d$ are constants.<br /><br />We know that the product of the first terms $ac$ should be equal to the coefficient of $x^2$, which is $6$. So, we have $ac = 6$.<br /><br />Next, we need to find the values of $b$ and $d$ such that their product is equal to the constant term, which is $5$. So, we have $bd = 5$.<br /><br />Now, we need to find the values of $b$ and $d$ such that their sum is equal to the coefficient of $x$, which is $-17$. So, we have $b + d = -17$.<br /><br />Let's try the first option: $(3x - 1)(2x - 5)$.<br /><br />Expanding this expression, we get:<br />$(3x - 1)(2x - 5) = 6x^2 - 15x - 2x + 5 = 6x^2 - 17x + 5$<br /><br />This matches the original quadratic expression, so the factored form of $6x^2 - 17x + 5$ is $(3x - 1)(2x - 5)$.<br /><br />Therefore, the correct answer is: $(3x - 1)(2x - 5)$.