inomial: 5x^2+39x+28 Attempt 1 out of 2

To factor the trinomial $5x^{2}+39x+28$, we need to find two numbers whose product is equal to the product of the coefficient of $x^2$ (which is 5) and the constant term (which is 28), and whose sum is equal to the coefficient of $x$ (which is 39).<br /><br />The product of the coefficient of $x^2$ and the constant term is $5 \times 28 = 140$.<br /><br />We need to find two numbers whose product is 140 and whose sum is 39. After some trial and error, we find that the numbers 35 and 4 satisfy these conditions.<br /><br />Now, we can rewrite the trinomial as $5x^{2}+35x+4x+28$.<br /><br />Next, we can factor by grouping. We group the first two terms and the last two terms together:<br /><br />$5x(x+7)+4(x+7)$.<br /><br />Now, we can factor out the common factor of $(x+7)$:<br /><br />$(5x+4)(x+7)$.<br /><br />Therefore, the factored form of the trinomial $5x^{2}+39x+28$ is $(5x+4)(x+7)$.