Answer:
Explanation:
Given the expression:
[tex]3y^2+5y-2[/tex]
We want to write the given expression in the form:
[tex](ay-b)(y+c)[/tex]
That is, to factorize the expression.
When an expression is to be factorized, follow the steps below:
Step 1: Multiply the coefficient of x² and the constant.
[tex]-2\times3y^2=-6y^2[/tex]
Step 2: Find two terms that multiply to give the product -6y², and add to give the middle term, 5y. To do this, list the factors of -6: 1, 2,3, and 6
[tex]\begin{gathered} 6y\times-1y=-6y^2 \\ 6y+-y=5y \end{gathered}[/tex]
Step 3: Rewrite the middle term, 5y with those numbers.
[tex]\begin{gathered} 3y^{2}+5y-2 \\ =3y^2+6y-y-2 \end{gathered}[/tex]
Step 4: Factor the first two and last two terms separately. Ensure that the expression in the brackets is the same.
[tex]\begin{gathered} =3y(y+2)-1(y+2) \\ =(3y-1)(y+2) \end{gathered}[/tex]
