Which of the following trinomials can be represented by a rectangle?

1.	Which of the following trinomials can be represented by a rectangle? a. y^2 + 3y +12 b. y^2 + 12y + 5 c. y^2 +8y + 15 d.y^2 + 14y +3
Answer» ong>Answer: ✏️ ${\huge{\blue{\mathbb{\underline{\underline{Question}}}}}}$ ✏️ Which of the FOLLOWING trinomials can be represented by a rectangle? $a. {y}^{2} + 3y +12$ $b. {y}^{2} + 12y + 5$ $c. {y}^{2} +8y + 15$ $d.{y}^{2}+ 14y +3$ ✏️ ${\huge{\blue{\mathbb{\underline{\underline{Important\ point}}}}}}$ ✏️ For being a rectangle: A trinomial have to be two different terms; One as length of the rectangle. Second as breadth of the rectangle. ✏️ ${\huge{\blue{\mathbb{\underline{\underline{Solution}}}}}}$ ✏️ So, let's factorise each trinomial to check which is a rectangle; $a. {y}^{2} + 3y +12$ ✈️This TERM can't be factorise as we don't get any FACTORS by multiplying first and last term✈️ ----------------------------------------------------------- $b. {y}^{2} + 12y + 5$ ✈️This term also can't be factorise as here also we don't get any factors by multiplying first and last term✈️ ----------------------------------------------------------- $c. {y}^{2} +8y + 15$ $=>{y}^{2}+5y+3y+15$ $=>y(y+5)+3(y+5)$ $=>(y+5)(y+3)$ As, here we get two terms as one as length (y+5) and one as breadth (y+3); So,this trinomial is represented by a rectangle. ${\pink{\mathfrak{Option\ c\ is\ correct}}}$