Chapter 8, Problem 42SGR

To determine

To find: The factor of each trinomial, if trinomial cannot be factored find the prime.

Answer to Problem 42SGR

The factor of the trinomial cannot be written as a product of two trinomial and hence, it is prime.

Explanation of Solution

Given information:

The given expression is $2y^2-9y+3$

Calculation:

Considering the expression:

The objective is to factor the given expression $2y^2-9y+3$

The product of $2y^2$ term and constant term is $2y^2\times \left(3\right)=6y^2$

The middle term of the trinomial is $-9y$ .

The expression can be factored as below:-

Consider $\left(y+m\right)\left(y+p\right)$ be the factor of the trinomial $2y^2-9y+3$ .

The coefficient of product of $y^2$ term and constant term is negative and coefficient of middle term of the polynomial is negative. Thus, the value of m and p are negative.

Calculate the value of $m$ and $p$ as,

  $\begin{array}{l}\text{Factors of }9\text{ Sum of Factors}\\ 1,910\\ 3,36\end{array}$

Therefore, the factor of the trinomial cannot be written as a product of two trinomial and hence, it is prime.