Question

question 1-6
which of the following expressions is a factor of ( 2y^2 - 11y + 5 )?
( 2y - 1 )
( 2y - 5 )
( 5y - 1 )
( 2y - 10 )

Explanation:

Step1: Factor the quadratic expression

We need to factor \(2y^{2}-11y + 5\). We look for two numbers that multiply to \(2\times5 = 10\) and add up to \(- 11\). The numbers are \(-10\) and \(-1\).
So we rewrite the middle term:
\(2y^{2}-10y-y + 5\)

Step2: Group and factor

Group the first two terms and the last two terms:
\((2y^{2}-10y)-(y - 5)\)
Factor out the common factors from each group:
\(2y(y - 5)-1(y - 5)\)
Now we can factor out \((y - 5)\):
\((2y - 1)(y - 5)\)
So the factors of \(2y^{2}-11y + 5\) are \((2y - 1)\) and \((y - 5)\).

Answer:

A. \(2y - 1\)