Question

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

Explanation:

Step1: Factor the quadratic expression

To factor \(2y^2 - 11y + 5\), we need to find two numbers that multiply to \(2\times5 = 10\) and add up to \(-11\). The numbers are \(-10\) and \(-1\).
Rewrite the middle term: \(2y^2 - 10y - y + 5\)
Group the terms: \((2y^2 - 10y) + (-y + 5)\)
Factor out the common factors from each group: \(2y(y - 5) - 1(y - 5)\)
Now, factor out \((y - 5)\): \((2y - 1)(y - 5)\)

Step2: Identify the factor

From the factored form \((2y - 1)(y - 5)\), we can see that \(2y - 1\) is a factor.

Answer:

\(2y - 1\)