Question

which expression is a factor of $10x^2 + 11x + 3$?
$\circ$ $x - 3$
$\circ$ $2x + 1$
$\circ$ $5x - 3$
$\circ$ $10x + 3$

Explanation:

Step1: Factor the quadratic expression

We need to factor \(10x^2 + 11x + 3\). We look for two numbers that multiply to \(10\times3 = 30\) and add up to \(11\). The numbers are \(5\) and \(6\) since \(5\times6 = 30\) and \(5 + 6 = 11\).
Rewrite the middle term: \(10x^2+5x + 6x + 3\)
Group the terms: \((10x^2 + 5x)+(6x + 3)\)
Factor out the common factors from each group: \(5x(2x + 1)+3(2x + 1)\)
Now, factor out the common binomial factor \((2x + 1)\): \((5x + 3)(2x + 1)\)

Step2: Identify the factor from the options

From the factored form \((5x + 3)(2x + 1)\), we can see that \(2x + 1\) is a factor.

Answer:

B. \(2x + 1\) (assuming the options are labeled with A, B, C, D where A is \(x - 3\), B is \(2x + 1\), C is \(5x - 3\), D is \(10x + 3\))