Question

Thinking: Two students were having a discussion. They stated:“Since we factored f(x) = 2x2 + 3x + 1 into (2x+1)(x+1) we could say this:If we let h(x) = 2x + 1 and g(x) = x + 1, then we can say f(x) = h(x)g(x)” Howmight you verify their statement?

Answer 1

Given:

If we let h(x) = 2x + 1 and g(x) = x + 1 and

$f(x)=2x^2+3x+1$

Required:

How might you verify their statement?

Explanation:

We have h(x) and g(x)

$\begin{gathered} =h(x)g(x) \\ =(2x+1)(x+1) \\ =2x^2+2x+x+1 \\ 2x^2+3x+1=f(x) \\ f(x)=h(x)g(x) \end{gathered}$

Answer:

Hence, verified the statement.