Question

you try it: which graph has a factor of (x - 1)?

Explanation:

Step1: Recall Factor Theorem

The Factor Theorem states that if \((x - a)\) is a factor of a polynomial \(f(x)\), then \(f(a)=0\), meaning the graph of the polynomial intersects the \(x\)-axis at \(x = a\). For the factor \((x - 1)\), we need to find the graph where the polynomial has a root at \(x = 1\) (i.e., the graph crosses or touches the \(x\)-axis at \(x = 1\)).

Step2: Analyze the Graphs

• For the first graph (left), we check the \(x\)-intercepts. From the grid, one of the \(x\)-intercepts appears to be at \(x = 1\) (since it crosses the \(x\)-axis at a point where \(x = 1\) based on the grid lines).
• For the second graph (right), the \(x\)-intercepts are at negative values (around \(x=-2\) or \(x = 3\) maybe, but not \(x = 1\)) as per the grid (with \(x = 0\) in the middle, and the intercepts are left of \(0\) and right but not at \(1\)).

So the graph with a root at \(x = 1\) (hence factor \((x - 1)\)) is the first graph (left one, assuming the left graph has an \(x\)-intercept at \(x = 1\)).

Answer:

The left - hand graph (the first graph shown) has a factor of \((x - 1)\) because it intersects the \(x\)-axis at \(x = 1\) (by the Factor Theorem, since \(f(1)=0\) implies \((x - 1)\) is a factor).