1. **State the problem:** We are given the function $$G(x) = (x + 1)^2 (x - 1)$$ and asked to find: (a) The x-intercepts of the graph of $$G$$. (b) The x-intercepts of the graph of $$y = G(x + 5)$$. 2. **Recall the formula and rules:** The x-intercepts of a function are the values of $$x$$ for which $$G(x) = 0$$. For a product of factors, the function equals zero when any factor equals zero. 3. **Find x-intercepts of $$G(x)$$:** Set $$G(x) = 0$$: $$ (x + 1)^2 (x - 1) = 0 $$ This product is zero if either: $$ (x + 1)^2 = 0 \quad \text{or} \quad (x - 1) = 0 $$ Solve each: $$ (x + 1)^2 = 0 \implies x + 1 = 0 \implies x = -1 $$ $$ (x - 1) = 0 \implies x = 1 $$ So the x-intercepts of $$G$$ are $$x = -1$$ and $$x = 1$$. 4. **Find x-intercepts of $$y = G(x + 5)$$:** Substitute $$x + 5$$ into $$G$$: $$ G(x + 5) = ((x + 5) + 1)^2 ((x + 5) - 1) = (x + 6)^2 (x + 4) $$ Set equal to zero: $$ (x + 6)^2 (x + 4) = 0 $$ This is zero if: $$ (x + 6)^2 = 0 \implies x + 6 = 0 \implies x = -6 $$ or $$ (x + 4) = 0 \implies x = -4 $$ 5. **Final answers:** (a) The x-intercepts of $$G$$ are $$-1, 1$$. (b) The x-intercepts of $$y = G(x + 5)$$ are $$-6, -4$$.