Algebra

Y=(X-1)(x+2)(x-4)

Step-by-step solution with explanation

Final Answer

Step-by-step solution

Identify the zeros from each factor

We set Y equal to zero to find where the graph crosses the x-axis. A product of factors equals zero when ANY one of the factors equals zero.

Set first factor equal to zero

If the first factor is zero, the whole product is zero. Add 1 to both sides to solve.

Set second factor equal to zero

If the second factor is zero, the whole product is zero. Subtract 2 from both sides to solve.

Set third factor equal to zero

If the third factor is zero, the whole product is zero. Add 4 to both sides to solve.

State all three solutions together

These are the three x-intercepts (roots) of the cubic function. The graph of Y crosses the x-axis at exactly these three points.

Understanding this problem

Learning Insight

This method is called the Zero Product Property. It says: if A × B × C = 0, then at least one of A, B, or C must be zero. Factored form makes finding roots easy because each factor hands you a root directly.

Quick Tip

The root from each factor is always the OPPOSITE sign of the number inside. For (x − 4), the root is +4; for (x + 2), the root is −2. Just flip the sign!

Common Mistake

Students often forget to flip the sign and write the root as the same number inside the parentheses — for example, writing x = −1 instead of x = 1 from the factor (x − 1).