(x%2B4)(x-3).jpeg "(x-1)(x+4)(x-3)")
Factoring and Finding the Roots of (x-1)(x+4)(x-3)
The expression (x-1)(x+4)(x-3) is already in factored form. This makes it easy to find its roots and understand its behavior.
What is Factoring?
Factoring is the process of breaking down an expression into its multiplicative components. In other words, we're finding the things that, when multiplied together, give us the original expression.
The Roots of the Expression
The roots of an expression are the values of x that make the expression equal to zero. To find the roots of (x-1)(x+4)(x-3), we can set each factor equal to zero and solve for x:
- x - 1 = 0 => x = 1
- x + 4 = 0 => x = -4
- x - 3 = 0 => x = 3
Therefore, the roots of the expression (x-1)(x+4)(x-3) are x = 1, x = -4, and x = 3.
Significance of the Roots
The roots of an expression tell us where the graph of the corresponding function crosses the x-axis. In the case of (x-1)(x+4)(x-3), the graph will cross the x-axis at the points (1, 0), (-4, 0), and (3, 0).
Expanding the Expression
If we wanted to, we could expand the expression (x-1)(x+4)(x-3) by multiplying each factor together. This would give us a polynomial in standard form.
(x-1)(x+4)(x-3) = (x^2 + 3x - 4)(x-3)
= x^3 - 7x + 12
However, the factored form is often more useful for understanding the behavior of the expression, as it clearly shows the roots and the factors that make up the expression.