First, factor out the common term x: x(x^2 - 3x - 4). Now, factor the quadratic x^2 - 3x - 4 to get x(x - 4)(x + 1).
Factor the polynomial x^3 - 3x^2 - 4x.
Practice Questions
Q1
Factor the polynomial x^3 - 3x^2 - 4x.
x(x^2 - 3x - 4)
x(x + 4)(x - 1)
x^2(x - 3) - 4
x(x^2 + 4)
Questions & Step-by-Step Solutions
Factor the polynomial x^3 - 3x^2 - 4x.
Step 1: Look at the polynomial x^3 - 3x^2 - 4x and find the common term in all parts. Here, the common term is x.
Step 2: Factor out the common term x from the polynomial. This gives us x(x^2 - 3x - 4).
Step 3: Now, we need to factor the quadratic expression x^2 - 3x - 4. We look for two numbers that multiply to -4 (the constant term) and add to -3 (the coefficient of x).
Step 4: The two numbers that work are -4 and +1 because -4 * 1 = -4 and -4 + 1 = -3.
Step 5: Rewrite the quadratic as (x - 4)(x + 1).
Step 6: Combine everything together. The fully factored form of the polynomial is x(x - 4)(x + 1).
Factoring Polynomials – The process of breaking down a polynomial into simpler components (factors) that, when multiplied together, give the original polynomial.
Common Factor Extraction – Identifying and factoring out the greatest common factor from all terms in a polynomial.
Quadratic Factoring – The method of factoring a quadratic expression into the product of two binomials.
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