Which Of The Following Is The Factored Form Of X^3 + 3x^2 2013 10x 2013 24?, A. (X + 4)(X 2013 3)(X + 2) , B. (X 2013 4)(X 2013 3)(X 2013 2) , C. (X 2
Which of the following is the factored form of x^3 + 3x^2 – 10x – 24?
a. (x + 4)(x – 3)(x + 2)
b. (x – 4)(x – 3)(x – 2)
c. (x – 4)(x – 3)(x + 2)
d. (x + 4)(x + 3)(x – 2)
Factoring Polynomials:
Listing Method:
The factored form of x³ + 3x² – 10x – 24 is (x + 4)(x – 3)(x + 2).
Solution:
- List all the possible factors of the first term.
x³ = (x)(x)(x)
2. List all the possible factors of the last term.
-24 = (1)(-24); (-1)(24); (2)(-12); (-2)(12); (3)(-8); (-3)(8); (4)(-6); (-4)(6)
3. From the list above, form the factors. Make sure that the 3 factors of
-24 will have a sum of -10 which is the middle term of the given
polynomial.
(x + 2)(x – 3)(x + 4)
4. To check multiply (x + 2)(x – 3)(x + 4).
x + 2
x – 3
x² + 2x
-3x – 6
x² – x – 6
x + 4
x³ – x² – 6x
4x² – 4x – 24
x³ + 3x² – 10x - 24
Definition:
A polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, with exponents which are not negative numbers.
Code: 10.3.1.2
For more details regarding division of polynomials, go to the following links:
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