Need to calculate:The factorization of x^{3}+8x^{2}-3x-24.

Need to calculate:The factorization of x^{3}+8x^{2}-3x-24.

Question
Polynomial factorization
asked 2021-01-06
Need to calculate:The factorization of \(x^{3}+8x^{2}-3x-24\).

Answers (1)

2021-01-07
Formula used:
The factors of a polynomial can be find by taking a common factor and this method is called factor by grouping,
\(ab+ac+bd+cd=a(b+c)+d(b+c)\)
\(=(a+d)(b+c)\)
Or,
\(ab-ac+bd-cd=a(b-c)+d(b-c)\)
\(=(a+d)(b-c)\)
Calculation:
Consider the polynomial \(x^{3}+8x^{2}—3x—24\).
This is a four term polynomial, factorization of this polynomial can be find by factor by grouping as,
\(x^{3}+8x^{2}—3x—24=(x^{3}+8x^{2})—(3x+24)\)
\(=x^{2}(x+8)-3(x+8)\)
As, \((x+8)\) is the common factor of the polynomial,
The polynomial can be factorized as,
\(x^{2}(x+8)—3(x+8)=(x+8)(x^{-3})\)
Therefore, the factorization of the polynomial \(x^{3}+8x^{2}—3x—24\ is\ (x + 8)(x^{2}-3)\).
0

Relevant Questions

asked 2021-05-08
Write the linear factorization and list all the zeros of \(p(x)=x^{4}+x^{3}-8x^{2}-2x+12\).
asked 2021-05-09
Choose the complete factorization of \(4x^{2} - 8x - 60\).
a)2(x + 3) (x - 5)
b)\(4(x^{2} - 2x - 15)\)
c)(2x + 6) (2x - 10)
d)4(x + 3) (x - 5)
asked 2021-06-03
Find the complete factorization of \(P(x)= x^{4} - 2x^{3} + 5x^{2} - 8x + 4\).
asked 2021-05-28
Let \(P(x)=x^{3}-3x^{2}+x-3\)
Find all the zeros of P.
Find the complete factorization of P.
asked 2021-05-27
Calculate the following limits using the factorization formula
\(x^{n}-a^{n}=1x-a21x^{n-1}+ax^{n-2}+a^{2}x^{n-3}+...+a^{n-2}x+a^{n-1}2\), where n is a positive integer a is a real number.
\(\lim_{x\rightarrow 2}\frac{x^{5}-32}{x-2}\)
asked 2021-05-27
Solve by factorization.
\(x^{2}-11x+24=0\)
asked 2021-05-01
Find all zeros of p(x), real or imaginary. \(p(x) = x^{4} + 6x^{3} + 6x^{2} -18x -27\) List all of the possible rational zeros according to the rational zero theorem and state the values for C, A, B and D in the following partial factorization of \(p(x) = (x-c)(x^{3}+Ax^{2}+Bx+D)\) State the exact answer and a decimal approximation of each zero to the tenths place
asked 2021-05-30
Use the factorization theorem to determine whether \(x-\frac{1}{2}\) is a factor of \(f(x) = 2x^{4}-x^{3}=2x-1\).
asked 2021-05-13
What is the complete factorization of \(12x^{6}-3x^{2}\)?
asked 2021-05-28
Which of the following is the correct factorization of \(x^{3} + 8\)?
...