Ask question

# Write the final factorization for each problem. 12a^3 + 20a^2b - 9ab^2 - 15b^3 # Write the final factorization for each problem. 12a^3 + 20a^2b - 9ab^2 - 15b^3

Question
Polynomial factorization asked 2021-02-25
Write the final factorization for each problem.
$$\displaystyle{12}{a}^{{3}}+{20}{a}^{{2}}{b}-{9}{a}{b}^{{2}}-{15}{b}^{{3}}$$

## Answers (1) 2021-02-26
Step 1
GCF of $$\displaystyle{12}{a}^{{3}}{\quad\text{and}\quad}{20}{a}^{{2}}{b}{i}{s}={4}{a}^{{2}}$$
GCF of $$\displaystyle-{9}{a}{b}^{{2}}{\quad\text{and}\quad}-{15}{b}^{{3}}{i}{s}=-{3}{b}^{{2}}$$
Factor out $$\displaystyle{4}{a}^{{2}}$$ from the first two terms and then factor out $$\displaystyle-{3}{b}^{{2}}$$ from the last two terms.
$$\displaystyle{12}{a}^{{3}}+{20}{a}^{{2}}{b}-{9}{a}{b}^{{2}}-{15}{b}^{{3}}$$
$$\displaystyle={4}{a}^{{2}}{\left({3}{a}+{5}{b}\right)}-{3}{b}^{{2}}{\left({3}{a}+{5}{b}\right)}$$
Step 2
Then we can factor out (3a+5b) from both terms.
$$\displaystyle{4}{a}^{{2}}{\left({3}{a}+{5}{b}\right)}-{3}{b}^{{2}}{\left({3}{a}+{5}{b}\right)}$$
$$\displaystyle={\left({3}{a}+{5}{b}\right)}{\left({4}{a}^{{2}}-{3}{b}^{{2}}\right)}$$
Result:$$\displaystyle{\left({3}{a}+{5}{b}\right)}{\left({4}{a}^{{2}}-{3}{b}^{{2}}\right)}$$

### Relevant Questions 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 2021-05-08
Write the linear factorization and list all the zeros of $$p(x)=x^{4}+x^{3}-8x^{2}-2x+12$$. asked 2021-05-03
Write the prime factorization
1)20
2)36
3)28
4)60 asked 2021-05-31
Compute the LU factorization of each of the following matrices.
$$\begin{bmatrix}-2 & 1 & 2 \\4 & 1 & -2 \\-6 & -3 & 4\end{bmatrix}$$ asked 2021-05-07
For each of the following pairs, write a and b in standard form and use these factorizations to find (a, b) and [a, b].
a = 3780, b = 16,200 asked 2021-05-14
For each of the following pairs, write a and b in standard form and use these factorizations to find (a, b) and [a, b].
a=52920, b = 25200 asked 2021-05-18
For each of the following pairs, write a and b in standard form and use these factorizations to find (a, b) and [a, b].
a=1400, b = 980 asked 2021-05-12
Use the unique factorization theorem to write the following integers in standard factored form.
2205 asked 2021-05-26
Use the unique factorization theorem to write the following integers in standard factored form.
1617 asked 2021-05-21
Use the unique factorization theorem to write the following integers in standard factored form.
4116
...