Given:
[tex]1. -3 x^{2}\left(4 x^{3}-7\right)\\$2. $(6 x-5)(2 x+3)$\\3. $(3 x-1)\left(x^{2}+5 x-2\right)$[/tex]
To find:
The product of the polynomials.
Solution:
1. [tex]-3 x^{2}\left(4 x^{3}-7\right)[/tex] [tex]=-3 x^{2}(4 x^{3}) -3 x^{2}(-7)[/tex]
Multiply the numerical coefficient and add the powers of x.
[tex]=-12 x^{5}+21 x^{2}[/tex]
2. [tex](6 x-5)(2 x+3)=6 x(2 x+3)-5(2x+3)[/tex]
Multiply each term of first polynomial with each term of 2nd polynomial.
Multiply the numerical coefficient and add the powers of x.
[tex]=12 x^2+18x-10 x-15[/tex]
[tex]=12 x^2+8x-15[/tex]
3. [tex](3 x-1)\left(x^{2}+5 x-2\right)=3 x(x^{2}+5 x-2)-1(x^{2}+5 x-2)[/tex]
Multiply each term of first polynomial with each term of 2nd polynomial.
Multiply the numerical coefficient and add the powers of x.
[tex]=3x^{3}+15 x^2-6x-x^{2}-5 x+2[/tex]
Add or subtract like terms together.
[tex]=3x^{3}+14 x^2-11x+2[/tex]
The answer for multiplying polynomials:
[tex]1. -12 x^{5}+21 x^{2}[/tex]
[tex]2. \ 12 x^2+8x-15[/tex]
[tex]3. \ 3x^{3}+14 x^2-11x+2[/tex]
