Answer:
20. [tex]x\left(x-6\right)\left(x+8\right)[/tex]
22. [tex]2\left(x+1\right)\left(x+4\right)[/tex]
24. [tex]5m\left(m-1\right)\left(m+7\right)[/tex]
Step-by-step explanation:
20. [tex]x^3+2x^{2} -48x[/tex]
The GCF is x, so you group it out of the equation first.
[tex]x(x^{2} +2x-48)[/tex]
Then, you find 2 numbers that will equal to 2 when you add them and will equal to -48 when you multiply them.
[tex]?+?=2\\?*?=-48[/tex]
The two numbers would be -6 and 8. You then differentiate the squares.
[tex]x\left(x-6\right)\left(x+8\right)[/tex]
22. [tex]2x^{2} +10x+8[/tex]
The GCF is 2, so you must group it out.
[tex]2(x^{2} +5x+4)[/tex]
Find the two numbers that will equal to 5 when you add them and will equal to 4 when you multiply them.
[tex]?+?=5\\?*?=4[/tex]
The two numbers would be 1 and 4. Finally, differentiate the squares.
[tex]2\left(x+1\right)\left(x+4\right)[/tex]
24. [tex]5m^{3} +30m^2-35m[/tex]
The GCF is 5m, so you must group it out.
[tex]5m(m^2+6m-7)[/tex]
Find the two numbers that will equal to 6 when you add them and will equal to -7 when you multiply them.
[tex]?+?=6\\?*?=-7[/tex]
The two numbers would be -1 and 7. Finally, differentiate the squares.
[tex]5m\left(m-1\right)\left(m+7\right)[/tex]
