Answer:
[tex]\boxed{\boxed{\sf~a,b,and~e~are~True.}}[/tex]
Solution Steps:
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a.) [tex]\bold{(2x-1) (x^2+4x+3)= 2x^3+7x^2+2x-3}[/tex]:
Use the distributive property to multiply [tex]2x-1[/tex] by [tex]x^2+4x+3[/tex] and combine like terms:
[tex]=2x^3+7x^2+2x-3[/tex]
- So this is True.
b.) [tex]\bold{(4x^2-3x+6)+(5x^2-8)=9x^2-3x-2}[/tex]:
Combine like terms and subtract 8 from 6 to get −2:
[tex]=9x^2-3x-2[/tex]
- So this is True.
c.) [tex]\bold{(8x-4x^2)+(2x^2-5x)=-2x^4+3x}[/tex]:
Combine like terms:
[tex]=3x-2x^2[/tex]
- So this is False.
d.) [tex]\bold{(4x^2+4x-5)-(6x^2-5x-3)=-2x^2-x-8}[/tex]:
Combine like terms and add -5 and 3 to get -2:
[tex]=-2x^2+9x-2[/tex]
- So this is False.
e.) [tex]\bold{(3x^3-5+2x)-(5x-6+x^3)=2x^3-3x+1}[/tex]:
Combine like terms and add -5 and 6 to get 1:
[tex]=2x^3-3x+1[/tex]
- So this is True.
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