which is a factor of trinomial t^4-5qt^2-24q^2
A (t^2+8q)
B (t^2+3q)
C (t^2+3)
D (t^2+8)
2 answers
(t^2 - 8q)(t^2 + 3q)
t ^ 4 - 5 q t ^ 2 - 24 q ^ 2 =
t ^ 4 - 8 q t ^ 2 + 3 q t ^ 2 - 24 q ^ 2 =
t ^ 4 - 8 q t ^ 2 + 3 q t ^ 2 - 24 q ^ 2 =
( - 24 q ^ 2 + 3 q t ^ 2 ) + ( - 8 q t ^ 2 + t ^ 2 * t ^ 2 ) =
3 q ∙ ( - 8 q + t ^ 2 ) + t ^ 2 ∙ ( - 8 q + t ^ 2 ) =
( - 8 q + t ^ 2 ) ∙ 3 q + ( - 8 q + t ^ 2 ) ∙ t ^ 2 =
( - 8 q + t ^ 2 ) ∙ ( 3 q + t ^ 2 ) =
( t ^ 2 - 8 q ) ∙ ( t ^ 2 + 3 q )
( t ^ 2 - 8 q ) ∙ ( t ^ 2 + 3 q ) are factors of t ^ 4 - 5 q t ^ 2 - 24 q ^ 2
So t ^ 2 + 3 q is one factor of trinomial
Answer B
t ^ 4 - 8 q t ^ 2 + 3 q t ^ 2 - 24 q ^ 2 =
t ^ 4 - 8 q t ^ 2 + 3 q t ^ 2 - 24 q ^ 2 =
( - 24 q ^ 2 + 3 q t ^ 2 ) + ( - 8 q t ^ 2 + t ^ 2 * t ^ 2 ) =
3 q ∙ ( - 8 q + t ^ 2 ) + t ^ 2 ∙ ( - 8 q + t ^ 2 ) =
( - 8 q + t ^ 2 ) ∙ 3 q + ( - 8 q + t ^ 2 ) ∙ t ^ 2 =
( - 8 q + t ^ 2 ) ∙ ( 3 q + t ^ 2 ) =
( t ^ 2 - 8 q ) ∙ ( t ^ 2 + 3 q )
( t ^ 2 - 8 q ) ∙ ( t ^ 2 + 3 q ) are factors of t ^ 4 - 5 q t ^ 2 - 24 q ^ 2
So t ^ 2 + 3 q is one factor of trinomial
Answer B