Polynomial Multiplication

5x² * tx + -6x * 4x² = -54 x^3

5t - 24 = -54

5t = -30

t =-6

(5x² - 6x + 7)(4x² + tx + 10)

= 20x⁴ + 5tx³ + 50 x² - 24x³ - 6tx² - 60x + 28x² + 7tx + 70
 

= 20x⁴ + (5t - 24)x³ + (78 - 6t)x² + (7t - 60)x + 70

-54x³ = (5t - 24)x³
         t = -6
 

114x² = (78 - 6t)x²

        t = -6

 

-102x = (7t - 60)x

        t = -6

Don't you two realize that this child is blatently cheating.  She is not trying to learn anything.

By answering all her questions (often in full) you are condoning her behaviour.