Polynomial Multiplication

Question

0

485

3

+193

Find the constant $t$ such that

$(5x^2 - 6x + 7)(4x^2 +tx + 10) = 20x^4 -54x^3 +114x^2 -102x +70.$

clairepow Feb 14, 2021

ElectricPavlov · Answer 1 · 2021-02-14T08:50:53

5x² * tx + -6x * 4x² = -54 x^3

5t - 24 = -54

5t = -30

t =-6

Logarhythm · Answer 2 · 2021-02-14T08:57:36

(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)x³t = -6

114x² = (78 - 6t)x²

t = -6

-102x = (7t - 60)x

t = -6

Melody · Answer 3 · 2021-02-14T10:06:41

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.