Final answer:
Factored polynomial:
(1) 3x²+x+10= 5x-8 : 3x² - 4x + 18 = 0 { This quadratic equation cannot be factored further into linear factors.}
(2) r^2-36r : r = 0 or r = 36.
(3) 6t^2-17t=14 : t = 7/2 or t = -2/3.
Step-by-step explanation:
To factor the given polynomials, we need to find the common factors of the terms and group them together. Let's solve each equation step by step:
(1) 3x² + x + 10 = 5x - 8
Subtracting 5x and adding 8 to both sides, we get:
3x² - 5x + x + 10 + 8 = 0
Combining like terms, we have:
3x² - 4x + 18 = 0
This quadratic equation cannot be factored further into linear factors.
(2) r² - 36r = 0
Factoring out r from both terms, we get:
r(r - 36) = 0
Setting each factor equal to zero and solving for r, we have:
r = 0 or r - 36 = 0
Therefore, r = 0 or r = 36.
(3) 6t² - 17t = 14
Subtracting 14 from both sides, we get:
6t² - 17t - 14 = 0
Factoring the quadratic equation, we have:
(2t - 7)(3t + 2) = 0
Setting each factor equal to zero, we find:
2t - 7 = 0 or 3t + 2 = 0
Therefore, t = 7/2 or t = -2/3.