Question

The expression (a + 1)x^3 + (2 – 3a)x^2 – (3a – 1)x +

2a – 13 has a factor x – 3. Find the value of a and
hence find the other two factors of the expression.​

Answer 1

the other two factors, (2x+1)(3x+1)

Explanation:

(a + 1)x³ + (2 – 3a)x² – (3a – 1)x + 2a – 13 = 0 ...(1)

x-3 = 0 x = 3

(a + 1)*3³ + (2 – 3a)*3² – (3a – 1)*3 + 2a – 13 = 0

-7a + 35 = 0

a = 5 .. substitute to (1)

6x³ -13x² – 14x -3 = 0

(x-3)(6x²+px+1) = 0 ..... 1*x * 6x² = 6x³, -3 * 1 = -3

6x³ +(p-18)x² +(1-3p)x -3 = 0

p-18 = -13

p = 5

6x²+5x+1 = (2x+1)(3x+1)