Question

facktorize the 2xcube-7xsquare10x+24 polynomials usingsynthetic division method​

Answer 1

Step-by-step explanation:

Let p(x) = x3 – 3x2 – 10x + 24 Sum of all the co-efficients = 1 – 3 – 10 + 24 = 25 – 13 = 12 ≠ 0 Hence (x – 1) is not a factor. Sum of co-efficient of even powers with constant = -3 + 24 = 21 Sum of co-efficients of odd powers = 1 – 10 = – 9 21 ≠ -9 Hence (x + 1) is not a factor. p (2) = 23 – 3(22) – 10 x 2 + 24 = 8 – 12 – 20 + 24 = 32 – 32 = 0 ∴ (x – 2) is a factor. Now we use synthetic division to find other factor Thus (x – 2) (x + 3) (x – 4) are the factors. ∴ x3 – 3x2 – 10x + 24 = (x – 2) (x + 3) (x – 4)