SOLVINGS Given the polynomial f(x) = 6x^4 – 21x^3 – 4x^2 + 24x – 35
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, The Leading Coefficient is 6 The Trailing Constant is -35.
Factors of the Leading Coefficient are 1, 2, 3 and 6 Factors of the Trailing Constant are 1, 5, 7, and 35
Testing for the rational roots, If P= 7 and Q = 2 P/Q = 3.5 F (P/Q) = 0.00
Using the Factor Theorem; which states that if P/Q is root of a polynomial then this polynomial can be divided by Q.x – PTherefore, the polynomial 6x^4 – 21x^3 – 4x^2 + 24x – 35 is divisible by 2x – 7
Factorizing 2x – 7 Divide the polynomial into two groups (6x^4 – 21x^3 and – 4x^2 + 24x – 35)
