Question

please feel me how to solve this equation
2x³-13x²+6x+45​

Answer 1

Answer:

By the Rational Zero Theorem, if p/q is a rational zero, then p is a divisor of 45 and q is a divisor of 2.

So, p = ±(1, 3, 5, 15, 45) and q = ±(1, 2)

p/q = ±(1, 1/2, 3, 3/2, 5, 5/2, 15, 15/2, 45, 45/2)

Testing the various possibilities, we find that 5 is a zero of the polynomial.

Divide synthetically by x - 5:

5⌋ 2 -13 6 45

________10___-15___ -45

2 -3 -9 0

So, 2x3 - 13x2 + 6x + 45 = (x-5)(2x2-3x-9) = (x-5)(2x+3)(x-3)

Answer 2

Answer:

By the Rational Zero Theorem, if p/q is a rational zero, then p is a divisor of 45 and q is a divisor of 2.

So, p = ±(1, 3, 5, 15, 45) and q = ±(1, 2)

p/q = ±(1, 1/2, 3, 3/2, 5, 5/2, 15, 15/2, 45, 45/2)

Testing the various possibilities, we find that 5 is a zero of the polynomial.

Divide synthetically by x - 5:

5⌋ 2 -13 6 45

________10___-15___ -45

2 -3 -9 0

So, 2x3 - 13x2 + 6x + 45 = (x-5)(2x2-3x-9) = (x-5)(2x+3)(x-3)