Question

help me as soon as possible ​

Answer 1

Answer:

2x³ - 3x² - 17x + 30 = ( x - 2 ) ( x + 3 ) ( 2x - 5 )

Step-by-step explanation:

The product of the roots is -30/2 = -15.

Hoping for an integer root, just need to check divisors of -15.

f(1) = 2 - 3 - 17 + 30 ≠ 0 ... so 1 is not a root.

f(2) = 16 - 12 - 34 + 30 = 0 ... so 2 is a root, which means (x-2) is a factor.

2x³ - 3x² - 17x + 30 = ( x - 2 ) ( ax² + bx + c )

Either do long division or equate coefficients:

coeff of x³ => 2 = a

coeff of x² => -3 = b - 2a => b = 2a - 3 = 4 - 3 = 1

coeff of 1 => 30 = -2c => c = -15

2x³ - 3x² - 17x + 30 = ( x - 2 ) ( 2x² + x - 15 )

Factorizing the quadratic:

2x² + x - 15 = ( x + 3 ) ( 2x - 5 )

So...

2x³ - 3x² - 17x + 30 = ( x - 2 ) ( x + 3 ) ( 2x - 5 )