Question

show that (x-2) and (x+3) are the factors of x^3-6x^2-13x+42.

Answer 1

Step-by-step explanation:

Hi ,

Let p( x ) = x³ - 6x² - 13x + 42

i ) p( 2 ) = 2³ - 6 × 2² - 13 × 2 + 42

= 8 - 24 - 26 + 42

= 50 - 50

p( 2 ) = 0

( x - 2 ) is a factor of p( x )

ii ) p( 3 ) = 3³ - 6 × 3² - 13 × 3 + 42

= 27 - 54 - 39 + 42

= 69 - 93

= - 24

p( 3 ) ≠ 0

Therefore ,

x - 3 is not a factor of p( x ).

iii ) p( 7 ) = 7³ - 6 × 7² - 13 × 7 + 42

= 343 - 294 - 91 + 42

= 385 - 385

p( 7 ) = 0

x - 7 is a factor of p( x )

I hope this helps you.

Answer 2

Answer:

Just verify both solutions by equating to zero and then substitute in main equation

Step-by-step explanation:

Follow steps according to the image