Check whether the following are factors of x^3-5x^2-2x+24or not check for (x+4) ,(x+3),(x+2),(x+8).
Answers
Answer:
Step-by-step explanation:
→ p(x) = x³ - 5x² - 2x + 24
→ Factor : (x+4)
x + 4 = 0
x = -4
p(-4) = (-4)³ - 5(-4)² - 2(-4) + 24
= -64 - 5(16) - (-8) + 24
= -64 - 80 + 8 +24
= -112
-112 ≠ 0
Hence (x+4) is not a factor.
→ Factor : (x+3)
x + 3 = 0
x = -3
p(-3) = (-3)³ - 5(-3)² - 2(-3) + 24
= -27 - 45 + 6 + 24
= -42
-42 ≠ 0
Hence (x+3) is not a factor.
→ Factor : (x+2)
x + 2 = 0
x = -2
p(-2) = (-2)³ - 5(-2)² - 2(-2) + 24
= -8 - 5(4) - (-4) + 24
= -8 - 20 + 4 + 24
= 0
0 = 0
Hence (x+2) is a factor.
→ Factor : (x+8)
x + 8 = 0
x = -8
P(-8) = (-8)³ -5(-8)² - 2(-8) + 24
= -512 - 5(64) - (-16) + 24
= -512 - 320 +16 +24
= -792
-792 ≠ 0
Hence (x+8) is not a factor.
→ (x + 2) is a factor of x³ - 5x² - 2x + 24