Question

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the

following cases:

p(x) = 2x³+x²-2x-1,g(x)=x+1.





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Answer 1

Answer:

Step-by-step explanation:

first find the zero of the polynomial then subsitute it your answer is ready  x=-1

Answer 2

ɢɪᴠᴇɴ:

• p(x) = 2x³+x²-2x-1
• g(x)= x+1

ᴛᴏ ғɪɴᴅ:

• To find g(x) is the factor of p(x)?

sᴏʟᴜᴛɪᴏɴ:

p(x) = 2x³+x²–2x–1 , g(x) = x+1

So,

g(x) = 0

⇒ x+1 = 0

⇒ x = −1

∴ Zero of g(x) is -1.

Now,

p(−1) = 2(−1)³ + (−1)²– 2(−1) –1

= −2 + 1 +2 −1

= 0

∴ By factor theorem, g(x) is a factor of p(x).