using factor theorem show that g(x) is a factor of p(x) when - p(x) = 2x³ + 9x² - 11x - 30 , g(x) = x - 5
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Answers
Answer:
g(x) is NOT a factor of p(x)
Step-by-step explanation:
p(x) = 2x³ + 9x² - 11x -30
g(x) = x - 5
zero of g(x) is 5
p(5) = 2 (5)³ + 9 (5)² - 11 (5) - 30
= 2 (125) + 9 (25) - 55 - 30
= 250 + 225 - 55 - 30
= 475 - 85
= 390
≠ 0
Since p(5) ≠ 0
By factor theorem , g(x) is not a factor of p(x)
Answer:
Given ⤵
➡p(x) = 2x³ + 9x² - 11x - 30 , g(x) = x - 5
To find ⤵
➡g(x) is factor of p(x) using factor theorem.
Solution ⤵
⚫If f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0. Also, we can say, if (x-a) is a factor of polynomial f(x), then f(a) = 0
⚫So according to factor theorem
➡p(5) =2×5³+9×5²-11×5-30
➡2×125+9×25-55-30
➡250+225-85
➡475-85
➡390
⚫Here p(5) is not equal to zero.
✅Hence g(x) is not factor of p(x).
By long division method ⤵
x-5) 2x³+9x²-11x-30(2x²+19x+84
2x³-20x²
- +
__________
× 19x²-11x
19x²-95x
- +
___________
× 84x-30
84x-420
- +
___________
× 390
Extra points ⤵
✔According to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and 'a' is any real number, then, (x-a) is a factor of f(x), if f(a)=0. Also, we can say, if (x-a) is a factor of polynomial f(x), then f(a) = 0
Hope this is helpful to you!