Question

For what value of a if ,x-3 is a factor of x³ + x² -17x + a​

Answer 1

Answer:

X-3=0

X=3

X^3+X^2-17X+a=0

put x is equal to 3

3^3+3^2-17(3)+a=0

27+9-51+a=0

36-51+a=0

-15+a=0

a=15

Answer 2

Required Answer:-

Given:

• (x - 3) is a factor of the polynomial x³ + x² - 17x + a

To Find:

• The value of a.

Solution:

Given that,

→ f(x) = x³ + x² - 17x + a

If x - 3 is a factor of f(x), then,

→ f(3) = 0

→ (3)³ + (3)² - 17 × 3 + a = 0

→ 27 + 9 - 51 + a = 0

→ a + 36 - 51 = 0

→ a - 15 = 0

→ a = 15

→ Therefore, the value of a is 15.

Answer:

• a = 15

Learn More:

• Factor Theorem: If f(x) is a polynomial and α is a real number such that f(α) = 0, then, f(x - α) is a factor of f(x).
• Using the concept of factor theorem, the problem is solved.