Find the value of ‘a’, if (x – a) is a factor of x3 – ax2 + x + 2.

Find the value of ‘a’, if (x – a) is a factor of x³ – ax² + x + 2.

Sum

Let f(x) = x³ – ax² + x + 2

It is given that (x – a) is a factor of f(x).

∴ Remainder = f(a) = 0

a³ – a³ + a + 2 = 0

a + 2 = 0

a = –2

shaalaa.com

Is there an error in this question or solution?

Find the value of ‘k’ if (x – 2) is a factor of x3 + 2x2 – kx + 10. Hence determine whether (x + 5) is also a factor.

Show that 3x + 2 is a factor of 3x² – x – 2.

If x + a is a common factor of expressions f(x) = x² + px + q and g(x) = x² + mx + n; show that : `a = (n - q)/(m - p)`

Use factor theorem to determine whether x + 3 is factor of x² + 2x − 3 or not.

Prove that (x - y) is a factor of yz( y² - z²) + zx( z² - x²) + xy ( x² - y²)

Find the value of a , if (x - a) is a factor of x³ - a²x + x + 2.

If x – 2 is a factor of 2x³ - x² - px - 2.
Find the value of p

Show that (x – 1) is a factor of x³ – 5x² – x + 5 Hence factorise x³ – 5x² – x + 5.

If (x + 2) and (x – 3) are factors of x³ + ax + b, find the values of a and b. With these values of a and b, factorise the given expression.

If (x – 1) divides the polynomial kx³ – 2x² + 25x – 26 without remainder, then find the value of k