Advertisements
Advertisements
प्रश्न
Is (x – 2) a factor of x3 – 4x2 – 11x + 30?
पर्याय
Yes
No
Nothing can be said
None of the above is true
Advertisements
उत्तर
Yes
Explanation:
Let f(x) = x3 – 4x2 – 11x + 30
Here f(2) = 23 – 4 × 22 – 11 × 2 + 30
= 8 – 16 – 22 + 30
= 0
∴ x – 2 is a factor of f(x)
संबंधित प्रश्न
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)`
(3x + 5) is a factor of the polynomial (a – 1)x3 + (a + 1)x2 – (2a + 1)x – 15. Find the value of ‘a’, factorise the given polynomial completely.
Prove that ( p-q) is a factor of (q - r)3 + (r - p) 3
Prove that (x+ 1) is a factor of x3 - 6x2 + 5x + 12 and hence factorize it completely.
Prove that (5x - 4) is a factor of the polynomial f(x) = 5x3 - 4x2 - 5x +4. Hence factorize It completely.
Show that (2x + 1) is a factor of 4x3 + 12x2 + 11 x + 3 .Hence factorise 4x3 + 12x2 + 11x + 3.
Find the value of the constants a and b, if (x – 2) and (x + 3) are both factors of the expression x3 + ax2 + bx – 12.
If ax3 + 3x2 + bx – 3 has a factor (2x + 3) and leaves remainder – 3 when divided by (x + 2), find the values of a and b. With these values of a and b, factorise the given expression.
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
If x – 3 is a factor of x2 + kx + 15; the value of k is ______.
