What is the HCF of x^{3}-19x+30 and x^{2}-5x+6?
- A. (x+2)(x-3)
- B. (x-2)(x+3)
- C. (x+2)(x-1)
- D. (x-3)(x-2) ✓
Correct Answer: D. (x-3)(x-2)
Explanation
The polynomial x^2-5x+6 factorizes as (x-2)(x-3). Checking these roots in x^3-19x+30: for x=2, 8-38+30=0; for x=3, 27-57+30=0. Since both are factors, the HCF is (x-2)(x-3).
Related questions on Algebra
- If p + q + r = 0, then what is z^{\frac{p^2}{qr}} \times z^{\frac{q^2}{rp}} \times z^{\frac{r^2}{pq}} equal to ?
- What is the value of k for which (k^2 - 5k + 4)x^2 + (k^2 - 3k - 4)x + (k^2 - 4k) = 0 is an identity ?
- If \frac{a^2}{b^2 + c^2} = \frac{b^2}{c^2 + a^2} = \frac{c^2}{a^2 + b^2}, then what is the value of a^4 + b^4 + c^4 equal to ?
- If \frac{1}{x} = \frac{1}{p} + \frac{1}{q}, then what is \frac{pq}{p^2 - q^2}\left(\frac{x + p}{x - p} - \frac{x + q}{x - q}\right) equa...
- If (x - 5) is the HCF of x^2 - x - p and x^2 - qx - 10, then what is the value of (p + q) ?