Advertisements
Advertisements
Question
If mx2 – nx + 8 has x – 2 as a factor, then ______.
Options
2m – n = 4
2m + n = 4
2n + m = 4
n – 2m = 4
Solution
If mx2 – nx + 8 has x – 2 as a factor, then n – 2m = 4.
Explanation:
Let f(x) = mx2 – nx + 8
Given x – 2 is a factor of f(x).
Then f(2) = 0
`\implies` m × 22 – n × 2 + 8 = 0
`\implies` 4m – 2n + 8 = 0
`\implies` 2m – n + 4 = 0
`\implies` n – 2m = 4
RELATED QUESTIONS
Using the Factor Theorem, show that (x – 2) is a factor of x3 – 2x2 – 9x + 18. Hence, factorise the expression x3 – 2x2 – 9x + 18 completely.
Find the value of ‘a’, if (x – a) is a factor of x3 – ax2 + x + 2.
(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.
Show that (x - 1) is a factor of x3 - 7x2 + 14x - 8. Hence, completely factorise the above expression.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 + x2 + 3x + 175 and g(x) = x + 5.
Using factor theorem, show that (x - 3) is a factor of x3 - 7x2 + 15x - 9, Hence, factorise the given expression completely.
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 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.
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
Factors of 3x3 – 2x2 – 8x are ______.
