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प्रश्न
If x – 2 is a factor of 2x3 - x2 - px - 2.
with the value of p, factorize the above expression completely.
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उत्तर
Given expression is 2x3 - x2 - px - 2 and x - 2 is the factor.
Putting the value of P
(2x2 + 3x + 1)
`x - 2)overline(2x3 - x2 - 5x - 2)(`
2x3 - 4x2
- +______
3x2 - 5x
3x2 - 6x
- +_______
x - 2
x - 2
- +_____
. x
∴ 2x3 - x2 - 5x - 2 = (x - 2) (2x2 + 3x + 1)
The expression can be the written as
(2x2 + 3x + 1) (x - 2) or (2x + 1) (x + 1) (x -2).
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)`
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = x3 − x2 − x − 1, q(x) = x − 1
By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.
p(x) = 2x3 − x2 − 45, q(x) = x − 3
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Prove that (x+ 1) is a factor of x3 - 6x2 + 5x + 12 and hence factorize it completely.
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Find the value of the constant a and b, if (x – 2) and (x + 3) are both factors of expression x3 + ax2 + bx - 12.
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If x – 3 is a factor of p(x), then the remainder is
