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प्रश्न
If x – 2 is a factor of 2x3 - x2 - px - 2.
Find the value of p
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उत्तर
Given expression is 2x3 - x2 - px - 2 and x - 2 is the factor.
x - 2 = 0, x = 2 in expression
2(2)3 - (2)2 - p(2) - 2 = 0
16 - 4 - 2p - 2 = 0
10 - 2p = 0
p = 5
संबंधित प्रश्न
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.
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Using the Factor Theorem, show that (x + 5) is a factor of 2x3 + 5x2 – 28x – 15. Hence, factorise the expression 2x3 + 5x2 – 28x – 15 completely.
If x - 2 and `x - 1/2` both are the factors of the polynomial nx2 − 5x + m, then show that m = n = 2
Prove by factor theorem that
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In the following problems use the factor theorem to find if g(x) is a factor of p(x):
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By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x2 + 5x – 3.
Show that (x – 2) is a factor of 3x2 – x – 10 Hence factorise 3x2 – x – 10.
What number should be subtracted from 2x3 – 5x2 + 5x so that the resulting polynomial has 2x – 3 as a factor?
Determine whether (x – 1) is a factor of the following polynomials:
x3 + 5x2 – 10x + 4
