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प्रश्न
Show that 2x – 3 is a factor of x + 2x3 – 9x2 + 12.
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उत्तर
Let p(x) = 2x3 – 9x2 + x + 12
We have to show that, 2x – 3 is a factor of p(x).
i.e., `p(3/2) = 0`
Now, `p(3/2) = 2(3/2)^3 - 9(3/2)^2 + 3/2 + 12`
= `2 xx 27/8 - 9 xx 9/4 + 3/2 + 12`
= `27/4 - 81/4 + 3/2 + 12`
= `(27 - 81 + 6 + 48)/4`
= `(81 - 81)/4`
= 0
Hence, (2x – 3) is a factor of p(x).
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संबंधित प्रश्न
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:
p(x) = 2x3 + x2 – 2x – 1, g(x) = x + 1
Factorise:
12x2 – 7x + 1
Factorise:
x3 – 2x2 – x + 2
Find the factor of the polynomial given below.
`sqrt 3 x^2 + 4x + sqrt 3`
Factorize the following polynomial.
(x2 – 2x + 3) (x2 – 2x + 5) – 35
Factorize the following polynomial.
(y + 2) (y – 3) (y + 8) (y + 3) + 56
Factorise:
84 – 2r – 2r2
Factorise the following:
9x2 – 12x + 3
Factorise the following:
9x2 – 12x + 4
If both x – 2 and `x - 1/2` are factors of px2 + 5x + r, show that p = r.
