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प्रश्न
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
p(x) = x3 - 3x2 + 4x - 4 and g(x) = x - 2
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उत्तर
p(x) = x3 - 3x2 + 4x - 4 and g(x) = x - 2
To check whether x - 2 is a factor of p(x) now put x = 2 in equation (i), we get
p(2) = (2)3 - 3(2)2 + 4(2) -4
= 8 - 3 x 4 + 8 - 4
= 8 - 12 + 8 - 4
= 16 - 16 = 0
Since, p(2) = 0, so by factor theorem (x - 2) is a factor of p(x).
संबंधित प्रश्न
If (x – 2) is a factor of the expression 2x3 + ax2 + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.
Show that 3x + 2 is a factor of 3x2 – x – 2.
Using the Remainder Theorem, factorise each of the following completely.
3x3 + 2x2 – 23x – 30
Find the value of k, if 2x + 1 is a factor of (3k + 2)x3 + (k − 1).
Prove that (5x - 4) is a factor of the polynomial f(x) = 5x3 - 4x2 - 5x +4. Hence factorize It completely.
In the following problems use the factor theorem to find if g(x) is a factor of p(x):
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Show that 2x + 7 is a factor of 2x3 + 5x2 - 11 x - 14. Hence factorise the given expression completely, using the factor theorem.
Show that (x – 2) is a factor of 3x2 – x – 10 Hence factorise 3x2 – x – 10.
Show that 2x + 7 is a factor of 2x3 + 5x2 – 11x – 14. Hence factorise the given expression completely, using the factor theorem.
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.
