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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) = 2x3 + 4x + 6 and g(x) = x + 1
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उत्तर
p(x) = 2x3 + 4x + 6 and g(x) = x + 1
Now put x = -1 in equation (i), we get
p(-1) = 2(-1)3 + 4(-1) + 6
= 2 x - 1 - 4 + 6
= -2 - 4 + 6
= -6 + 6 = 0
Since, p(-1) = 0, so by factor theorem (x = 1) is a factor of p(x).
संबंधित प्रश्न
Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x3 + ax2 + bx – 12.
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Prove that (x+ 1) is a factor of x3 - 6x2 + 5x + 12 and hence factorize it completely.
Use the factor theorem to determine that x - 1 is a factor of x6 - x5 + x4 - x3 + x2 - x + 1.
Find the value of the constants a and b, if (x – 2) and (x + 3) are both factors of the expression x3 + ax2 + bx – 12.
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.
Determine whether (x – 1) is a factor of the following polynomials:
x4 + 5x2 – 5x + 1
Factors of 4 + 4x – x2 – x3 are ______.
