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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 + x2 + 3x + 175 and g(x) = x + 5.
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उत्तर
p(x) = x3 + x2 + 3x + 175 and g(x) = x + 5 ...(i)
To check whether (x + 5) is a factor of p(x), we have to find p(-5), put x = -5 in equation (i), we get
p(-5) = (-5)3 + (-5)2 + 3(-5) + 175
= -125 + 25 - 15 + 175
= -140 + 200 = 60
Since, p(-5) ≠ 0, so by factor theorem (x + 5) is not a factor of p(x).
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.
Find the value of k, if 3x – 4 is a factor of expression 3x2 + 2x − k.
Find the values of constants a and b when x – 2 and x + 3 both are the factors of expression x3 + ax2 + bx – 12.
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.
Use factor theorem to determine whether x + 3 is factor of x 2 + 2x − 3 or not.
Use the factor theorem to factorise completely x3 + x2 - 4x - 4.
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
By factor theorem, show that (x + 3) and (2x – 1) are factors of 2x2 + 5x – 3.
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.
Using factor theorem, show that (x – 5) is a factor of the polynomial
2x3 – 5x2 – 28x + 15
