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xa is a factor of p(x) = ax^{2}+bx+c. Which of the following is true?
See if g(x) = x a
Then g(x) is a factor of p(x)
The zero of polynomial = a
Therefore p(a)= 0
If x+1 is a factor of x^{3}+3x^{2}+3x+a, then a = ?
Given, x^{3} + 3x^{2} + 3x + a = 0
and its factor is x + 1 = 0
⇒ x = 1
Put the value in equation i.e. x^{3} + 3x^{2} + 3x + a = 0
it becomes = (1) + 3 (1) + 3(1) + a = 0
⇒ 1 + 3  3 + a = 0
⇒ a = 1
If (x2) is the factor of x^{2} + 2x+ a, find the value of ‘a’.
If x2 is a factor then 2 is the zero of the polynomial
by substituting 2 in the given polynomial,we get
2^2+2(2)+a=0
8+a=0
a=8
If a polynomial p(x) is divided by a linear divisor (xa), then the remainder is
The value of p for which x + p is a factor of x^{2} + px + 3 – p is:
For two polynomials p(x) and q(x), xa and xb are their factors, respectively.Which of the following is true?
Find the value of a such that (x – 2) is the factor of the polynomial x^{4} + ax^{3} + 2x^{2}– 3x
Zero of the polynomial is x 2 =0 =>x = 2 put the value of x = 2 (2²)² + a(2)³ + 2(2)²  3(2) = 16 + 8a + 8  6 = 18 + 8a = 0 = 8a = 18 = a = 18/8 = a = 9/4
One of the linear factors of 3x^{2} + 8x + 5 is
What is the value of b such that x+3 is a factor of x^{2}  bx 12?
Find the value of ‘a’ so that (x1) is the factor of x^{2}+a+1
For a polynomial p(x), x2 is a factor, so p(2) is _______
x+1 is a factor of p(x) = x^{3}+3x^{2}+3x+1, so what is the value of p(1)
If (x1) is a factor of ax – a, then find the value of a
ANSWER : d
Solution : f(x) = ax  a……………………..(1)
x  1 = 0
x = 1
Putting in eq(1)
(1)x  1 => x  1
For eg : if we put x = 100
Putting in eq(1)
(100)x  100 => x  100
So, all the values of a
For a polynomial p(x), p(1) and p(2) are both equal to zero .So, we can conclude that,
For a polynomial, x^{2} – 3x +2, which of the following is a factor ?
If (2x + 5) is a factor of 2x^{2} – k, then the value of k is.
Let p(x) = 2x^{2} − k
Since, (2x+5) is a factor of p(x), then by factor
theorem,
(x + 2) is a factor of 2x^{3} + 5x^{2}  x  k. The value of k is:
If x2 is a factor of ax^{2}x6, so what should be the value of a?
Find the value of p(2) if p(x) has (x2) as its factor
Which of the following polynomials has 3 as a zero?
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