Test: Factorisation Factor Theorem
20 Questions MCQ Test Mathematics (Maths) Class 9 | Test: Factorisation Factor Theorem
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x-a is a factor of p(x) = ax2+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
Given, x3 + 3x2 + 3x + a = 0
and its factor is x + 1 = 0
⇒ x = -1
Put the value in equation i.e. x3 + 3x2 + 3x + a = 0
it becomes = (-1) + 3 (1) + 3(-1) + a = 0
⇒ -1 + 3 - 3 + a = 0
⇒ a = 1
If (x-2) is the factor of x2 + 2x+ a, find the value of ‘a’.
If x-2 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 (x-a), then the remainder is
The value of p for which x + p is a factor of x2 + px + 3 – p is:
For two polynomials p(x) and q(x), x-a and x-b 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 x4 + ax3 + 2x2– 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
What is the value of b such that x+3 is a factor of x2 - bx -12?
Find the value of ‘a’ so that (x-1) is the factor of x2+a+1
For a polynomial p(x), x-2 is a factor, so p(2) is _______
x+1 is a factor of p(x) = x3+3x2+3x+1, so what is the value of p(-1)
If (x-1) 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, x2 – 3x +2, which of the following is a factor ?
If (2x + 5) is a factor of 2x2 – k, then the value of k is.
Let p(x) = 2x2 − k
Since, (2x+5) is a factor of p(x), then by factor
theorem,
(x + 2) is a factor of 2x3 + 5x2 - x - k. The value of k is:
If x-2 is a factor of ax2-x-6, so what should be the value of a?
Find the value of p(2) if p(x) has (x-2) as its factor
Which of the following polynomials has -3 as a zero?
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