Download Grade 9 Polynomials

ID : ww-9-Polynomials [1]
Grade 9
Polynomials
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Answer t he quest ions
(1)
If x75 + 75 is divided by (x - 1), f ind the remainder.
(2)
If f (x) = ax2 + bx + c, and f (1) = 7 and f (-1) = 4, then f ind the value of a + c.
(3)
If -3x2 + kx - 8 = ( -3x + 4)(x - 2), f ind the value of k.
(4) If f (q) = q2 + 4q + 1, the value of f (2q) + f (-q) = ?
(5)
If
, f ind the value of
.
(6) Find multiplication of zeroes of polynomial y2 - 2y - 48.
(7) Find sum of zeroes of polynomial -p2 + 12p - 32.
Choose correct answer(s) f rom given choice
(8)
If f (x) = 7x + 6, f ind the inverse of f , f -1.
a. f -1(x) =
c. f -1(x) =
1
7x+6
x- 6
7
b. f -1(x) =
x- 6
d. f -1(x) = 7x + 6
7
(9) If
, f ind value of x3 - y3.
a. 1
b. 0
c. -1
d. 2
Fill in t he blanks
(10)
If (x - 2) is a f actor of kx4 - 2x3 + x2 + x + 26, the value of k =
(11)
If x3 + 2x2 + 2x + 9 is divide by x + 2, the remainder =
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.
.
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ID : ww-9-Polynomials [2]
Check True/False
(12) (x - 2) is a f actor of -x4 - x3 + x2 - x + 23.
T rue
False
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ID : ww-9-Polynomials [3]
Answers
(1)
76
(2)
5.5
Step 1
f (1) = 7
a(12) + b(1) + c = 7
a + b + c = 7 ______________ (1)
Step 2
Similarly f (-1) = 4
a(-12) + b(-1) + c = 4
a - b + c = 4 ______________ (2)
Step 3
On adding eq. (1) and (2)
2a + 2c = 11
a + c = 5.5
(3)
10
Step 1
T he given equation is:
-3x2 + kx - 8 = ( -3x + 4)(x - 2)
⇒ -3x2 + kx - 8 = -3x2 + 10x - 8
⇒ kx = 10x
⇒ k = 10
Step 2
T hus, the value of k is 10.
(4) 5q2 + 4q + 2
Step 1
It is given that, f (q) = q2 + 4q + 1
T heref ore, f (2q) = (2q)2 + 4(2q) + 1 = 4q2 + 8q + 1,
and f (-q) = (-q)2 + 4(-q) + 1 = q2 - 4q + 1
Step 2
Now, f (2q) + f (-q) = 4q2 + 8q + 1 + q2 - 4q + 1
= 5q2 + 4q + 2
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ID : ww-9-Polynomials [4]
(5)
8
Step 1
It is given that,
.
T heref ore, f (2√3) = 2(2√3)2 - 3√3(2√3) + 2
= 24 -18 + 2
=8
Step 2
T hus, the value of
is 8.
(6) -48
(7) 12
(8)
c. f -1(x) =
x- 6
7
Step 1
f (x) = 7x + 6
x = [f (x) - 6]/7
Step 2
T heref ore f -1(x) =
x- 6
7
(9) b. 0
Step 1
It is given that,
⇒
x2 + y2
= -1
xy
⇒ x2 + y2 = xy
⇒ x2 + y2 + xy = 0 ------(1)
Step 2
Now, x3 - y3 can be written as:
(x - y)(x2 + xy + y2)
= (x - y)(0) ...[From equation (1)]
=0
Step 3
T heref ore, the value of x3 - y3 is 0.
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ID : ww-9-Polynomials [5]
(10)
-1
Step 1
We have been told that (x - 2) is a f actor of kx4 - 2x3 + x2 + x + 26. T hus, when the value
of (x - 2) is zero, the value of the polynomial kx4 - 2x3 + x2 + x + 26 must also be zero.
Step 2
T he value of (x - 2) will be zero when x = 2. T hus, if we put x = 2 in the given polynomial, we
can equate it to zero and solve the equation to f ind the value of k:
k(2)4 - 2(2)3 + (2)2 + (2) + 26 = 0
⇒ k = -1
Step 3
T hus, the value of k is -1.
(11)
5
(12) False
Step 1
Let's assume (x - 2) is a f actor of -x4 - x3 + x2 - x + 23.
Step 2
(x - 2) being a f actor, when (x - 2) is zero, the polynomial -x4 - x3 + x2 - x + 23 must also be
equal to zero. In other words, when x = 2, the polynomial -x4 - x3 + x2 - x + 23 must also be
equal to zero.
Step 3
Let us put the value of x as 2 in the given polynomial and see if its value becomes zero or
not:
p(x) = -x4 - x3 + x2 - x + 23,
p(2) = -(2)4 - (2)3 + (2)2 - (2) + 23 = 1
Step 4
Since, p(2) ≠ 0, (x - 2) is not a f actor of -x4 - x3 + x2 - x + 23.
Step 5
Hence, the given statement is False.
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