Factoring Trinomials Worksheet

Factoring Trinomials Worksheet
  • Page 1
 1.  
Solve 2x2 + 3x - 18 = x2 by factorizing.
a.
x = -6 or x = -3
b.
x = 6 or x = 3
c.
x = -6 or x = 3
d.
None of the above


Solution:

2x2 + 3x - 18 = x2
[Original equation.]

x2 + 3x - 18 = 0
[Write the equation in the standard form.]

(x + 6) (x - 3) = 0
[Factorize the equation.]

x + 6 = 0 or x - 3 = 0
[Apply zero product property.]

x = -6 or x = 3

The values of x are -6, 3.


Correct answer : (3)
 2.  
Factor: x2 + 12x + 35
a.
(x - 7)(x - 5)
b.
(x + 7)(x + 5)
c.
(x - 8)(x + 5)
d.
(x + 7)(x - 5)


Solution:

The factors of a trinomial x2 + bx + c are in the form (x + p)(x + q), where b = p + q and c = pq.

Compare the equation with x2 + bx + c to get b and c values. So, b = 12 and c = 35.

Find the numbers p and q whose product is 35 and sum is 12.

p and q    p + q
1,35            36
7, 5            12

The required values of p and q are 7 and 5.

So, the factors of the equation x2 + 12x + 35 are (x + 7)(x + 5).


Correct answer : (2)
 3.  
Factor: x2 - 3x + 2
a.
(x - 1)(x + 2)
b.
(x - 1)(x - 2)
c.
(x + 1)(x - 2)
d.
(x + 1)(x + 2)


Solution:

The factors of a trinomial x2 + bx + c are in the form (x + p)(x + q), where b = p + q and c = pq.

Compare the equation with x2 + bx + c to get b and c values. So, b = -3 and c = 2.

Since c is positive, find the numbers p and q with the same sign, whose product is 2 and sum is -3.

p and q    p + q
-1, -2           - 3

The required values of p and q are -1 and -2.

So, the factors of the equation x2 - 3x + 2 are (x - 1)(x - 2).


Correct answer : (2)
 4.  
Factor: x2 + 3x - 10
a.
(x - 2)(x - 5)
b.
(x + 2)(x - 5)
c.
(x + 2)(x + 5)
d.
(x - 2)(x + 5)


Solution:

The factors of a trinomial x2 + bx + c are in the form (x + p)(x + q), where b = p + q and c = pq.

Compare the equation with x2 + bx + c to get b and c values. So, b = 3 and c = -10.

Since c is negative, find the numbers p and q with different signs, whose product is -10 and sum is 3.

p and q    p + q
-1, 10         9
-2, 5            3

The required values of p and q are -2 and 5.

The factors of the equation x2 + 3x - 10 are (x - 2)(x + 5).


Correct answer : (4)
 5.  
Factor: x2 - 3x - 18
a.
(x - 6)(x + 3)
b.
(x - 6)(x - 3)
c.
(x + 6)(x - 3)
d.
(x + 6)(x + 3)


Solution:

The factors of a trinomial x2 + bx + c are in the form (x + p)(x + q), where b = p + q and c = pq.

Compare the equation with x2 + bx + c to get b and c values. So, b = -3 and c = -18.

Since c is negative, find the numbers p and q with different signs, whose product is -18 and sum is -3.

p and q    p + q
-3, 6           3
-6, 3          -3

The required values of p and q are -6 and 3.

The factors of equation x2 - 3x - 18 are (x + 3)(x - 6).


Correct answer : (1)
 6.  
Factor: x2 - 4x - 21
a.
(x + 7)(x - 3)
b.
(x + 7)(x + 3)
c.
(x - 7)(x + 3)
d.
(x - 7)(x - 3)


Solution:

The factors of a trinomial x2 + bx + c are in the form (x + p)(x + q), where b = p + q and c = pq.

Compare the equation with x2 + bx + c to get b and c values. So, b = -4 and c = -21.

Since c is negative, find the numbers p and q with different signs, whose product is -21 and sum is -4.

p and q    p + q
-3, 7           4
-7, 3           -4

The required values of p and q are -7 and 3.

So, the factors of equation x2 - 4x - 21 are (x + 3)(x - 7).


Correct answer : (3)
 7.  
Factor: x2 + 4x - 12
a.
(x - 2)(x - 6)
b.
(x + 2)(x + 6)
c.
(x + 2)(x - 6)
d.
(x - 2)(x + 6)


Solution:

The factors of a trinomial x2 + bx + c are in the form (x + p)(x + q), where b = p + q and c = pq.

Compare the equation with x2 + bx + c to get b and c values. So, b = 4 and c = -12.

Since c is negative, find numbers p and q with different signs, whose product is -12 and sum is 4.

p and q     p + q
-6, 2            -4
-2, 6             4

The required values of p and q are -2 and 6.

So, the factors of the equation x2 + 4x - 12 are (x - 2)(x + 6).


Correct answer : (4)
 8.  
Factor: x2 - 7x + 10
a.
(x + 5)(x - 2)
b.
(x + 5)(x + 2)
c.
(x - 5)(x - 2)
d.
(x - 5)(x + 2)


Solution:

The factors of a trinomial x2 + bx + c are in the form (x + p)(x + q), where b = p + q and c = pq.

Compare the equation with x2 + bx + c to get b and c values. So, b = -7 and c = 10.

Since c is positive, find the numbers p and q with the same sign, whose product is 10 and sum is -7.

p and q    p + q
-5, -2           -7

The required values of p and q are -5 and -2.

So, the factors of the equation x2 - 7x + 10 are (x - 5)(x - 2).


Correct answer : (3)
 9.  
Solve: x2 + 17x + 70 = 0
a.
x = -7 or x = -10
b.
x = 7 or x = 10
c.
x = 7 or x = -10
d.
x = -7 or x = 10


Solution:

x2 + 17x + 70 = 0
[Original equation.]

The factors are 7 and 10.
[7 + 10 = 17 and 7 x 10 = 70]

(x + 7) (x +10) = 0
[Factorize the equation.]

x + 7 = 0 or x + 10 = 0
[Apply zero product property.]

x = -7 or x = -10

The values of x are -7, -10.


Correct answer : (1)
 10.  
Solve: x2 - 19x + 88 = 0
a.
x = 8 or x = 11
b.
x = -8 or x = -11
c.
x = -8 or x = 11
d.
x = 8 or x = -11


Solution:

x2 - 19x + 88 = 0
[Original equation.]

The factors are -8 and -11.
[-8 + (-11) = -19 and (-8) x (-11) = 88]

(x - 8) (x - 11) = 0
[Factorize the equation.]

x - 8 = 0 or x - 11 = 0
[Apply zero product property.]

x = 8 or x = 11.

The values of x are 8, 11.


Correct answer : (1)

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