Here we are going to see some practice questions on factoring quadratic equations.

(1)  Factor x² + 7 x + 12

(2)  Factor y² - 16 y + 60

(3)  Factor x² + 9x - 22

(4)  Factor x² - 2x - 99

(5)  Factor 3x² + 19x + 6

(6)  Factor 9x² - 16x + 7

(7)  Factor 2x² + 17x - 30

(8)  Factor 18x² - x - 4

Question 1 :

Factor x² + 7 x + 12

Solution :

Step 1 :

By multiplying the coefficient of x2 by the constant term 12, we get 12.

Step 2 :

Now we need to spit this 12 as two parts, and the product of those parts must be equal to 12 and simplified value must be equal to the middle term (7).

=  x2 + 3x + 4x + 12

Step 3 :

Grouping into linear factors

=  x (x + 3) + 4 (x + 3)

=  (x + 4) (x + 3)

Let us look into the solution of next problem on "Factoring quadratics worksheet".

Question 2 :

Factor y² - 16 y + 60

Solution :

Step 1 :

By multiplying the coefficient of y2 by the constant term 60, we get 60.

Step 2 :

Now we need to spit this 60 as two parts, and the product of those parts must be equal to 60 and simplified value must be equal to the middle term (-16).

Since the middle term is negative, both factors will be negative.

=  y2 - 10y - 6y + 60

Step 3 :

Grouping into linear factors

=  y (y - 10) - 6 (y - 10)

=  (y - 10) (y - 6)

Question 3 :

Factor x² + 9x - 22

Solution :

Step 1 :

By multiplying the coefficient of x2 by the constant term -22, we get -22.

Step 2 :

Now we need to spit this -22 as two parts, and the product of those parts must be equal to -22 and simplified value must be equal to the middle term (9).

Since the last term is negative, the factors will be in the combination of positive and negative.

=  x2 + 11x - 2x - 22

Step 3 :

Grouping into linear factors

=  x (x + 11) - 2 (x + 11)

=  (x + 11) (x - 2)

Question 4 :

Factor x² - 2x - 99

Solution :

Step 1 :

By multiplying the coefficient of x2 by the constant term -99, we get -99.

Step 2 :

Now we need to spit this -99 as two parts, and the product of those parts must be equal to -99 and simplified value must be equal to the middle term (-2).

Since the middle and last term are negative, the factors will be in the combination of positive and negative.

=  x2 - 11x + 9x - 99

Step 3 :

Grouping into linear factors

=  x (x - 11) + 9 (x - 11)

=  (x - 11) (x + 9)

Question 5 :

Factor 3x² + 19x + 6

Solution :

Step 1 :

By multiplying the coefficient of x2 by the constant term 18, we get 18.

Step 2 :

Now we need to spit this 18 as two parts, and the product of those parts must be equal to 18 and simplified value must be equal to the middle term (19).

=  3x2 + 1x + 18x + 6

Step 3 :

Grouping into linear factors

=  x (3x + 1) + 6 (3x + 1)

=  (x + 6) (3x + 1)

Question 6 :

Factor 9x² - 16x + 7

Solution :

Step 1 :

By multiplying the coefficient of x2 by the constant term 63, we get 63.

Step 2 :

Now we need to spit this 63 as two parts, and the product of those parts must be equal to 63 and simplified value must be equal to the middle term (-16).

Since the middle term is negative, both factors will be negative.

=  9x2 - 9x - 7x + 7

Step 3 :

Grouping into linear factors

=  9x (x - 1) - 7 (x - 1)

=  (x - 1) (9x - 7)

Example 7 :

Factor 2x² + 17x - 30

Solution :

Step 1 :

By multiplying the coefficient of x2 by the constant term -30, we get -30.

Step 2 :

Now we need to spit this -30 as two parts, and the product of those parts must be equal to -30 and simplified value must be equal to the middle term (17).

Since the last term is negative, the factors will be in the combination of positive and negative.

=  2x2 + 20x - 3x - 30

Step 3 :

Grouping into linear factors

=  2x (x + 10) - 3 (x + 10)

=  (x + 10) (2x - 3)

Question 8 :

Factor 18x² - x - 4

Solution :

Step 1 :

By multiplying the coefficient of x2 by the constant term -72, we get -72.

Step 2 :

Now we need to spit this -72 as two parts, and the product of those parts must be equal to -72 and simplified value must be equal to the middle term (-1).

Since the middle and last term are negative, the factors will be in the combination of positive and negative.

=  18x2 - 9x + 8x - 4

Step 3 :

Grouping into linear factors

=  9x (2x - 1) + 4 (2x - 1)

=  (2x - 1) (9x + 4)

Related topics

After having gone through the stuff given above, we hope that the students would have understood "Factoring quadratics worksheet"

If you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6