In this page factoring worksheet we are going to see some practice questions of the topic factoring. You can find a solution for each questions with detailed explanation.

Problems on factoring worksheet.

(1) Solve the following quadratic equations by factorization method

(i)(2x + 3)²
- 81 = 0 Solution

(ii) 3 x² – 5 x – 12 = 0 Solution

(iii) √5 x² + 2 x – 3√5 = 0 Solution

(iv) 3 (x² – 6) = x (x + 7) – 3 Solution

(v) 3 x – (8/x) = 2 Solution

(vi) x + (1/x) = (26/5) Solution

(vii) [x/(x+1)] + [(x + 1)/x] = 34/15 Solution

(viii) a²b²x² – (a² - b²) x + 1 = 0 Solution

(ix) 2(x + 1)² – 5 (x + 1) = 12 Solution

(x) 3 (x – 4)² – 5(x – 4) = 12 Solution

**Factoring-Quadratic equations:**

An equation which is in the form of ax² + b x + c =0,where a,b,c ∈ R and a≠0 is called a quadratic equation. Finding the roots of a quadratic equation is called as solving the quadratic equation.

**Procedure:**

(i) Arrange the terms of the expression in the standard form.

(ii) Find the product of coefficients of x² and the constant term.

(iii) Split that value into two terms and the simplified value must be equal to the middle term.

(iv) Therefore x² + (a+b) x + ab = (x+a) (x+b)

(2) Solve the following quadratic equations by completing the square

(i) x² + 6 x – 7 = 0 Solution

(ii) x² + 3 x + 1 = 0 Solution

(iii) 2x² + 5 x - 3 = 0 Solution

(iv) 4x² + 4 b x – (a² - b²) = 0 Solution

(v) x² – (√3 + 1) x + √3 = 0 Solution

(vi) (5 x + 7)/(x – 1) = 3 x + 2 Solution

**Procedure:**

(i) First, we have to divide the whole equation by the coefficient of x².

(ii)
Now we have to make the second term as the multiple of 2. For example,
if it is 6 we have to write them as 2 x 3. If it is not a multiple of 2
that is 3 or 7 something like that we have to write multiply and divide
it by 2.

(iii) For compensating b² we have to use -b² also.

More problems on factoring worksheet.

(3) Solve the following quadratic equations using quadratic formula

(i) x² – 7 x + 12 = 0 Solution

(ii) 15x² – 11 x + 2 = 0 Solution

(iii) x + (1/x) = 2 ½ Solution

(iv) 3 a²x² – a b x - 2b² = 0 Solution

(v) a (x² + 1) = x (a² + 1) Solution

(vi) 36 x² – 12 a x + (a² - b²) = 0 Solution

(vii) [(x – 1)/(x + 1)] + [(x – 3)/(x – 4)] = 10/3 Solution

(viii) a² x² + (a² - b²) x - b² = 0 Solution

**Procedure:**

(i) We have to compare the given equation with the general form of quadratic equation ax² + b x + c = 0.

(ii) After getting the values a,b and c we have to apply those values in the formula -b ± √(b² – 4 a c)/2a

factoring worksheet1 factoring worksheet1

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