FACTORIZATION

Here are few short questions and answers for a factorization quiz:

Q1. Factorize the expression: 6x^2 – 15x.

Ans. 3x(2x – 5).

Q2. What are the factors of y^2 – 16?

Ans. (y + 4)(y – 4).

Q3. Simplify the expression by factoring: (12a^2 – 8a).

Ans. 4a(3a – 2).

Q4. Factor the trinomial: (x^2 – 10x + 21).

Ans. (x – 7)(x – 3).

Q5. Find the common factors of (15m^2n – 30mn^2).

Ans. 15mn(m – 2n).

Q6. Factorize the quadratic expression: (4p^2 – 25).

Ans. (2p + 5)(2p – 5).

Q7. What is the factored form of (z^2 + 6z + 9)?

Ans (z + 3)^2.

Q8. Simplify the expression by factoring: (9x^3 – 27x^2 + 18x).

Ans. 9x(x – 3)(x – 2).

Q9. Factor the perfect square trinomial: (x^2 + 10x + 25).

Ans. (x + 5)^2.

Q10. Determine the factors of (20y^2 – 5).

Ans. 5(4y^2 – 1) = 5(2y + 1)(2y – 1).

Do your best!

Times Up!

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Mathematics I

FACTORIZATION

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Category: Factorization

1. Factors of 16x² – y4

(4x – y²) (4x – y²)

(4x + y²) (4x + y²)

(4x – y²) (4x+y²)

(2x – y²) (8x + y²)

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Category: Factorization

2. Factors of  y3 – 27z3

(y‒3z) (y2+3z+9z²)

(y‒3z) (y2‒3z+9z²)

(y‒3z) (y2+3z‒9z²)

(y‒3z) (y2‒3z‒9z²)

3 / 15

Category: Factorization

3. Factors of  x3 – y3

(x + y)(x² +xy +y²)

(x – y)(x² +xy +y²)

(x + y)(x² ‒ xy +y²)

(x ‒ y)(x² ‒xy +y²)

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Category: Factorization

4. If x²+4x+m is a complete square, then m =

16

6

4

5

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Category: Factorization

5. Factors of  x² - y²

(x+y) (x – y)

(x ‒ y) (x – y)

None of these

(x+y) (x+y)

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Category: Factorization

6. If 9x²+6x+m is a complete square, then m=

1

4

3

2

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Category: Factorization

7. Factors of  x2 – x – 6

(x – 3 )(x – 2)

(x – 3 )(x + 2)

(x + 3 )(x + 2)

None of these

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Category: Factorization

8. Factors of a² +2a‒24

(a+6)(a+4)

(a+6)(a–4)

(a – 6)(a–4)

(a – 6)(a+4)

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Category: Factorization

9. Factors of x³ – 64y³

(x – 4y) (x2 – 4xy + 16y2)

(x + 4y) (x2 + 4xy + 16y2)

(x – 4y) (x2 + 4xy + 16y2)

(x + 4y) (x2 – 4xy + 16y2)

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Category: Factorization

10. Factors of x2+5x+6

(x + 2)(x – 3)

(x–2)(x – 3)

(x – 2)(x + 3)

(x + 2)(x + 3)

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Category: Factorization

11. Factors of  a4 – b4

(a – b)4

(a – b) (a + b) (a² + b²)

(a – b)(a3 – b3)

(a + b) (a3+ b3)

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Category: Factorization

12. Factors of a² +2ab+ b² ‒ c²

(a–b+c)(a+b+c)

(a – b+c)(a+b – c)

(a+b+c)(a+b-c)

(a+b+c)(a+b+c)

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Category: Factorization

13. It is the process in which we express the given polynomial (expression) as a product of two or more expressions.

None of these

Simplification

Factorization

Rationalization

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Category: Factorization

14. Factors of  x3 + y3

(x+y)(x²‒2xy+y²)

(x+y)(x²‒xy+y²)

(x+y)(x²+2xy+y²)

(x+y)(x² +xy+y²)

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Category: Factorization

15. Factors of  y3 + 27z3

(y+3z) (y²-3yz+9z²)

(y+3z) (y²‒3yz‒9z²)

(y‒3z) (y²‒3yz+9z²)

(y+3z) (y²+3yz+9z²)

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Frequently Asked Questions (FAQs):

Q1. What is factoring in algebra?

Ans. Factoring in algebra is the process of expressing an algebraic expression as the product of its factors.

Q2. Why is factorization important?

Ans. Factorization is crucial in simplifying expressions, solving equations, and understanding mathematical relationships.

Q3. What is a quadratic trinomial?

Ans. A quadratic trinomial is a polynomial of degree 2, represented as (ax^2 + bx + c), where ‘a’, ‘b’, and ‘c’ are constants.

Q4. How do you factor a difference of squares?

Ans. The difference of squares (a^2 – b^2) can be factored as (a – b)(a + b).

Q5. Can all quadratic expressions be factored?

Ans. Not all quadratic expressions can be factored over the set of real numbers, but they may factor over the set of complex numbers.

Q6. What is the difference between factoring and simplifying?

Ans. Factoring involves expressing an expression as a product of factors, while simplifying focuses on reducing an expression to its simplest form.

Q7. How do you factor a perfect square trinomial?

Ans. A perfect square trinomial can be factored as the square of a binomial, such as (a + b)^2.

Q8. Can factoring be used to solve equations?

Ans. Yes, factoring is often used to solve equations by setting the factored expression equal to zero and solving for the variable.

Q9. What is the difference between prime and composite factors?

Ans. Prime factors are irreducible, while composite factors can be further broken down into smaller factors.

Q10. Are there different methods for factoring quadratic expressions?

Ans. Yes, various methods exist, including factoring by grouping, factoring trinomials, and recognizing special patterns like the difference of squares and perfect square trinomials.