Math 9th Chap 4 : Topic 2 - Maryam Publications

Math Chapter 4 : Topic 2

Quadratic and Cubic Factors

1 / 25

The expression $(x^{2} + px + q)$ is generally factorized into:

A) $(p + q)(x + 1)$

B) $(x + p)(x + q)$

C) $(x + a)(x + b)$

D) $(x + p + q)$

2 / 25

Factorize: $(x^{2} + 5x + 6)$

A) $(x + 5)(x + 1)$

B) $(x + 2)(x + 3)$

C) $(x + 4)(x + 2)$

D) $(x + 1)(x + 6)$

3 / 25

The expression $({ax}^{2} + bx + c)$ is a:

A) Cubic expression

B) Quadratic expression

C) Linear expression

D) Constant expression

4 / 25

Factorization of $({ax}^{2} + bx + c)$ mainly involves:

A) Splitting middle term

B) Adding constants

C) Division only

D) Graph plotting

5 / 25

Which identity helps in factoring $a^{3} + b^{3}$?

A) ${(a + b)}^{2}$

B) ${(a - b)}^{2}$

C) $(a + b)(a^{2} - ab + b^{2})$

D) $(a - b)(a^{2} + ab + b^{2})$

6 / 25

Factorize: $(a^{3} - b^{3})$

A) ${(a + b)}^{2}$

B) ${(a - b)}^{2}$

C) $(a + b)(a^{2} - ab + b^{2})$

D) $(a - b)(a^{2} + ab + b^{2})$

7 / 25

Which expression is a perfect cube identity?

A) $a^{3} + {3a}^{2}b + {3ab}^{2} + b^{3}$

B) $a + b$

C) $a^{2} + b^{2}$

D) $a^{3} + b^{3}$

8 / 25

Factorize: $(a^{3} + {3a}^{2}b + {3ab}^{2} + b^{3})$

A) ${(a + b)}^{2}$

B) ${(a + b)}^{3}$

C) ${(a - b)}^{3}$

D) $(a + b)$

9 / 25

The expression $(a^{3} - {3a}^{2}2b + {3ab}^{2} - b^{3})$ equals:

A) ${(a - b)}^{2}$

B) $(a^{2} - b^{2})$

C) ${(a - b)}^{3}$

D) ${(a + b)}^{3}$

10 / 25

Factorize: $(a^{4} - b^{4})$

A) ${(a - b)}^{4}$

B) ${(a^{2} + b^{2})}^{2}$

C) $(a^{2} - b^{2})(a^{2} + b^{2})$

D) ${(a + b)}^{4}$

11 / 25

Which is a correct factorization of $(a^{4} + b^{4})$ (basic form)?

A) ${(a + b)}^{4}$

B) ${(a^{2} - b^{2})}^{2}$

C) ${(a^{2} + b^{2})}^{2} - {2a}^{2}b^{2}$

D) ${(a - b)}^{4}$

12 / 25

Expression $({ax}^{2} + bx + c)({ax}^{2} + bx + d) + k)$ is generally:

A) Product of quadratics with constant adjustment

B) Quadratic form

C) Simple binomial

D) Linear

13 / 25

In $(x + a)(x + b)(x + c)$, expansion results in a:

A) Cubic expression

B) Quadratic expression

C) Linear expression

D) Constant

14 / 25

Factorization of $(x + a)(x + b)(x + c) + k$ involves:

A) Only division

B) Special identities or substitution

C) Only expansion

D) Only grouping

15 / 25

Expression $(x + a)(x + b)(x + c)(x + d) + {kx}^{2}$ is:

A) Linear

B) Constant

C) Quadratic $(4th$ degree$)$

D) Quadratic

16 / 25

Factorization of $x^{2} + px + q$ depends on:

A) Only $q$

B) Only $x$

C) Two numbers whose sum is $p$ and product is $q$

D) Only $p$

17 / 25

Which identity is used in cubic factorization?

A) ${(a + b)}^{2}$

B) $(a^{2} + b^{2})$

C) ${(a \pm b)}^{3}$ formulas

D) $(a - b)$

18 / 25

Factorize: $(a^{3} + b^{3})$

A) $(a - b)(a^{2} + ab + b^{2})$

B) $(a + b)(a^{2} + ab + b^{2})$

C) $(a + b)(a^{2} - ab + b^{2})$

D) $(a - b)(a^{2} - ab + b^{2})$

19 / 25

Which is true for $(a^{3} - {3a}^{2}b + {3ab}^{2} - b^{3})$?

A) ${(a + b)}^{2}$

B) ${(a - b)}^{3}$

C) ${(a^{2} - b^{2})}^{3}$

D) ${(a + b)}^{3}$

20 / 25

Factorizing quadratic expressions usually involves:

A) Only addition

B) Random guessing

C) Ignoring middle terms

D) Pairing and identities

21 / 25

Which expression is cubic?

A) $x^{3} + 2x$

B) $x + 1$

C) $x^{2} + 1$

D) $x^{2} + x + 1$

22 / 25

Factorization makes expressions:

A) Longer

B) Simpler

C) Unsolvable

D) Random

23 / 25

Which is NOT a factorization identity?

A) ${(a + b)}^{2}$ expansion

B) Random sum of numbers

C) $a^{3} + b^{3}$

D) $a^{2} - b^{2}$

24 / 25

Which method is used for $({ax}^{2} + bx + c)$?

A) Splitting middle term

B) Division only

C) Graph method

D) Completing square

25 / 25

Why are identities important in factorization?

A) They help simplify expressions quickly

B) They avoid solutions

C) They remove variables

D) They complicate equations

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