Math 9th Chap 4 : Topic 1 - Maryam Publications

Math Chapter 4 : Topic 1

Common Factors and Trinomials

1 / 25

The greatest common factor $(GCF)$ of $6x$ and $9x$ is:

A) $6x$

B) $3x$

C) ${3x}^{2}$

D) $9x$

2 / 25

Which expression shows factoring by common factor?

A) $x^{2} + 5x = x(x + 5)$

B) $x - y$

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

D) $x + y$

3 / 25

Factorize: $4x + 8$

A) $4(x + 2)$

B) $2(x + 4)$

C) $8(x + 1)$

D) $x(4 + 8)$

4 / 25

Which method is used when a common factor is removed from all terms?

A) Quadratic formula

B) Factoring by grouping

C) Common factor method

D) Trinomial splitting

5 / 25

Factorize: ${3x}^{2} + 6x$

A) $6x(x + 3)$

B) $3(x^{2} + 2x)$

C) $x(3x + 6)$

D) $3x(x + 2)$

6 / 25

A trinomial has:

A) Three terms

B) Four terms

C) Two terms

D) One term

7 / 25

Which is a trinomial?

A) $2x$

B) $x + 2$

C) $x^{2}$

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

8 / 25

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

A) $(x + 1)(x + 6)$

B) $(x + 4)(x + 2)$

C) $(x + 2)(x + 3)$

D) $(x + 5)(x + 1)$

9 / 25

In trinomial factoring, we look for:

A) Only division

B) Product and sum of coefficients

C) Sum and difference only

D) Only multiplication

10 / 25

Factorize: $x^{2} + 7x + 10$

A) $(x + 5)(x + 2)$

B) $(x + 10)(x + 1)$

C) $(x + 7)(x + 3)$

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

11 / 25

Which is the first step in factoring a polynomial?

A) Solve equation

B) Use graph

C) Take common factor

D) Multiply terms

12 / 25

Factorize: ${2x}^{2} + 4x + 6$

A) $x(2x + 4 + 6)$

B) $6(x^{2} + 4x + 2)$

C) $2(x^{2} + 2x + 3)$

D) $2x(x + 2 + 3)$

13 / 25

Which represents pictorial understanding of factoring?

A) Story explanation

B) Algebraic symbols only

C) Random numbers

D) Area model using rectangles

14 / 25

Symbolic representation of factoring uses:

A) Diagrams only

B) Algebraic expressions

C) Words only

D) Pictures only

15 / 25

Factorize: $5x + 10$

A) $5x(1 + 2)$

B) $10(x + 5)$

C) $5(x + 2)$

D) $x(5 + 10)$

16 / 25

Which trinomial is factorable?

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

B) $x + 1$

C) $x^{3} + 1$

D) $x^{2} + 2$

17 / 25

Factorize: $x^{2} + 4x + 4$

A) $(x + 3)(x + 1)$

B) $(x + 2)(x + 1)$

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

D) $(x + 4)(x + 1)$

18 / 25

Which method helps in visualizing factorization using blocks or areas?

A) Equation method

B) Graph method

C) Statistical method

D) Concrete method

19 / 25

Factorize: ${6x}^{2} + 9x$

A) $3x(2x + 3)$

B) $9x(6x + 1)$

C) $x(6x + 9)$

D) $6x(x + 9)$

20 / 25

Which pair is used in trinomial factoring?

A) Addition only

B) Sum and product

C) Division and subtraction

D) Multiplication only

21 / 25

Factorize: $x^{2} + x$

A) $1(x + x)$

B) $x^{2}(1 + 1)$

C) $x(x + 1)$

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

22 / 25

Which expression shows correct common factor extraction?

A) $x^{2} + x = x + 1$

B) $x^{2} + x = x^{2}(x + 1)$

C) $x^{2} + x = x(x + 1)$

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

23 / 25

In trinomial $x^{2} + bx + c$, we find factors of:

A) $b$ only

B) $x$ only

C) $c$ only

D) $b$ and $c$

24 / 25

Which is NOT a step in factoring?

A) Splitting middle term

B) Grouping terms

C) Finding $GCF$

D) Random guessing only

25 / 25

Why is factoring useful?

A) Simplifies expressions

B) Removes variables

C) Avoids equations

D) Makes numbers larger

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