Trinomials of the Form ax² ± bx ± c

Q.

Factorise: $2x^2-\frac{5}{6}x+\frac{1}{12}$

Q.

Factorize:

$x^2+6\sqrt{2}x+10$

Q.

Factorise:

$x^2+\frac{12}{35}x+\frac{1}{35}$

Q. Factorize
x³—2x²—x+2

Q.

Factorize:

$2x^2+3\sqrt{5}x+5$

Q.

Factorize:

$x^2-2\sqrt{2}x-30$

Q.

Factorize:

$x^2+5\sqrt{5}x+30$

Q.

the factors of $x^3-7x+6$ are

1. $x9x-6(x-1)$
   
   

2. $(x^2-6)(x-1)$

3. $(x+1)(x+2)(x-3)$

4. $(x-1)(x+3)(x-2)$

Q.

Factorize:

$x^2+2\sqrt{3}x-24$

Q.

Factorise:- 1-x³

Q.

Factorise:

$21x^2-2x+\frac{1}{21}$

Q.

If (x-1) is a factor of $x^4+x^3-2x^2+x+1$. Find the other factor using the factor theorem.

1. $x^3+2x^2+x+1$

2. $x^3+x^2+x$

3. $x^3+2x^2+1$

4. $x^3+2x^2+1$

Q. Factorize: $3a^2-1-2a$

1. $(3a-1)(a+1)$
2. $(a-1)(3a+1)$
3. $(3a+1)(a+1)$
4. $(a-1)(3a-1)$

Q.

Find the factors of $x^2+22x+112$ by splitting the middle term.

1. $(x+16)(x+3)$

2. $(x+9)(x+8)$

3. $(x+11)(x+8)$

4. $(x+14)(x+8)$

Q.

Factorize:

$x^2-\sqrt{3}x-6$

Q.

Factorize:

$5\sqrt{5}{x}^2+20x+3\sqrt{5}$

Q.

$4yz(z^2+6z-16)÷2y(z+8)$ gives

1. z-2

2. z(z-2)

3. 2z(z-2)

4. None of these

Q. Factorize: $(2x+3y{)}^2-12x-18y-7$

1. $(2x+3y+1)(2x+3y-7)$
2. $(2x+3y+1)(2x+3y+7)$
3. $(2x+3y-1)(2x+3y-7)$
4. $(2x+3y-1)(2x+3y+7)$

Q. $\text{If}(x+a)(x+b)=x^2+5x+6,\text{what is the value of}(a-b)\text{if}(a-b)>0?$

1. 1

Q. Factorize $4x^4-x^2-12x-36$

1. $(2x+3)(x+2)(2x^2+x+6)$
   
2. $(2x-3)(x-2)(2x^2+x+6)$
   
3. $=(2x+3)(x-2)(2x^2+x+6)$
   
4. $(2x+3)(x-2)(2x^2-x-6)$
   

Q. Factorize: $25x^2-90xy+81y^2$

1. $(9x+5y{)}^2$
2. $(9x-5y{)}^2$
3. $(5x-9y{)}^2$
4. $(5x-9y{)}^2$

Q. $a{x}^2+bx+c$ can be factorised using the method of 'splitting the middle term' if $b^2-4ac$ is a perfect square.

1. False
2. True

Q. Factorise:
$\left(i\right)x^3-2x^2-x+2$

$\left(ii\right)x^3-3x^2-9x-5$

$\left(iii\right)x^3+13x^2+32x+20$

$\left(iv\right)2y^3+y^2-2y-1$
[ 5 marks ]

Q. Factorise $2(ab+cd)-a^2-b^2+c^2+d^2$

1. $(c+d-a+b)(c+d-a-b)$
2. $(c+d+a+b)(c+d-a-b)$
3. $(c+d+a-b)(c-d-a-b)$
4. $(c-d+a+b)(c-d-a-b)$

Q.

$\text{Which of the following are the factors of}12ab+9a+12+16b?$

1. $(3a-4)\text{and}(4b-3)$

2. $(3a-4)\text{and}(4b+3)$

3. $(3a+4)\text{and}(4b+3)$
4. $(3a+4)(4b-3)$

Q. Factorize: $6a^2-a-15$

1. $(2a-3)(3a-5)$
2. $(2a+3)(5a-3)$
3. $(2a+3)(3a-5)$
4. $(3a+2)(2a-5)$

Q. If $x-2$ is a factor of $x^2+3ax-2a$, then $a=$

Q. If $x-3$ is a factor of $x^2-ax-15,thena=$

Q. Factorize: $4x^2-16xy$

1. $4x(x+4y)$
2. $2x(4x-y)$
3. $x(4x-6y)$
4. $4x(x-4y)$

Q. Factorize:
$x^2-14x+45$