WorksheetsFactoring Techniques Quiz
Total questions: 103
Worksheet time: 2hrs 22mins
Determine which of the following statements are correct, mark '✓' in the box:
x - 1 is a factor of 5x^2 + 3x - 2
x + 1 is a factor of 5x^2 + 3x - 2
15x + 1 is a factor of 5x^2 + 3x - 2
5x^2 + 3x - 2 is a multiple of 5x - 2
Given 7x^2 + 48x - 7 = (x + 7)(7x - 1), determine the following:
7x - 1 is a factor of 7x^2 + 48x - 7
7x - 1 is a multiple of 7x^2 + 48x - 7
x - 7 is a factor of 7x^2 + 48x - 7
x + 7 is a factor of 7x^2 + 48x - 7
Given -x^2 + 4 = -(x + 2)(x - 2), determine the following:
x + 2 is a factor of -x^2 + 4
-x^2 + 4 is a multiple of x - 2
-x - 2 is a factor of -x^2 + 4
x - 4 is a factor of -x^2 + 4
Given 6x^2 + 7x + 1 = (x + 1)(6x + 1), determine the following:
6x + 1 is a multiple of 6x^2 + 7x + 1
x + 1 is a multiple of 6x^2 + 7x + 1
6x^2 + 7x + 1 is a multiple of x + 1
6x^2 + 7x + 1 is a multiple of 6x + 1
Given 12x^2 + 19x + 4 = (3x + 4)(4x + 1), determine the following:
3x + 4 is a factor of 12x^2 + 19x + 4
12x^2 + 19x + 4 is a multiple of 4x + 1
3x + 1 is a factor of 12x^2 + 19x + 4
(3x + 4)(4x + 1) is a factor of 12x^2 + 19x + 4
Determine if 5x - 4 is a factor of 15x^2 - 7x - 4. If so, factor 15x^2 - 7x - 4.
Determine if x - 1 is a factor of 7x^2 - 11x + 4. If so, factor 7x^2 - 11x + 4.
Determine if 3x - 4 is a factor of 15x^2 - 29x + 12. If so, factor 15x^2 - 29x + 12.
Determine if x - 3 is a factor of 2x^2 + 5x - 3. If so, factor 2x^2 + 5x - 3.
Determine if 2x - 5 is a factor of 6x^2 - 19x + 15. If so, factor 6x^2 - 19x + 15.
Is 29x + 12 a factor? If so, factor 15x^2 - 29x + 12.
Is x - 3 a factor of 2x^2 + 5x - 3? If so, factor 2x^2 + 5x - 3.
Is 2x - 5 a factor of 6x^2 - 19x + 15? If so, factor 6x^2 - 19x + 15.
Factor the following expressions: 3b^2 + b.
(a)
Factor the following expressions: 5b + 2b^2.
(a)
Factor the following expressions: y^2 - 2y.
(a)
Factor the following expressions: 5x^2 + 2x.
(a)
Factor the following expressions: 2x^2 + 8x.
(a)
Factor the following expressions: x^2 + x.
(a)
Factor the following expressions: 5y^2 - 3y.
(a)
Factor the following expressions: 7x^2 + 49x.
(a)
Factor the following expressions: 5x^3 + 2x.
(a)
Factor the following expressions: 25x^2 + 5x.
(a)
Factor the following expressions: -5a^2 - 7a.
(a)
Factor the following expressions: 2a^2 + 4a^3.
(a)
Factor the following expressions: 37x + 9x^2.
(a)
Factor the following expressions: 13x^3 - 39x^2.
(a)
Factor the following expressions: a^2 + 15a.
Factor the following expressions: b(5b - 2) - 2b.
(a)
Factor the following expressions: x(x - 1) + 3(x - 1).
(a)
Factor the following expressions: (7x + 3)(4x + 3) + (2x - 5)(4x + 3).
Factor the following expressions: 4(x + 3) - 5x(x + 3).
(a)
Factor the following expressions: (3x - 2)(x + 3) - (2x - 1)(3x - 2).
Factor the following expressions: 3x(2x - 3) + 5(2x - 3).
Factor the following expressions: (x - 3)(2x - 3) - (x - 2)(x - 3).
(a)
Factor the following expressions: 2x(3x + 2) - 7(3x + 2).
Factor the following expressions: (y + 3)(y - 3) - (2y - 3)(y - 3).
(a)
Factor the following expressions: x(4x - 1) - 8(4x - 1).
(a)
Factor the following expressions: x(2x - 5) + (x + 1)(2x - 5).
Factor the following expressions: (3x + 5)^2 - (3x + 5).
Factor the following expressions: (3x + 1)(x - 2) - (2x + 1)(x - 2).
(a)
Factor the following expressions: 2x(7x + 3) + (7x + 3)(x + 5).
(1) Factor the expression x(2x-1) + (1-2x).
(a)
(2) Factor the expression 2x(2x-3) - 3(3-2x).
(a)
(3) Factor the expression x(x-1) - (1-x)(2x-5).
(a)
(4) Factor the expression (4x-3)^2 - 3x(3-4x).
(a)
(5) Factor the expression (3x+5)^2 + x(-3x-5).
(a)
(6) Factor the expression 2x(2x-7) + (7-2x)(x+7).
(a)
(7) Factor the expression (x-2)(4x-1) - 3x(2-x).
(a)
(8) Factor the expression (1-5x) - (5x-1)(x+4).
(a)
(9) Factor the expression (x+1)(x-3) - (x+4)(3-x).
(a)
(10) Factor the expression (5y-3)(y+1) - (3y-4)(3-5y).
(a)
(11) Factor the expression (1-2x)(x+3) + (2x-1)(3x+2).
(a)
(12) Factor the expression (y+2)(2y-1) + (1-2y)(3y-4).
(a)
(13) Factor the expression (2x-7)^2 - (x-6)(7-2x).
(a)
(14) Factor the expression (3x-2)^2 + (2-3x)(2+4x).
(a)
(15) Factor the expression (x+1)(2x-5) - (x+2)(5-2x).
(a)
(16) Factor the expression (3x+2)(5x-7) + (2-3x)(7-5x).
(a)
如下圖，有1個邊長為x的大正方形、5個長為x、寬為1的長方形、6個邊長為1的小正方形，在不重疊的情況下，這12個圖形可緊密拼出一個大長方形，若大長方形的寬為（x＋2），求大長方形的長。
如下圖，有1個邊長為x的大正方形、5個長為x、寬為1的長方形、4個邊長為1的小正方形，在不重疊的情況下，這10個圖形可緊密拼出一個大長方形，若大長方形的寬為（x＋1），求大長方形的長。
如下圖，有2個邊長為x的大正方形、3個長為x、寬為1的長方形、1個邊長為1的小正方形，在不重疊的情況下，這6個圖形可緊密拼出一個大長方形，若大長方形的長為（2x＋1），求大長方形的寬。
如下圖，有2個邊長為x的大正方形、5個長為x、寬為1的長方形、2個邊長為1的小正方形，在不重疊的情況下，這9個圖形可緊密拼出一個大長方形，若大長方形的長為（2x＋1），求大長方形的寬。
利用平方差公式因式分解因式分解下列各式： (1) x^2 - 81
(a)
利用平方差公式因式分解因式分解下列各式： (2) x^2 - 16
(a)
利用平方差公式因式分解因式分解下列各式： (3) 4y^2 - 9
(a)
利用平方差公式因式分解因式分解下列各式： (4) 36y^2 - 25
(a)
利用平方差公式因式分解因式分解下列各式： (5) 49x^2 - 1
(a)
利用平方差公式因式分解因式分解下列各式： (6) 9x^2 - 4
(a)
利用平方差公式因式分解因式分解下列各式： (7) 81y^2 - 100
(a)
利用平方差公式因式分解因式分解下列各式： (8) 100y^2 - 49
(a)
利用平方差公式因式分解因式分解下列各式： (9) (x+1)^2 - 4
(a)
Factor the expression (x+4)(x-4)
Factor the expression (2y+3)(2y-3)
Factor the expression (6y+5)(6y-5)
Factor the expression (7x+1)(7x-1)
Factor the expression (3x+2)(3x-2)
Factor the expression (9y+10)(9y-10)
Factor the expression (10y+7)(10y-7)
Factor the expression (x+1)(x-4)
Factor the expression (x+3)(x-1)
Factor the expression (x-3)(x-16)
Factor the expression 25-(y+5)(-y(y+10))
Factor the expression 36-(y+2)(-y-4)(y+8)
Factor the expression 49-(y-1)(-y-8)(y+6)
Factor the expression (2x+3)(-x-1)(3x+2)(x+4)
Factor the expression (5x-3)(-x-2)(6x-5)(4x-1)
Factor the expression (6x-7)(-5x+4)(11x-3)(x-11)
Factor the expression x^2 + 10x + 25
(a)
Factor the expression x^2 + 16x + 64
(a)
Factor the expression 9x^2 + 24x + 16
(a)
Factor the expression 49x^2 + 28x + 4
(a)
Factor the expression y^2 + 14y + 49
(a)
Factor the expression 9y^2 + 30y + 25
(a)
Factor the expression 4y^2 + 36y + 81
(a)
Factor the expression 25y^2 + 20y + 4
(a)
Factor the expression x^2 - 12x + 36
(a)
Factor the expression x^2 - 18x + 81
(a)
Factor the expression x^2 - 10x + 25
(a)
Factor the expression 16x^2 - 24x + 9
(a)
Factor the expression 25y^2 - 20y + 4
(a)
Factor the expression 36y^2 - 60y + 25
(a)
Factor the expression 49y^2 - 42y + 9
(a)
Factor the expression 4y^2 - 28y + 49
(a)
