Algebraic Expressions Factorization Competitive Exams
50 questions · Mathematics
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Question 1 of 50
The number of terms in 4x^3 - 2x + 7 is
ExplanationThe terms are 4x^3, -2x and 7.
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Question 2 of 50
If a + b + c = 0, then a^3 + b^3 + c^3 =
ExplanationThe identity a^3 + b^3 + c^3 - 3abc = (a + b + c)(...) vanishes when a + b + c = 0.
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Question 3 of 50
A polynomial of degree 2 is called
ExplanationDegree 1 is linear, 2 is quadratic and 3 is cubic.
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Question 4 of 50
(3x + 2) + (5x - 7) =
ExplanationAdd like terms: 3x + 5x = 8x and 2 - 7 = -5.
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Question 5 of 50
If a + b = 5 and ab = 6, then a^2 + b^2 =
Explanationa^2 + b^2 = (a + b)^2 - 2ab = 25 - 12 = 13.
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Question 6 of 50
(3x - 2)^2 =
Explanation(3x)^2 - 2(3x)(2) + 2^2.
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Question 7 of 50
Factorise: 3x^2 - 12
ExplanationTake 3 common, then x^2 - 4 = (x - 2)(x + 2).
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Question 8 of 50
If a + b = 4 and ab = 3, then a^3 + b^3 =
Explanationa^3 + b^3 = (a + b)^3 - 3ab(a + b) = 64 - 36 = 28.
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Question 9 of 50
Factorise: 9x^2 - 12x + 4
Explanation(3x)^2 - 2(3x)(2) + 2^2.
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Question 10 of 50
Factorise: x^2 + 5x
ExplanationThe common factor is x.
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Question 11 of 50
Factorise: 2x^2 + 7x + 3
ExplanationSplit the middle term: 2x^2 + 6x + x + 3.
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Question 12 of 50
3(x + 4) =
ExplanationMultiply each term by 3.
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Question 13 of 50
(7x + 3) - (2x - 4) =
ExplanationRemove brackets: 7x + 3 - 2x + 4 = 5x + 7.
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Question 14 of 50
Factorise: x^2 - 5x + 6
ExplanationTwo numbers with sum -5 and product 6: -2 and -3.
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Question 15 of 50
Simplify: (x^2 - 9)/(x - 3)
Explanationx^2 - 9 = (x - 3)(x + 3); cancel (x - 3).
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Question 16 of 50
(x + 5)^2 =
Explanation(a + b)^2 = a^2 + 2ab + b^2.
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Question 17 of 50
The degree of the polynomial 3x^4 + 2x^2 - 5 is
ExplanationThe degree is the highest power of the variable, which is 4.
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Question 18 of 50
(2x + 3)^2 =
Explanation(2x)^2 + 2(2x)(3) + 3^2.
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Question 19 of 50
Using an identity, 99^2 =
Explanation(100 - 1)^2 = 10,000 - 200 + 1 = 9,801.
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Question 20 of 50
(2a - 5)(2a + 5) =
ExplanationDifference of squares: (2a)^2 - 5^2.
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Question 21 of 50
(x + 2)(x + 3) =
Explanationx^2 + 3x + 2x + 6 = x^2 + 5x + 6.
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Question 22 of 50
Factorise: 8a^3 - 27b^3
Explanation(2a)^3 - (3b)^3 uses the difference of cubes identity.
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Question 23 of 50
Factorise: (x + y)^2 - z^2
Explanationa^2 - b^2 with a = x + y and b = z.
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Question 24 of 50
Factorise by grouping: ax + ay + bx + by
Explanationa(x + y) + b(x + y) = (a + b)(x + y).
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Question 25 of 50
Factorise: 2x^3 - 8x
ExplanationTake 2x common: 2x(x^2 - 4).
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Question 26 of 50
Factorise: 6x^2 - x - 2
ExplanationSplit the middle term: 6x^2 - 4x + 3x - 2.
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Question 27 of 50
x(x - 5) =
ExplanationDistribute x: x * x - x * 5.
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Question 28 of 50
If x - 1/x = 3, then x^2 + 1/x^2 =
ExplanationSquare both sides: x^2 - 2 + 1/x^2 = 9, so the value is 11.
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Question 29 of 50
Factorise: x^2 - 25
Explanationa^2 - b^2 = (a - b)(a + b).
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Question 30 of 50
If a - b = 3 and ab = 10, then a^2 + b^2 =
Explanationa^2 + b^2 = (a - b)^2 + 2ab = 9 + 20 = 29.
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Question 31 of 50
Factorise: 4x^2 - 9
Explanation(2x)^2 - 3^2.
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Question 32 of 50
Factorise: 6x + 9
ExplanationThe HCF of 6x and 9 is 3.
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Question 33 of 50
Factorise: x^3 - 27
Explanationa^3 - b^3 = (a - b)(a^2 + ab + b^2).
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Question 34 of 50
Using an identity, 103 x 97 =
Explanation(100 + 3)(100 - 3) = 10,000 - 9 = 9,991.
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Question 35 of 50
If a + b + c = 10 and ab + bc + ca = 31, then a^2 + b^2 + c^2 =
Explanation(a + b + c)^2 - 2(ab + bc + ca) = 100 - 62 = 38.
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Question 36 of 50
Factorise: x^3 + 8
Explanationa^3 + b^3 = (a + b)(a^2 - ab + b^2).
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Question 37 of 50
If x + 1/x = 5, then x^2 + 1/x^2 =
ExplanationSquare both sides: x^2 + 2 + 1/x^2 = 25, so the value is 23.
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Question 38 of 50
(x + 7)(x - 3) =
Explanationx^2 - 3x + 7x - 21.
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Question 39 of 50
(x - 3)^2 =
Explanation(a - b)^2 = a^2 - 2ab + b^2.
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Question 40 of 50
(x + 2)^3 =
Explanation(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.
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Question 41 of 50
(x - 1)^3 =
Explanation(a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3.
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Question 42 of 50
Factorise: x^2 + 10x + 25
ExplanationIt is a perfect square: a^2 + 2ab + b^2.
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Question 43 of 50
Factorise: x^2 + 7x + 12
ExplanationFind two numbers with sum 7 and product 12: 3 and 4.
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Question 44 of 50
Using an identity, 47^2 - 43^2 =
Explanation(47 - 43)(47 + 43) = 4 x 90 = 360.
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Question 45 of 50
Simplify: (x^2 - 5x + 6)/(x - 2)
Explanationx^2 - 5x + 6 = (x - 2)(x - 3).
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Question 46 of 50
(x - 4)(x + 4) =
Explanation(a - b)(a + b) = a^2 - b^2.
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Question 47 of 50
Factorise: x^2 + 2x - 15
ExplanationTwo numbers with sum 2 and product -15: 5 and -3.
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Question 48 of 50
The value of 2x + 3 when x = 4 is
Explanation2(4) + 3 = 11.
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Question 49 of 50
Factorise: x^4 - 16
Explanationx^4 - 16 = (x^2 - 4)(x^2 + 4), and x^2 - 4 factorises further.
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Question 50 of 50
The coefficient of x in 5x^2 - 7x + 3 is
ExplanationThe coefficient is the number multiplying x, including its sign: -7.
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