Grade 9 Exam > Grade 9 Notes > Mathematics: Algebra 1 > Worksheet (with Solutions): Quadratics: Multiplying & Factoring
Worksheet (with Solutions): Quadratics: Multiplying & Factoring
Section A: Multiple Choice Questions
Q1: What is the product of \((x + 5)(x + 3)\)?
(a) \(x^2 + 8x + 15\)
(b) \(x^2 + 15x + 8\)
(c) \(x^2 + 8x + 8\)
(d) \(x^2 + 15x + 15\)
Q2: Which expression is the factored form of \(x^2 + 7x + 12\)?
(a) \((x + 3)(x + 4)\)
(b) \((x + 2)(x + 6)\)
(c) \((x + 1)(x + 12)\)
(d) \((x + 3)(x + 5)\)
Q3: What is \((2x + 3)(x - 4)\)?
(a) \(2x^2 - 5x - 12\)
(b) \(2x^2 + 5x - 12\)
(c) \(2x^2 - 8x - 12\)
(d) \(2x^2 - 11x - 12\)
Q4: Factor completely: \(x^2 - 9\)
(a) \((x - 3)(x - 3)\)
(b) \((x + 3)(x + 3)\)
(c) \((x - 9)(x + 1)\)
(d) \((x - 3)(x + 3)\)
Q5: What is the factored form of \(x^2 - 5x + 6\)?
(a) \((x - 2)(x - 3)\)
(b) \((x + 2)(x + 3)\)
(c) \((x - 1)(x - 6)\)
(d) \((x - 2)(x + 3)\)
Q6: Multiply: \((x - 7)(x + 7)\)
(a) \(x^2 - 49\)
(b) \(x^2 + 49\)
(c) \(x^2 - 14x - 49\)
(d) \(x^2 + 14x - 49\)
Q7: Factor: \(3x^2 + 12x\)
(a) \(3x(x + 4)\)
(b) \(x(3x + 12)\)
(c) \(3(x^2 + 4x)\)
(d) \(3x(x + 12)\)
Q8: What is \((x + 2)^2\)?
(a) \(x^2 + 4x + 4\)
(b) \(x^2 + 2x + 4\)
(c) \(x^2 + 4\)
(d) \(x^2 + 2x + 2\)
Section B: Fill in the Blanks
Q9: The product of two binomials can be found using the __________ method, which stands for First, Outer, Inner, Last.Q10: When factoring \(x^2 + bx + c\), you need to find two numbers that multiply to __________ and add to b.Q11: The expression \(a^2 - b^2\) can be factored as \((a - b)\)__________.Q12: The expansion of \((x + 5)^2\) is \(x^2 + 10x +\) __________.Q13: Before factoring a polynomial, always look for a __________ that can be factored out first.Q14: The factored form of \(x^2 - 16\) is \((x - 4)\)__________.Section C: Word Problems
Q15: A rectangular garden has a length of \((x + 8)\) feet and a width of \((x + 3)\) feet. Write an expression in standard form for the area of the garden.Q16: A square picture frame has side length \((x + 6)\) inches. What is the area of the picture frame in terms of x?
Q17: The area of a rectangular whiteboard is \(x^2 + 9x + 20\) square inches. If the length is \((x + 5)\) inches, what is the width?
Q18: A square patio has an area of \(x^2 - 100\) square feet. What is the length of one side of the patio? Express your answer in factored form.
Q19: A construction company is building a parking lot with length \((2x + 5)\) meters and width \((x - 3)\) meters. Find the area of the parking lot in standard form.
Q20: The product of two consecutive even integers can be represented as \(x(x + 2)\) where x is the first even integer. If their product is \(x^2 + 2x\), factor this expression completely and verify it represents the product of the two consecutive even integers.
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Document Description: Worksheet (with Solutions): Quadratics: Multiplying & Factoring for Grade 9 2026 is part of Mathematics: Algebra 1 preparation. The notes and questions for Worksheet (with Solutions): Quadratics: Multiplying & Factoring have been prepared according to the Grade 9 exam syllabus. Information about Worksheet (with Solutions): Quadratics: Multiplying & Factoring covers topics like and Worksheet (with Solutions): Quadratics: Multiplying & Factoring Example, for Grade 9 2026 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Worksheet (with Solutions): Quadratics: Multiplying & Factoring.
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