Gr 10 Math Ch 1: Factorization

What is the first step in the general procedure for factorising a trinomial?

Identify any common factors (correct)
Write down two brackets with an x in each bracket
List the coefficients of the terms
Expand the pairs to find the matching term

Which identity represents the difference of two squares?

x^2 - 2xy + y^2 = (x - y)^2
x^2 - y^2 = (x - y)(x + y)
a^2 - b^2 = (a + b)(a - b) (correct)
x^2 + y^2 = (x + y)(x - y)

When factorising by grouping in pairs, what is required?

Only use pairs of coefficients
Extract the smallest term as the factor
Group terms based on common factors (correct)
Identify two distinct prime factors

Which of these expressions can be factorised using the sum of two cubes identity?

x^3 - 8 (A) Signup and view all the answers

For the quadratic trinomial ax^2 + bx + c, what is needed to continue the factorisation process after setting up initial brackets?

Expand all possible factors to find one that fits (A) Signup and view all the answers

What are the factors of the expression x^3 + y^3?

(x + y)(x^2 + xy + y^2) (D) Signup and view all the answers

What is the result of factorising the expression using the difference of two squares identity for the expression $x^2 - 9$?

$(x - 3)(x + 3)$ (C) Signup and view all the answers

Which factorisation process allows for extracting a common factor from all terms in the expression?

Factorising by Taking Out a Common Factor (B) Signup and view all the answers

What is the correct factorisation of the quadratic trinomial $2x^2 + 7x + 3$?

$(2x + 3)(x + 1)$ (C), $(2x + 3)(x + 1)$ (D) Signup and view all the answers

Which identity is used to factorise the expression $x^3 - y^3$?

$x^3 - y^3 = (x - y)(x^2 + xy + y^2)$ (A) Signup and view all the answers

When factorising by grouping in pairs, what is the primary goal?

To group terms with similar factors and extract them (A) Signup and view all the answers

Which pair of factors could be generated for the expression $x^2 + 5x + 6$ during the factorisation process?

(2, 3) (A) Signup and view all the answers

What must be true for an expression to be factorised using the difference of two squares identity?

It must consist of two squared terms separated by a negative sign. (D) Signup and view all the answers

Which method involves creating pairs of terms to simplify expressions for factorisation?

Factorising by grouping (A) Signup and view all the answers

Which of the following is NOT a step in factorising a quadratic trinomial?

Write two separate expressions with common variables. (D) Signup and view all the answers

For the expression $x^3 + 8$, which identity is appropriate for factorisation?

Sum of two cubes (B) Signup and view all the answers

Which statement is true regarding the general procedure for factorising a trinomial?

You begin by placing $x$ in each of the two brackets. (C) Signup and view all the answers

What does the expression $16 - x^2$ factor into using the difference of two squares identity?

$(4 + x)(4 - x)$ (D) Signup and view all the answers

What is the result of factorising the expression $4x^2 - 25$ using the difference of two squares identity?

(2x + 5)(2x - 5) (C) Signup and view all the answers

Which set of values correctly represents the factors of the quadratic trinomial $3x^2 + 14x + 8$?

(3x + 2)(x + 4) (D) Signup and view all the answers

When applying the sum of two cubes identity, which of the following is the correct factorisation of $x^3 + 27$?

(x + 3)(x^2 - 3x + 9) (B) Signup and view all the answers

Which expression cannot be factored using the identity for the difference of two squares?

$x^2 - y^2 - 1$ (D) Signup and view all the answers

What is the first step in factorising the expression $2x^3 - 8x$ by taking out a common factor?

Factor out $2$ and then $x$. (A) Signup and view all the answers