Factoring quadratic expressions (ACT) Practice Questions (Grade 9)

Question 1easy

Which is a factored form of $x^2 + 5x + 6$ ?

Find two numbers with product $6$ and sum $5$ : $2$ and $3$ . So $x^2 + 5x + 6 = (x+2)(x+3)$ .

Question 2easy

Which is a factored form of $x^2 + x - 12$ ?

Find two numbers with product $-12$ and sum $1$ : $4$ and $-3$ . So $x^2 + x - 12 = (x+4)(x-3)$ .

Question 3easy

Which expression is equivalent to $x^2 - 6x + 8$ ?

Find two numbers with product $8$ and sum $-6$ : $-2$ and $-4$ . So $x^2 - 6x + 8 = (x-2)(x-4)$ .

Question 4easy

Which expression is equivalent to $x^2 + 7x + 12$ ?

Find two numbers with product $12$ and sum $7$ : $3$ and $4$ . So $x^2 + 7x + 12 = (x+3)(x+4)$ .

Question 5easy

Which is a factored form of $x^2 - x - 20$ ?

Find two numbers with product $-20$ and sum $-1$ : $4$ and $-5$ . So $x^2 - x - 20 = (x+4)(x-5)$ .

Question 6easy

Which expression is equivalent to $x^2 + 2x - 15$ ?

Find two numbers with product $-15$ and sum $2$ : $5$ and $-3$ . So $x^2 + 2x - 15 = (x+5)(x-3)$ .

Question 7easy

Which is a factored form of $x^2 - 8x + 15$ ?

Find two numbers with product $15$ and sum $-8$ : $-3$ and $-5$ . So $x^2 - 8x + 15 = (x-3)(x-5)$ .

Question 8medium

Which expression is equivalent to $2x^2 + 4x - 6$ ?

Factor out $2$ first: $2x^2 + 4x - 6 = 2(x^2 + 2x - 3)$ . Then find two numbers with product $-3$ and sum $2$ : $3$ and $-1$ . So $2x^2 + 4x - 6 = 2(x+3)(x-1)$ .

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