Practice - Algebra 1

8.7.5 Practice

8.7.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

For questions 1 – 7, find the factored form of the quadratic expression.

$x^2+4x − 12$

$(x − 2)(x + 6)$
$(x + 2)(x − 6)$
$(x + 3)(x − 4)$
$(x − 2)(x − 6)$

$x^2−3x −18$

$(x − 7)(x + 3)$
$(x − 18)(x + 1)$
$(x − 6)(x + 3)$
$(x − 9)(x + 2)$

$x^2− 12x − 45$

$(x − 15)(x + 3)$
$(x − 9)(x + 5)$
$(x − 8)(x − 4)$
$(x − 45)(x + 1)$

$x^2−x −20$

$(x + 5)(x − 4)$
$(x − 20)(x + 1)$
$(x − 5)(x + 4)$
$(x − 10)(x + 2)$

$x^2+2x −35$

$(x − 5)(x − 7)$
$(x + 5)(x − 7)$
$(x + 5)(x + 7)$
$(x − 5)(x + 7)$

$x^2−23x −50$

$(x − 10)(x − 13)$
$(x − 25)(x + 2)$
$(x − 50)(x + 1)$
$(x − 10)(x + 5)$

$x^2+7x −60$

$(x − 4)(x + 15)$
$(x − 10)(x + 3)$
$(x − 20)(x + 3)$
$(x − 5)(x + 12)$

Consider the expression $x^2+bx - 80$ , where the leading coefficient equals 1. Identify all the pairs of factors of –80 that would result in positive values of $b$ .

$80$ and $-1$ , $40$ and $-2$ , $20$ and $-4$ , $16$ and $-5$ , $10$ and $-8$
$-80$ and $-1$ , $-40$ and $-2$ , $-20$ and $-4$ , $-16$ and $-5$ , $-10$ and $-8$
$-80$ and $1$ , $-40$ and $2$ , $-20$ and $4$ , $-16$ and $5$ , $-10$ and $8$
$80$ and $1$ , $40$ and $2$ , $20$ and $4$ , $16$ and $5$ , $10$ and $8$

Consider the expression $x^2+ bx - 80$ , where the leading coefficient equals 1. Identify all the pairs of factors of $-80$ that would result in negative values of $b$ .

$80$ and $-1$ , $40$ and $-2$ , $20$ and $-4$ , $16$ and $-5$ , $10$ and $-8$
$-80$ and $-1$ , $-40$ and $-2$ , $-20$ and $-4$ , $-16$ and $-5$ , $-10$ and $-8$
$-80$ and $1$ , $-40$ and $2$ , $-20$ and $4$ , $-16$ and $5$ , $-10$ and $8$
$80$ and $1$ , $40$ and $2$ , $20$ and $4$ , $16$ and $5$ , $10$ and $8$

Here are pairs of equivalent expressions: one in standard form and the other in factored form. Identify the missing symbols:

$x^2\; ◻\; 15x \ ◻\; 34$ and $(x + 2)(x − 17)$

– and +
+ and +
+ and –
– and –