Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

9.3.5 • Practice

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

For the expressions in questions 1 – 4, choose which number would make the expression a perfect square. Then, choose an equivalent expression in factored form.

$x^2+3x$

What number can be added to make $x^2+3x$ a perfect square?

$-\frac23$
$\frac94$
$\frac49$
$\frac23$

Which expression is equivalent to $x^2+3x$ ?

$3(x + 1)$
$(x + 3)(x + 3)$
$x(3x)$
$x(x + 3)$

$x^2+0.6x$

What number can be added to make $x^2+0.6x$ a perfect square?

0.03
0.36
0.81
0.09

Which expression is equivalent to $x^2+0.6x$ ?

$0.6(x+1)$
$x(0.6x)$
$x(x+0.6)$
$x(x+0.6x)$

$x^2-11x$

What number can be added to make $x^2-11x$ a perfect square?

$\frac{121}{4}$
$\frac52$
$\frac{25}{2}$
$\frac{11}{2}$

Which expression is equivalent to $x^2-11x$ ?

$11x(x-1)$
$11(x-1)$
$x(x-11)$
$x(x-11x)$

$x^2-\frac{5}{2}x$

What number can be added to make $x^2-\frac{5}{2}x$ a perfect square?

$\frac68$
$\frac58$
$\frac{25}{16}$
$\frac{25}{4}$

Which expression is equivalent to $x^2-\frac{5}{2}x$ ?

$\frac{5}{2}(x-1)$
$\frac{5}{2}x(x-1)$
$x(x-\frac{5}{2}x)$
$x(x-\frac52)$

What number can be added to make $x^2+x$ a perfect square?

0
1
$\frac12$
$\frac14$

What number can be added to make $x^2-\frac{3}{2}x$ a perfect square?

$-\frac23$
$\frac{9}{16}$
$\frac49$
$\frac23$

Noah is solving the equation $x^2+8x+15=3$ . He begins by rewriting the expression on the left in factored form and writes $(x+3)(x+5)=3$ . He does not know what to do next.

Do you think using the factored form is the best way for Noah to solve this equation?

No
Yes

Solve the original equation, then choose the two roots.

$x = -4$
$x = 12$
$x = -2$
$x = -6$
$x = 4$

An equation and its solutions are given. Solve the equation by completing the square, then choose whether you agree or disagree with the given solutions.

$x^2+20x+50=14$ . The solutions are $x=-18$ and $x=-2$ .

Agree
Disagree

$x^2+1.6x=0.36$ . The solutions are $x=-1.8$ and $x=0.2$ .

Agree
Disagree

$x^2-5x=\frac{11}{4}$ . The solutions are $x=\frac{11}{4}$ and $x=-12$ .

Agree
Disagree

Solve each equation, then choose the two roots.

$x^2-0.5x=0.5$

$x = -0.5$
$x = 1$
$x = 0$
$x = 2$
$x = -1$

$x^2+0.8x=0.09$

$x = -0.9$
$x = 0.8$
$x = 0.4$
$x = 0.1$
$x = 0.81$

$x^2+\frac{13}{3}x=\frac{56}{36}$

$x = \frac{28}{3}$
$x =\frac{1}{9}$
$x=\frac{112}{36}$
$x=-\frac{14}{3}$
$x = \frac13$

9.3.5 Practice