Question

directions: determine which method of factoring to use for each of the given quadratics. then, find the zeros.

1. what are the roots of $f(x) = x^2 - 4$?

which method of factoring should we use?

1. what are the zeros of the function $f(x) = x^2 - 5x - 6$

you try!
directions: use factoring to determine the roots of the following quadratic functions.

1. $r(x) = x^2 + 3x - 18$
2. $f(x) = 4x^2 - 100$
3. $k(x) = 3x^2 - 3x - 6$
4. $x^2 - 5x - 14$

Explanation:

Step1: Solve $r(x)=x^2+3x-18$

Set $x^2+3x-18=0$, factor:
$(x+6)(x-3)=0$
Solve each factor:
$x+6=0 \implies x=-6$; $x-3=0 \implies x=3$

Step2: Solve $f(x)=4x^2-100$

Set $4x^2-100=0$, factor out 4:
$4(x^2-25)=0$
Difference of squares:
$4(x+5)(x-5)=0$
Solve each factor:
$x+5=0 \implies x=-5$; $x-5=0 \implies x=5$

Step3: Solve $k(x)=3x^2-3x-6$

Set $3x^2-3x-6=0$, factor out 3:
$3(x^2-x-2)=0$
Factor quadratic:
$3(x-2)(x+1)=0$
Solve each factor:
$x-2=0 \implies x=2$; $x+1=0 \implies x=-1$

Step4: Solve $x^2-5x-14=0$

Factor the quadratic:
$(x-7)(x+2)=0$
Solve each factor:
$x-7=0 \implies x=7$; $x+2=0 \implies x=-2$

Answer:

1. Roots of $r(x)$: $x=-6$ and $x=3$
2. Roots of $f(x)$: $x=-5$ and $x=5$
3. Roots of $k(x)$: $x=-1$ and $x=2$
4. Roots of $x^2-5x-14$: $x=-2$ and $x=7$