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QUESTION IMAGE

directions: factor each trinomial. the answers to each problem are insi…
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Question

directions: factor each trinomial. the answers to each problem are inside the picture. color the picture using the colors given for each problem.

green

  1. $x^{2}+x-20$
  2. $x^{2}+4x-45$
  3. $x^{2}-x-6$

purple

  1. $x^{2}+6x-7$
  2. $x^{2}+9x+14$
  3. $x^{2}-25$

orange

  1. $x^{2}+11x+28$
  2. $x^{2}-16x+60$
  3. $x^{2}+14x+48$

red

  1. $x^{2}+5x-6$
  2. $x^{2}+3x-10$
  3. $x^{2}+19x+90$

blue

  1. $x^{2}-5x-36$
  2. $x^{2}+6x-27$
  3. $x^{2}+13x+40$

yellow

  1. $x^{2}+4x-5$
  2. $x^{2}+4x-21$
  3. $x^{2}+14x+48$

Explanation:

Step1: Factor $x^2+x-20$

Find two numbers: $5$ and $-4$, since $5+(-4)=1$, $5\times(-4)=-20$.
$\boldsymbol{x^2+x-20=(x+5)(x-4)}$

Step2: Factor $x^2+4x-45$

Find two numbers: $9$ and $-5$, since $9+(-5)=4$, $9\times(-5)=-45$.
$\boldsymbol{x^2+4x-45=(x+9)(x-5)}$

Step3: Factor $x^2-x-6$

Find two numbers: $2$ and $-3$, since $2+(-3)=-1$, $2\times(-3)=-6$.
$\boldsymbol{x^2-x-6=(x+2)(x-3)}$

Step4: Factor $x^2+6x-7$

Find two numbers: $7$ and $-1$, since $7+(-1)=6$, $7\times(-1)=-7$.
$\boldsymbol{x^2+6x-7=(x+7)(x-1)}$

Step5: Factor $x^2+9x+14$

Find two numbers: $7$ and $2$, since $7+2=9$, $7\times2=14$.
$\boldsymbol{x^2+9x+14=(x+7)(x+2)}$

Step6: Factor $x^2-25$

Use difference of squares: $a^2-b^2=(a+b)(a-b)$.
$\boldsymbol{x^2-25=(x+5)(x-5)}$

Step7: Factor $x^2+11x+28$

Find two numbers: $7$ and $4$, since $7+4=11$, $7\times4=28$.
$\boldsymbol{x^2+11x+28=(x+4)(x+7)}$

Step8: Factor $x^2-16x+60$

Find two numbers: $-10$ and $-6$, since $-10+(-6)=-16$, $-10\times(-6)=60$.
$\boldsymbol{x^2-16x+60=(x-10)(x-6)}$

Step9: Factor $x^2+14x+48$

Find two numbers: $8$ and $6$, since $8+6=14$, $8\times6=48$.
$\boldsymbol{x^2+14x+48=(x+6)(x+8)}$

Step10: Factor $x^2+5x-6$

Find two numbers: $6$ and $-1$, since $6+(-1)=5$, $6\times(-1)=-6$.
$\boldsymbol{x^2+5x-6=(x+6)(x-1)}$

Step11: Factor $x^2+3x-10$

Find two numbers: $5$ and $-2$, since $5+(-2)=3$, $5\times(-2)=-10$.
$\boldsymbol{x^2+3x-10=(x+5)(x-2)}$

Step12: Factor $x^2+19x+90$

Find two numbers: $10$ and $9$, since $10+9=19$, $10\times9=90$.
$\boldsymbol{x^2+19x+90=(x+10)(x+9)}$

Step13: Factor $x^2-5x-36$

Find two numbers: $4$ and $-9$, since $4+(-9)=-5$, $4\times(-9)=-36$.
$\boldsymbol{x^2-5x-36=(x+4)(x-9)}$

Step14: Factor $x^2+6x-27$

Find two numbers: $9$ and $-3$, since $9+(-3)=6$, $9\times(-3)=-27$.
$\boldsymbol{x^2+6x-27=(x+9)(x-3)}$

Step15: Factor $x^2+13x+40$

Find two numbers: $8$ and $5$, since $8+5=13$, $8\times5=40$.
$\boldsymbol{x^2+13x+40=(x+8)(x+5)}$

Step16: Factor $x^2+4x-5$

Find two numbers: $5$ and $-1$, since $5+(-1)=4$, $5\times(-1)=-5$.
$\boldsymbol{x^2+4x-5=(x+5)(x-1)}$

Step17: Factor $x^2+4x-21$

Find two numbers: $7$ and $-3$, since $7+(-3)=4$, $7\times(-3)=-21$.
$\boldsymbol{x^2+4x-21=(x+7)(x-3)}$

Step18: Factor $x^2+14x+48$

Find two numbers: $8$ and $6$, since $8+6=14$, $8\times6=48$.
$\boldsymbol{x^2+14x+48=(x+6)(x+8)}$

Answer:

  1. $\boldsymbol{(x+5)(x-4)}$
  2. $\boldsymbol{(x+9)(x-5)}$
  3. $\boldsymbol{(x+2)(x-3)}$
  4. $\boldsymbol{(x+7)(x-1)}$
  5. $\boldsymbol{(x+7)(x+2)}$
  6. $\boldsymbol{(x+5)(x-5)}$
  7. $\boldsymbol{(x+4)(x+7)}$
  8. $\boldsymbol{(x-10)(x-6)}$
  9. $\boldsymbol{(x+6)(x+8)}$
  10. $\boldsymbol{(x+6)(x-1)}$
  11. $\boldsymbol{(x+5)(x-2)}$
  12. $\boldsymbol{(x+10)(x+9)}$
  13. $\boldsymbol{(x+4)(x-9)}$
  14. $\boldsymbol{(x+9)(x-3)}$
  15. $\boldsymbol{(x+8)(x+5)}$
  16. $\boldsymbol{(x+5)(x-1)}$
  17. $\boldsymbol{(x+7)(x-3)}$
  18. $\boldsymbol{(x+6)(x+8)}$

To color the picture:

  • Green: Color the sections with $\boldsymbol{(x+5)(x-4)}$, $\boldsymbol{(x+9)(x-5)}$, $\boldsymbol{(x+2)(x-3)}$
  • Purple: Color the sections with $\boldsymbol{(x+7)(x-1)}$, $\boldsymbol{(x+7)(x+2)}$, $\boldsymbol{(x+5)(x-5)}$
  • Orange: Color the sections with $\boldsymbol{(x+4)(x+7)}$, $\boldsymbol{(x-10)(x-6)}$, $\boldsymbol{(x+6)(x+8)}$
  • Red: Color the sections with $\boldsymbol{(x+6)(x-1)}$, $\boldsymbol{(x+5)(x-2)}$, $\boldsymbol{(x+10)(x+9)}$
  • Blue: Color the sections with $\boldsymbol{(x+4)(x-9)}$, $\boldsymbol{(x+9)(x-3)}$, $\boldsymbol{(x+8)(x+5)}$
  • Yellow: Color the sections with $\boldsymbol{(x+5)(x-1)}$, $\boldsymbol{(x+7)(x-3)}$, $\boldsymbol{(x+6)(x+8)}$