Factoring Quadratic Equations

solving quadratics by factoring

Multiple Choice

The product of two numbers is 10 and their sum is 24. What are the numbers?

• 8 and 2

• 6 and 4

• 12 and 12

• 10 and 14

Multiple Choice

The product of two numbers is 16 and their sum is 8. What are the numbers?

• 8 and 8

• 4 and 4

• 12 and 4

• 8 and 2

Multiple Choice

The product of two numbers is 30 and their sum is 11. What are the numbers?

• 9 and 2

• 10 and 3

• 3 and 8

• 6 and 5

Multiple Choice

The product of two numbers is 48 and their sum is 16. What are the numbers?

• 12 and 4

• 8 and 8

• 10 and 6

• 11 and 5

Multiple Choice

The product of two numbers is 15 and their sum is 16. What are the numbers?

• 12 and 4

• 8 and 8

• 5 and 11

• 1 and 15

What do you think those two numbers are?

​Whose product is 36 and sum is 12.

1. SPLIT THE MIDDLE TERM: To do that in the above, find two numbers:

Solve the equation: x²+20x+36=0

What do you think those two numbers are? 18 and 2

​Whose product is 36 and sum is 12.

1. SPLIT THE MIDDLE TERM: To do that in the above, find two numbers:

Solve the equation: x²+20x+36=0

2. SPLIT THE MIDDLE TERM using those two numbers:

x²+ +36=0

Solve the equation: x²+20x+36=0

2. SPLIT THE MIDDLE TERM:

x²+18x+2x+36=0

Solve the equation: x²+20x+36=0

Multiple Choice

Split the middle term in the quadratic equation correctlu:

$$x^2+13x+42=0$$

• $$x^2+8x+5x+42=0$$

• $$x^2+6x+7x+42=0$$

• $$x^2+10x+3x+42=0$$

• $$x^2+9x+4x+42=0$$

Multiple Choice

Split the middle term in the quadratic equation correctlu:

$$x^2+9x+14=0$$

• $$x^2+6x+3x+14=0$$

• $$x^2+4x+5x+14=0$$

• $$x^2+7x+2x+14=0$$

• $$x^2+10x+4x+14=0$$

Multiple Choice

Split the middle term in the quadratic equation correctlu:

$$x^2+50x+49=0$$

• $$x^2+7x+7x+49=0$$

• $$x^2+x+49x+49=0$$

• $$x^2+40x+9x+49=0$$

• $$x^2+7x+7x+49=0$$

Multiple Choice

Split the middle term in the quadratic equation correctlu:

$$x^2+12x+20=0$$

• $$x^2+10x+2x+20=0$$

• $$x^2+5x+4x+20=0$$

• $$x^2+x+20x+20=0$$

• $$x^2+10x+10x+20=0$$

Multiple Choice

Split the middle term in the quadratic equation correctlu:

$$x^2+10x+25=0$$

• $$x^2+10x+15x+25=0$$

• $$x^2+5x+20x+25=0$$

• $$x^2+x+25x+25=0$$

• $$x^2+5x+5x+25=0$$

( )+ ( )=0

what do you notice?

Solve the equation: x²+20x+36=0

3. FACTORISE IN PAIRS

x²+18x+2x+36=0

x(x+18)+2(x+18)=0

what do you notice?

Solve the equation: x²+20x+36=0

3. FACTORISE IN PAIRS

x²+18x+2x+36=0

Multiple Choice

Factorise the following in pairs:

$$x^2+15x+3x+45=0$$

• $$x\left(x+15\right)+3\left(x+15\right)=0$$

• $$x\left(x+15\right)+3\left(x+45\right)=0$$

• $$x\left(x+15x\right)+3\left(x+15\right)=0$$

• $$x\left(x+15\right)+5\left(x+9\right)=0$$

Multiple Choice

Factorise the following in pairs:

$$x^2+8x+4x+32=0$$

• $$x\left(x+4\right)+3\left(x+8\right)=0$$

• $$x\left(x+8\right)+4\left(x+32\right)=0$$

• $$x\left(x+8\right)+4\left(x+8\right)=0$$

• $$x\left(x+8\right)+4\left(x+32\right)=0$$

Multiple Choice

Factorise the following in pairs:

$$x^2+7x+5x+35=0$$

• $$x\left(x+20\right)+5\left(x+15\right)=0$$

• $$x\left(x+7\right)+5\left(x+35\right)=0$$

• $$x\left(x+5\right)+4\left(x+7\right)=0$$

• $$x\left(x+7\right)+5\left(x+7\right)=0$$

Multiple Choice

Factorise the following in pairs:

$$x^2+14x+2x+28=0$$

• $$x\left(x+14\right)+2\left(x+14\right)=0$$

• $$x\left(x+2\right)+2\left(x+14\right)=0$$

• $$x\left(x+5\right)+4\left(x+7\right)=0$$

• $$x\left(x+7\right)+5\left(x+7\right)=0$$

Multiple Choice

Factorise the following in pairs:

$$x^2+5x+10x+50=0$$

• $$x\left(x+14\right)+2\left(x+14\right)=0$$

• $$x\left(x+5\right)+5\left(x+10\right)=0$$

• $$x\left(x+5\right)+10\left(x+5\right)=0$$

• $$x\left(x+7\right)+5\left(x+7\right)=0$$

x(x+18)+2(x+18)=0

( )( )=0

Solve the equation: x²+20x+36=0

4. FACTORISE AGAIN:

x²+18x+2x+36=0

x(x+18)+2(x+18)=0

(x+18)(x+2)=0

Solve the equation: x²+20x+36=0

4. FACTORISE AGAIN:

x²+18x+2x+36=0

Multiple Choice

Factorise again the following:

$$x\left(x+2\right)+5\left(x+2\right)=0$$

• $$\left(x+2\right)\left(x+5\right)=0\ or\ \ \left(x+5\right)\left(x+2\right)=0$$

• $$\left(x+5\right)\left(5x+2\right)=0$$

• $$\left(x+2\right)\left(x+10\right)=0$$

• $$x^2+2x+5x+10=0$$

Multiple Choice

Factorise again the following:

$$x\left(x+6\right)+8\left(x+6\right)=0$$

• $$\left(x+8\right)\left(x+16\right)=0\$$

• $$\left(x+8\right)\left(x+8\right)=0$$

• $$\left(x+6\right)\left(x+8\right)=0$$

• $$x^2+8x+6x+48=0$$

Multiple Choice

Factorise again the following:

$$x\left(x+3\right)+4\left(x+3\right)=0$$

• $$\left(x+7\right)\left(x+3\right)=0\$$

• $$\left(x+4\right)\left(x+4\right)=0$$

• $$\left(x+1\right)\left(x+3\right)=0$$

• $$\left(x+3\right)\left(x+4\right)=0$$

Multiple Choice

Factorise again the following:

$$x\left(x+6\right)+6\left(x+6\right)=0$$

• $$\left(x+7\right)\left(x+3\right)=0\$$

• no answer

• $$\left(x+6\right)\left(x+6\right)=0$$

• $$\left(x+3\right)\left(x+4\right)=0$$

Multiple Choice

Factorise again the following:

$$x\left(x+14\right)+1\left(x+14\right)=0$$

• $$\left(x+7\right)\left(x+2\right)=0\$$

• $$\left(x+14\right)\left(x+1\right)=0$$

• $$\left(x+14\right)\left(x+14\right)=0$$

• $$\left(x+3\right)\left(x+4\right)=0$$

Solve the equation: x²+20x+36=0

5. SPLIT AND SOLVE FOR X:

x²+18x+2x+36=0

x(x+18)+2(x+18)=0

(x+18)(x+2)=0

x+18 =0 which means x = -18

x+2 =0 which means x = -2

Solve the equation: x²+20x+36=

Now go through all the steps again and solve the quadratic equations that follow:

x²+18x+2x+36=0

x(x+18)+2(x+18)=0

(x+18)(x+2)=0

x+18 =0 which means x = -18

x+2 =0 which means x = -2

Multiple Choice

Solve the following quadratic equation:

$$x^2+13x+42=0$$

• $$x=-2,\ x\ =-21$$

• $$x=-6,\ x\ =-7$$

• $$x=-1\ x\ =-41$$

• $$x=-3,\ x\ =-14$$

Multiple Choice

Solve the following quadratic equation:

$$x^2+50x+49=0$$

• $$x=-2,\ x\ =-21$$

• $$x=-7,\ x\ =-7$$

• $$x=-1\ x\ =-49$$

• $$x=-3,\ x\ =-14$$

Multiple Choice

Solve the following quadratic equation:

$$x^2+12x+20=0$$

• $$x=-2,\ x\ =-18$$

• $$x=-2,\ x\ =-10$$

• $$x=-5\ x\ =-4$$

• $$x=-20,\ x\ =-1$$

Multiple Choice

Solve the following quadratic equation:

$$x^2+17x+60=0$$

• $$x=-6,\ x\ =-10$$

• $$x=-2,\ x\ =-30$$

• $$x=-5\ x\ =-12$$

• $$x=-4,\ x\ =-15$$

Multiple Choice

Solve the following quadratic equation:

$$x^2+5x+6=0$$

• $$x=-2,\ x\ =-3$$

• $$x=3,\ x\ =2$$

• $$x=-5\ x\ =-1$$

• $$x=-4,\ x\ =-2$$

Multiple Choice

Solve the following quadratic equation:

$$x^2-9x+18=0$$

• $$x=-6,\ x\ =-3$$

• $$x=6,\ x\ =3$$

• $$x=-18\ x\ =-1$$

• $$x=-7,\ x\ =-2$$

Thank you and Good luck. 😌😊😊😊