Factorise Trinomials (Quadratics) 1

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Question 1 of 5

1. Question
Factor.

$x^{2} + 7 x + 12$ $x^2+7x+12$
- 1. $(x + 3) (x + 4)$ $(x+3)(x+4)$
- 2. $(x - 3) (x + 4)$ $(x-3)(x+4)$
- 3. $(x + 12) (x - 1)$ $(x+12)(x-1)$
- 4. $(x + 6) (x + 2)$ $(x+6)(x+2)$
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When factoring quadratics, use the Cross Method.

Use the cross method to factor $x^{2} + 7 x + 12$ $x^2+7x+12$

Start by drawing a cross.

Next, find two numbers that will multiply into $12$ $12$ and add up to $7$ $7$

Product Sum

$12$ $12$ and $1$ $1$ $12$ $12$ $13$ $13$

$6$ $6$ and $2$ $2$ $12$ $12$ $8$ $8$

$3$ $3$ and $4$ $4$ $12$ $12$ $7$ $7$

$3$ $3$ and $4$ $4$ fits this description.

Next, write $3$ $3$ and $4$ $4$ on the right side of the cross.

Now, find two values that will multiply into $x^{2}$ $x^2$ and write them on the left side of the cross.

$x$ $x$ and $x$ $x$ fits this description.

Finally, group the values in a row with a bracket and combine the brackets.

Therefore, the factored expression is $(x + 3) (x + 4)$ $(x+3)(x+4)$ .

$(x + 3) (x + 4)$ $(x+3)(x+4)$
Question 2 of 5

2. Question
Factor.

$y^{2} + 11 y + 30$ $y^2+11y+30$
- 1. $(y + 2) (y + 15)$ $(y+2)(y+15)$
- 2. $(y + 3) (y + 10)$ $(y+3)(y+10)$
- 3. $(y + 5) (y + 6)$ $(y+5)(y+6)$
- 4. $(2 + 15) (y + y)$ $(2+15)(y+y)$
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When factoring quadratics, use the Cross Method.

Use the cross method to factor $y^{2} + 11 y + 30$ $y^2+11y+30$

Start by drawing a cross.

Next, find two numbers that will multiply into $30$ $30$ and add up to $11$ $11$

Product Sum

$2$ $2$ and $15$ $15$ $30$ $30$ $17$ $17$

$3$ $3$ and $10$ $10$ $30$ $30$ $13$ $13$

$5$ $5$ and $6$ $6$ $30$ $30$ $11$ $11$

$5$ $5$ and $6$ $6$ fits this description.

Next, write $5$ $5$ and $6$ $6$ on the right side of the cross.

Now, find two values that will multiply into $y^{2}$ $y^2$ and write them on the left side of the cross.

$y$ $y$ and $y$ $y$ fits this description.

Finally, group the values in a row with a bracket and combine the brackets.

Therefore, the factored expression is $(y + 5) (y + 6)$ $(y+5)(y+6)$ .

$(y + 5) (y + 6)$ $(y+5)(y+6)$
Question 3 of 5

3. Question
Factor.

$m^{2} + 17 m + 60$ $m^2+17m+60$
- 1. $(m + 5) (m + 12)$ $(m+5)(m+12)$
- 2. $(m + 6) (m + 10)$ $(m+6)(m+10)$
- 3. $(m + 7) (m + 10)$ $(m+7)(m+10)$
- 4. $(m + 3) (m + 20)$ $(m+3)(m+20)$
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When factoring quadratics, use the Cross Method.

Use the cross method to factor $m^{2} + 17 m + 60$ $m^2+17m+60$

Start by drawing a cross.

Next, find two numbers that will multiply into $60$ $60$ and add up to $17$ $17$

Product Sum

$6$ $6$ and $10$ $10$ $60$ $60$ $16$ $16$

$3$ $3$ and $20$ $20$ $60$ $60$ $23$ $23$

$5$ $5$ and $12$ $12$ $60$ $60$ $17$ $17$

$5$ $5$ and $12$ $12$ fits this description.

Next, write $5$ $5$ and $12$ $12$ on the right side of the cross.

Now, find two values that will multiply into $m^{2}$ $m^2$ and write them on the left side of the cross.

$m$ $m$ and $m$ $m$ fits this description.

Finally, group the values in a row with a bracket and combine the brackets.

Therefore, the factored expression is $(m + 5) (m + 12)$ $(m+5)(m+12)$ .

$(m + 5) (m + 12)$ $(m+5)(m+12)$
Question 4 of 5

4. Question
Factor.

$m^{2} + 13 m - 30$ $m^2+13m-30$
- 1. $(m - 6) (m + 7)$ $(m-6)(m+7)$
- 2. $(m - 6) (m + 5)$ $(m-6)(m+5)$
- 3. $(m - 3) (m + 10)$ $(m-3)(m+10)$
- 4. $(m - 2) (m + 15)$ $(m-2)(m+15)$
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When factoring quadratics, use the Cross Method.

Use the cross method to factor $m^{2} + 13 m - 30$ $m^2+13m-30$

Start by drawing a cross.

Next, find two numbers that will multiply into $- 30$ $-30$ and add up to $13$ $13$

Product Sum

$5$ $5$ and $6$ $6$ $30$ $30$ $11$ $11$

$- 3$ $-3$ and $10$ $10$ $- 30$ $-30$ $7$ $7$

$- 2$ $-2$ and $15$ $15$ $- 30$ $-30$ $13$ $13$

$- 2$ $-2$ and $15$ $15$ fits this description.

Next, write $- 2$ $-2$ and $15$ $15$ on the right side of the cross.

Now, find two values that will multiply into $m^{2}$ $m^2$ and write them on the left side of the cross.

$m$ $m$ and $m$ $m$ fits this description.

Finally, group the values in a row with a bracket and combine the brackets.

Therefore, the factored expression is $(m - 2) (m + 15)$ $(m-2)(m+15)$ .

$(m - 2) (m + 15)$ $(m-2)(m+15)$
Question 5 of 5

5. Question
Factor.

$x^{2} + 8 x - 48$ $x^2+8x-48$
- 1. $(x - 4) (x + 12)$ $(x-4)(x+12)$
- 2. $(x + 2) (x + 24)$ $(x+2)(x+24)$
- 3. $(x + 6) (x + 8)$ $(x+6)(x+8)$
- 4. $(x + 3) (x - 16)$ $(x+3)(x-16)$
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When factoring quadratics, use the Cross Method.

Use the cross method to factor $x^{2} + 8 x - 48$ $x^2+8x-48$

Start by drawing a cross.

Next, find two numbers that will multiply into $- 48$ $-48$ and add up to $18$ $18$

Product Sum

$2$ $2$ and $24$ $24$ $48$ $48$ $26$ $26$

$3$ $3$ and $- 16$ $-16$ $- 48$ $-48$ $- 13$ $-13$

$- 4$ $-4$ and $12$ $12$ $- 48$ $-48$ $8$ $8$

$6$ $6$ and $8$ $8$ $48$ $48$ $14$ $14$

$- 4$ $-4$ and $12$ $12$ fits this description.

Next, write $- 4$ $-4$ and $12$ $12$ on the right side of the cross.

Now, find two values that will multiply into $x^{2}$ $x^2$ and write them on the left side of the cross.

$x$ $x$ and $x$ $x$ fits this description.

Finally, group the values in a row with a bracket and combine the brackets.

Therefore, the factored expression is $(x - 4) (x + 12)$ $(x-4)(x+12)$ .

$(x - 4) (x + 12)$ $(x-4)(x+12)$

Factorise Trinomials (Quadratics) 1

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Quiz summary

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1. Question

Hint

Great Work!

2. Question

Hint

Correct!

3. Question

Hint

Keep Going!

4. Question

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Fantastic!

5. Question

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Excellent!

Quizzes

	Product	Sum
$12$ $12$ and $1$ $1$	$12$ $12$	$13$ $13$
$6$ $6$ and $2$ $2$	$12$ $12$	$8$ $8$
$3$ $3$ and $4$ $4$	$12$ $12$	$7$ $7$

	Product	Sum
$2$ $2$ and $15$ $15$	$30$ $30$	$17$ $17$
$3$ $3$ and $10$ $10$	$30$ $30$	$13$ $13$
$5$ $5$ and $6$ $6$	$30$ $30$	$11$ $11$

	Product	Sum
$6$ $6$ and $10$ $10$	$60$ $60$	$16$ $16$
$3$ $3$ and $20$ $20$	$60$ $60$	$23$ $23$
$5$ $5$ and $12$ $12$	$60$ $60$	$17$ $17$

	Product	Sum
$5$ $5$ and $6$ $6$	$30$ $30$	$11$ $11$
$- 3$ $-3$ and $10$ $10$	$- 30$ $-30$	$7$ $7$
$- 2$ $-2$ and $15$ $15$	$- 30$ $-30$	$13$ $13$

	Product	Sum
$2$ $2$ and $24$ $24$	$48$ $48$	$26$ $26$
$3$ $3$ and $- 16$ $-16$	$- 48$ $-48$	$- 13$ $-13$
$- 4$ $-4$ and $12$ $12$	$- 48$ $-48$	$8$ $8$
$6$ $6$ and $8$ $8$	$48$ $48$	$14$ $14$