Factorise Trinomials (Quadratics) 2

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Question 1 of 5

1. Question
Factorise.

$f^{2} + 8 f - 9$ $f^2+8f-9$
- 1. $(f + 13) (f - 4)$ $(f+13)(f-4)$
- 2. $(f + 5) (f - 4)$ $(f+5)(f-4)$
- 3. $(f + 3) (f - 3)$ $(f+3)(f-3)$
- 4. $(f + 9) (f - 1)$ $(f+9)(f-1)$
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When factorising trinomials, use the Cross Method.

Use the cross method to factorise $f^{2} + 8 f - 9$ $f^2+8f-9$

Start by drawing a cross.

Next, find two numbers that will multiply into $- 9$ $-9$ and add up to $8$ $8$

Product Sum

$- 3$ $-3$ and $3$ $3$ $- 9$ $-9$ $0$ $0$

$9$ $9$ and $- 1$ $-1$ $- 9$ $-9$ $8$ $8$

$9$ $9$ and $- 1$ $-1$ fits this description.

Next, write $9$ $9$ and $- 1$ $-1$ on the right side of the cross.

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

$f$ $f$ and $f$ $f$ fits this description.

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

Therefore, the factorised expression is $(f + 9) (f - 1)$ $(f+9)(f-1)$ .

$(f + 9) (f - 1)$ $(f+9)(f-1)$
Question 2 of 5

2. Question
Factorise.

$y^{2} + y - 56$ $y^2+y-56$
- 1. $(y - 4) (y + 14)$ $(y-4)(y+14)$
- 2. $(y - 2) (y + 28)$ $(y-2)(y+28)$
- 3. $(y - 1) (y + 56)$ $(y-1)(y+56)$
- 4. $(y - 7) (y + 8)$ $(y-7)(y+8)$
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When factorising trinomials, use the Cross Method.

Use the cross method to factorise $y^{2} + y - 56$ $y^2+y-56$

Start by drawing a cross.

Next, find two numbers that will multiply into $- 56$ $-56$ and add up to $1$ $1$

Product Sum

$- 1$ $-1$ and $56$ $56$ $- 56$ $-56$ $55$ $55$

$- 2$ $-2$ and $28$ $28$ $- 56$ $-56$ $26$ $26$

$- 4$ $-4$ and $14$ $14$ $- 56$ $-56$ $10$ $10$

$- 7$ $-7$ and $8$ $8$ $- 56$ $-56$ $1$ $1$

$- 7$ $-7$ and $8$ $8$ fits this description.

Next, write $- 7$ $-7$ and $8$ $8$ 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 factorised expression is $(y - 7) (y + 8)$ $(y-7)(y+8)$ .

$(y - 7) (y + 8)$ $(y-7)(y+8)$
Question 3 of 5

3. Question
Factorise.

$a^{2} - 5 a - 36$ $a^2-5a-36$
- 1. $(a + 6) (a + 6)$ $(a+6)(a+6)$
- 2. $(a + 4) (a - 9)$ $(a+4)(a-9)$
- 3. $(a - 2) (a + 18)$ $(a-2)(a+18)$
- 4. $(a - 3) (a + 12)$ $(a-3)(a+12)$
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When factorising trinomials, use the Cross Method.

Use the cross method to factorise $a^{2} - 5 a - 36$ $a^2-5a-36$

Start by drawing a cross.

Next, find two numbers that will multiply into $- 36$ $-36$ and add up to $- 5$ $-5$

Product Sum

$- 2$ $-2$ and $18$ $18$ $- 36$ $-36$ $16$ $16$

$- 3$ $-3$ and $12$ $12$ $- 36$ $-36$ $9$ $9$

$4$ $4$ and $- 9$ $-9$ $- 36$ $-36$ $- 5$ $-5$

$6$ $6$ and $6$ $6$ $36$ $36$ $12$ $12$

$4$ $4$ and $- 9$ $-9$ fits this description.

Next, write $4$ $4$ and $- 9$ $-9$ on the right side of the cross.

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

$a$ $a$ and $a$ $a$ fits this description.

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

Therefore, the factorised expression is $(a + 4) (a - 9)$ $(a+4)(a-9)$ .

$(a + 4) (a - 9)$ $(a+4)(a-9)$
Question 4 of 5

4. Question
Factorise.

$x^{2} - 3 x - 28$ $x^2-3x-28$
- 1. $(x - 2) (x + 14)$ $(x-2)(x+14)$
- 2. $(x - 1) (x + 28)$ $(x-1)(x+28)$
- 3. $(x - 28) (x + 3)$ $(x-28)(x+3)$
- 4. $(x + 4) (x - 7)$ $(x+4)(x-7)$
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When factorising trinomials, use the Cross Method.

Use the cross method to factorise $x^{2} - 3 x - 28$ $x^2-3x-28$

Start by drawing a cross.

Next, find two numbers that will multiply into $- 28$ $-28$ and add up to $- 3$ $-3$

Product Sum

$- 1$ $-1$ and $28$ $28$ $- 28$ $-28$ $27$ $27$

$- 2$ $-2$ and $14$ $14$ $- 28$ $-28$ $12$ $12$

$4$ $4$ and $- 7$ $-7$ $- 28$ $-28$ $- 3$ $-3$

$4$ $4$ and $- 7$ $-7$ fits this description.

Next, write $4$ $4$ and $- 7$ $-7$ 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 factorised expression is $(x + 4) (x - 7)$ $(x+4)(x-7)$ .

$(x + 4) (x - 7)$ $(x+4)(x-7)$
Question 5 of 5

5. Question
Factorise.

$f^{2} - 2 f - 80$ $f^2-2f-80$
- 1. $(f + 8) (f - 10)$ $(f+8)(f-10)$
- 2. $(f - 2) (f + 40)$ $(f-2)(f+40)$
- 3. $(f - 4) (f + 20)$ $(f-4)(f+20)$
- 4. $(f - 5) (f + 16)$ $(f-5)(f+16)$
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When factorising trinomials, use the Cross Method.

Use the cross method to factorise $f^{2} - 2 f - 80$ $f^2-2f-80$

Start by drawing a cross.

Next, find two numbers that will multiply into $- 80$ $-80$ and add up to $- 2$ $-2$

Product Sum

$- 2$ $-2$ and $40$ $40$ $- 80$ $-80$ $38$ $38$

$- 4$ $-4$ and $20$ $20$ $- 80$ $-80$ $16$ $16$

$- 5$ $-5$ and $16$ $16$ $- 80$ $-80$ $11$ $11$

$8$ $8$ and $- 10$ $-10$ $- 80$ $-80$ $- 2$ $-2$

$8$ $8$ and $- 10$ $-10$ fits this description.

Next, write $8$ $8$ and $- 10$ $-10$ on the right side of the cross.

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

$f$ $f$ and $f$ $f$ fits this description.

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

Therefore, the factorised expression is $(f + 8) (f - 10)$ $(f+8)(f-10)$ .

$(f + 8) (f - 10)$ $(f+8)(f-10)$

Factorise Trinomials (Quadratics) 2

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Quiz summary

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1. Question

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2. Question

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Well Done!

3. Question

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Correct!

4. Question

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Fantastic!

5. Question

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Quizzes

	Product	Sum
$- 3$ $-3$ and $3$ $3$	$- 9$ $-9$	$0$ $0$
$9$ $9$ and $- 1$ $-1$	$- 9$ $-9$	$8$ $8$

	Product	Sum
$- 1$ $-1$ and $56$ $56$	$- 56$ $-56$	$55$ $55$
$- 2$ $-2$ and $28$ $28$	$- 56$ $-56$	$26$ $26$
$- 4$ $-4$ and $14$ $14$	$- 56$ $-56$	$10$ $10$
$- 7$ $-7$ and $8$ $8$	$- 56$ $-56$	$1$ $1$

	Product	Sum
$- 2$ $-2$ and $18$ $18$	$- 36$ $-36$	$16$ $16$
$- 3$ $-3$ and $12$ $12$	$- 36$ $-36$	$9$ $9$
$4$ $4$ and $- 9$ $-9$	$- 36$ $-36$	$- 5$ $-5$
$6$ $6$ and $6$ $6$	$36$ $36$	$12$ $12$

	Product	Sum
$- 1$ $-1$ and $28$ $28$	$- 28$ $-28$	$27$ $27$
$- 2$ $-2$ and $14$ $14$	$- 28$ $-28$	$12$ $12$
$4$ $4$ and $- 7$ $-7$	$- 28$ $-28$	$- 3$ $-3$

	Product	Sum
$- 2$ $-2$ and $40$ $40$	$- 80$ $-80$	$38$ $38$
$- 4$ $-4$ and $20$ $20$	$- 80$ $-80$	$16$ $16$
$- 5$ $-5$ and $16$ $16$	$- 80$ $-80$	$11$ $11$
$8$ $8$ and $- 10$ $-10$	$- 80$ $-80$	$- 2$ $-2$