Factor Quadratics with Leading Coefficient more than 1 (2)

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Question 1 of 4

1. Question
Factorise.

$5 x^{2} + 22 x + 8$ $5x^2+22x+8$
- 1. $(5 x + 15) (x + 7)$ $(5x+15)(x+7)$
- 2. $(5 x + 2) (x + 11)$ $(5x+2)(x+11)$
- 3. $(5 x + 1) (x + 8)$ $(5x+1)(x+8)$
- 4. $(5 x + 2) (x + 4)$ $(5x+2)(x+4)$
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When factorising trinomials, use the Cross Method.

Use the cross method to factorise $5 x^{2} + 22 x + 8$ $5x^2+22x+8$

Start by drawing a cross.

Now, find two values that will multiply into $5 x^{2}$ $5x^2$ and write them on the left side of the cross.

$5 x$ $5x$ and $x$ $x$ fits this description.

Next, find two numbers that will multiply into $8$ $8$ and, when cross-multiplied to the values to the left side, will add up to $22 x$ $22x$ .

Product Sum when Cross-Multiplied

$2$ $2$ and $4$ $4$ $8$ $8$ $(5 x \times 4) + (x \times 2) = 22 x$ $(5xtimes4)+(xtimes2)=22x$

$8$ $8$ and $1$ $1$ $8$ $8$ $(5 x \times 1) + (x \times 8) = 13 x$ $(5xtimes1)+(xtimes8)=13x$

$2$ $2$ and $4$ $4$ fits this description.

Now, write $2$ $2$ and $4$ $4$ on the right side of the cross.

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

Therefore, the factorised expression is $(5 x + 2) (x + 4)$ $(5x+2)(x+4)$ .

$(5 x + 2) (x + 4)$ $(5x+2)(x+4)$

	Product	Sum when Cross-Multiplied
$2$ $2$ and $4$ $4$	$8$ $8$	$(5 x \times 4) + (x \times 2) = 22 x$ $(5xtimes4)+(xtimes2)=22x$
$8$ $8$ and $1$ $1$	$8$ $8$	$(5 x \times 1) + (x \times 8) = 13 x$ $(5xtimes1)+(xtimes8)=13x$

Question 2 of 4

Factorise.

3 x^{2} - 26 x + 35

$3x^2-26x+35$

1. $(2 x - 3) (x + 7)$ $(2x-3)(x+7)$
2. $(3 x - 7) (x - 5)$ $(3x-7)(x-5)$
3. $(3 x - 5) (x - 7)$ $(3x-5)(x-7)$
4. $(3 x - 2) (2 x - 13)$ $(3x-2)(2x-13)$

	Product	Sum when Cross-Multiplied
$- 7$ $-7$ and $- 5$ $-5$	$35$ $35$	$[3 x \times (- 5)] + [x \times (- 7)] = - 22 x$ $[3xtimes(-5)]+[xtimes(-7)]=-22x$
$- 5$ $-5$ and $- 7$ $-7$	$35$ $35$	$[3 x \times (- 7)] + [x \times (- 5)] = - 26 x$ $[3xtimes(-7)]+[xtimes(-5)]=-26x$

Question 3 of 4

Factorise.

6 x^{2} - 17 x - 3

$6x^2-17x-3$

1. $(3 x + 1) (3 x - 3)$ $(3x+1)(3x-3)$
2. $(6 x + 3) (x - 1)$ $(6x+3)(x-1)$
3. $(6 x + 1) (x - 3)$ $(6x+1)(x-3)$
4. $(2 x + 1) (3 x - 3)$ $(2x+1)(3x-3)$

	Product	Sum when Cross-Multiplied
$1$ $1$ and $- 3$ $-3$	$- 3$ $-3$	$[6 x \times (- 3)] + (x \times 1) = - 17 x$ $[6xtimes(-3)]+(xtimes1)=-17x$
$3$ $3$ and $- 1$ $-1$	$- 3$ $-3$	$(6 x \times 1) + [x \times (- 6)] = - 5 x$ $(6xtimes1)+[xtimes(-6)]=-5x$

Question 4 of 4

Factorise.

5 u^{2} + 19 u + 12

$5u^2+19u+12$

1. $(5 u + 2) (u + 6)$ $(5u+2)(u+6)$
2. $(5 u + 1) (u + 12)$ $(5u+1)(u+12)$
3. $(5 u + 3) (u + 4)$ $(5u+3)(u+4)$
4. $(5 u + 4) (u + 3)$ $(5u+4)(u+3)$

	Product	Sum when Cross-Multiplied
$2$ $2$ and $6$ $6$	$12$ $12$	$(5 u \times 6) + (u \times 2) = 32 u$ $(5utimes6)+(utimes2)=32u$
$3$ $3$ and $4$ $4$	$12$ $12$	$(5 u \times 4) + (u \times 3) = 23 u$ $(5utimes4)+(utimes3)=23u$
$4$ $4$ and $3$ $3$	$12$ $12$	$(5 u \times 3) + (u \times 4) = 19 u$ $(5utimes3)+(utimes4)=19u$
$1$ $1$ and $12$ $12$	$12$ $12$	$(5 u \times 12) + (u \times 1) = 61 u$ $(5utimes12)+(utimes1)=61u$

Factor Quadratics with Leading Coefficient more than 1 (2)

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