Algebra - Factorising Non-Monic Quadratics

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Question 1


Factorise the following in pairs

a) $xy+3x+2y+6$a s v d
b) $xy+6x+5y+30$a s v d
c) $ab+7a+4b+28$a s v d
d) $mp+mq+np+nq$a s v d
e) $vw-5v+3w-15$a s v d
f) $gh-g+10h-10$a s v d
g) $xy+5x-2y-10$a s v d
h) $cd+2c-7d-14$a s v d
i) $xy-5x-3y+15$a s v d
j) $xy-x-y+1$a s v d
k) $ac-2ad-bc+2bd$a s v d
l) $x^2+4x+2x+8$a s v d


Question 2


Fully factorise

a) $2x^2+7x+6$a s v d
b) $2x^2+7x+5$a s v d
c) $3x^2+8x+4$a s v d
d) $5x^2+27x+10$a s v d
e) $5x^2+8x+3$a s v d
f) $7x^2+22x+3$a s v d
g) $4x^2+23x+15$a s v d
h) $6x^2+43x+7$a s v d
i) $8x^2+27x+9$a s v d
j) $10x^2+51x+5$a s v d
k) *$12x^2+115x+63$a s v d
l) *$12x^2+155x+132$a s v d


Question 3


Fully factorise

a) $2x^2-9x+9$a s v d
b) $2x^2-7x+5$a s v d
c) $3x^2-17x+10$a s v d
d) $7x^2-8x+1$a s v d
e) $11x^2-35x+6$a s v d
f) $4x^2-9x+2$a s v d
g) $8x^2-35x+12$a s v d
h) $10x^2-82x+16$a s v d
i) $9x^2-91x+10$a s v d
j) *$6x^2-31x+28$a s v d
k) *$12x^2-53x+20$a s v d
l) *$12x^2-103x+56$a s v d


Question 4


Fully factorise

a) $2x^2-x-3$a s v d
b) $3x^2+13x-10$a s v d
c) $5x^2-4x-1$a s v d
d) $4x^2+19x-5$a s v d
e) $3x^2+x-14$a s v d
f) $5x^2-8x-4$a s v d
g) $6x^2+31x-30$a s v d
h) $8x^2-77x-30$a s v d
i) $5x^2+14x-24$a s v d
j) *$12x^2-139x-60$a s v d
k) *$16x^2+55x-36$a s v d
l) *$20x^2-193x-70$a s v d


Question 5


Fully factorise

a) $6x^2+13x+6$a s v d
b) $15x^2+11x+2$a s v d
c) $4x^2+20x+21$a s v d
d) $14x^2+9x+1$a s v d
e) $15x^2+56x+49$a s v d
f) $12x^2+23x+5$a s v d
g) $30x^2+22x+4$a s v d
h) $24x^2+34x+5$a s v d
i) *$48x^2+74x+21$a s v d
j) *$60x^2+104x+45$a s v d
k) *$72x^2+138x+65$a s v d
l) *$200x^2+450x+63$a s v d


Question 6


Fully factorise

a) $6x^2-13x+5$a s v d
b) $10x^2-9x+2$a s v d
c) $21x^2-17x+2$a s v d
d) $2x^2-7x+5$a s v d
e) $2x^2-7x+5$a s v d
f) $7x^2-15x+2$a s v d
g) $15x^2-26x+8$a s v d
h) *$32x^2-28x+5$a s v d
i) *$72x^2-42x+3$a s v d
j) *$72x^2-43x+6$a s v d
k) *$15x^2-32x+16$a s v d
l) *$24x^2-39x+18$a s v d


Question 7


Fully factorise

a) $6x^2+x-2$a s v d
b) $6x^2-x-12$a s v d
c) $6x^2-13x-5$a s v d
d) $15x^2+13x-6$a s v d
e) $10x^2+4x-6$a s v d
f) $11x^2-10x-1$a s v d
g) $8x^2+2x-3$a s v d
h) $24x^2+26x-5$a s v d
i) $72x^2+6x-1$a s v d
j) $12x^2+26x-10$a s v d
k) *$38x^2-15x-2$a s v d
l) *$96x^2-20x-25$a s v d


Question 8


Find a common factor before factorising the quadratic

a) $30x^2+28x+6$a s v d
b) $10x^2-54x+20$a s v d
c) $24x^2-54x-15$a s v d
d) $96x^2+136x-40$a s v d
e) $-6x^2-11x+7$a s v d
f) $-12x^2-4x+5$a s v d
g) $-24x^2+62x-14$a s v d
h) $-128x^2-64x+120$a s v d


Question 9


Fully factorise

a) $8k^2-14k-15$a s v d
b) $8x^4-14x^2-15$a s v d
c) $15y^4+29y^2-14$a s v d
d) $72z^6+23z^3-4$a s v d
e) $4x^2-3x-\frac92$a s v d
f) *$5x^2+\frac{34x}{3}-\frac{16}{3}$a s v d
g) *$\frac{12x^3}{5}+\frac{28x^2}{5}-x$a s v d
h) *$\frac{45x^4}{4}-\frac{41x^3}{2}+4x^2$a s v d
i) *$-14z^5+\frac{2z^4}{3}+\frac{4z^3}{3}$a s v d
j) *$-\frac{81a^5b^4}{2}+\frac{261a^5b^2}{8}+\frac{33a^5}{8}$a s v d