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Algebra - Solving Monic Quadratics By Factorising

  a - answer    s - solution    v - video

Question 1


Solve

a) $x(x+3)=0$  a s v
b) $x(x-2)=0$  a s v
c) $3x(x-9)=0$  a s v
d) $4x(x-4)=0$  a s v
e) $6(x+5)=0$  a s v
f) $7x=0$  a s v


Question 2


Solve

a) $(x+1)(x+2)=0$  a s v
b) $(x+4)(x+8)=0$  a s v
c) $(x+2)(x+7)=0$  a s v
d) $(x-9)(x+3)=0$  a s v
e) $(x+2)(x-1)=0$  a s v
f) $(x-10)(x-3)=0$  a s v
g) $(x-5)(x-2)=0$  a s v
h) $(x-11)(x-3)=0$  a s v


Question 3


Solve

a) $x(x-4)(x-2)=0$  a s v
b) $x(x+5)(x-1)=0$  a s v
c) $x(x+10)(x-5)=0$  a s v
d) $2x(x+4)(x+3)=0$  a s v
e) $4x(3+x)(x-7)=0$  a s v
f) $2(4-x)(6+x)=0$  a s v


Question 4


Solve by factorising

a) $x^2+5x=0$  a s v
b) $x^2+9x=0$  a s v
c) $x^2-3x=0$  a s v
d) $x^2-11x=0$  a s v
e) $2x^2+6x=0$  a s v
f) $5x^2-30x=0$  a s v


Question 5


Solve by factorising

a) $x^2+3x+2=0$  a s v
b) $x^2+5x+4=0$  a s v
c) $x^2+6x+8=0$  a s v
d) $x^2+9x+14=0$  a s v
e) $x^2+21x+20=0$  a s v
f) $x^2+10x+16=0$  a s v
g) $x^2+9x+20=0$  a s v
h) $x^2+15x+44=0$  a s v


Question 6


Solve by factorising

a) $x^2+6x+9=0$  a s v
b) $x^2+10x+25=0$  a s v
c) $x^2+14x+49=0$  a s v
d) $x^2+24x+144=0$  a s v


Question 7


Solve by factorising

a) $x^2-5x+6=0$  a s v
b) $x^2-10x+9=0$  a s v
c) $x^2-11x+18=0$  a s v
d) $x^2-12x+36=0$  a s v
e) $x^2-17x+30=0$  a s v
f) $x^2-10x+24=0$  a s v
g) $x^2-15x+50=0$  a s v
h) $x^2-16x+63=0$  a s v


Question 8


Solve by factorising

a) $x^2-2x-8=0$  a s v
b) $x^2+x-12=0$  a s v
c) $x^2+6x-16=0$  a s v
d) $x^2-8x-20=0$  a s v
e) $x^2-9=0$  a s v
f) $x^2+11x-12=0$  a s v
g) $x^2-81=0$  a s v
h) $x^2+5x-36=0$  a s v


Question 9


Mixed Questions. Solve by factorising

a) $x^2+4x+3=0$  a s v
b) $x^2-9x+18=0$  a s v
c) $x^2+5x-14=0$  a s v
d) $x^2-18x+17=0$  a s v
e) $x^2-3x-28=0$  a s v
f) $x^2+11x+10=0$  a s v
g) $x^2+22x+121=0$  a s v
h) $x^2+15x+26=0$  a s v
i) $x^2-1=0$  a s v
j) $x^2-12x+32=0$  a s v
k) $x^2+13x+40=0$  a s v
l) $x^2-11x-12=0$  a s v
m) $x^2-100=0$  a s v
n) $x^2-14x+45=0$  a s v
o) $x^2-20x+51=0$  a s v
p) $x^2+28x-63=0$  a s v


Question 10


Factorise to form a monic quadratic and solve

a) $2x^2+12x+16=0$  a s v
b) $5x^2+5x-100=0$  a s v
c) $x^3-13x^2+42x=0$  a s v
d) $4x^4-8x^3-140x^2=0$  a s v


Question 11


Form a quadratic equation before solving

a) $x^2+7x=-6$  a s v
b) $x^2=2x+3$  a s v
c) $x^2-18=7x$  a s v
d) $x^2+2(7x+15)+3=0$  a s v
e) $2x^2-3(x+6)=x^2$  a s v
f) $2(x^2+4x)=4(12+2x)+x^2$  a s v
g) $x+12=\dfrac{64}{x}$  a s v
h) $(2x+9)^2-2(4-8x)=433$  a s v
i) $1+\dfrac{55}{x^2}=\dfrac{16}{x}$  a s v
j) $5=\dfrac{80}{x}+\dfrac{400}{x^2}$  a s v