Factor the following quadratics. a) 2x^{2}+7x+6 b) 4x^{2}-13x+9 c) 3x^{2}-10x+8 d) 2x^{2}-3x-2 e) 3x^{2}+17x+20 f) 4x^{2}-25x+25

berljivx8 2021-12-16 Answered
Factor the following quadratics.
a) 2x2+7x+6
b) 4x213x+9
c) 3x210x+8
d) 2x23x2
e) 3x2+17x+20
f) 4x225x+25
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Jimmy Macias
Answered 2021-12-17 Author has 30 answers
Step 1
a) 2x2+7x+6
Factor the quadratic 2x2+7x+6
The coefficient of x2 is 2 and the constant term 6
The product of 2 and 6 is 12
The factor of 12 which sum to 7 ae 3 and 4
So 2x2+7x+6=2x2+4x+3x+6
=2x(x+2)+3(x+2)
=(2x+3)(x+2)
2x2+7x+6=(2x+3)(x+2)
Step 2
4x213x+9
The coefficient of x2 is 4 and the constant term is 9. The product of 4 and 9 is 36
The factors of 36 which sum to -13 are -4 and -9
So 4x213x+9=4x29x4x+9
=x(4x9)1(4x9)
=(4x1)(4x9)
4x213x+9=(4x1)(4x9)
Step 3
3x210x+8
The coefficient of x2 is 3 and the constant term is 8
The product o 3 and 8 is 24
The factors a 24 which sm to -10 are -4 and -6
So 3x210x+8=3x26x4x+8
=3x(x2)4(x2)
=(3x4)(x2)
3x210x+8=(3x4)(x2)
Step 4
2x23x2
The coefficien of x2 is 2 and the constant term is -2
The product of 2 and -2 is -4
The factors of -4 which sum to -3 are 1 and -4
So 2x23x2=2x24x+x2
=2x(x2)+1(x2)
=(2x+1)(x2)
2x23x2=(2x+1)(x2)
Step 5
3x2+17x+20
The coefficient of x2 is 3 and the constant is 20
The product of 3 and 20 is 60
The factors of 60 which sum to 17 are 5 and 12
So
aquariump9
Answered 2021-12-18 Author has 40 answers
Step 1
a) 2x2+7x+6
a+b=7
ab=2×6=12 NKS 1, 12
2, 6
3, 4
1+12=13
2+6=8
3+4=7
a=3
b=4
Rewrite
(2x2+3x)+(4x+6)
x(2x+3)+2(2x+3)
(2x+3)(x+2)
b) 4x213x+9
a+b=13
ab=4×9=36
1, 36
2, 18
3, 12
4, 9
6, 6
136=37
218=20
312=15
49=13
66=12
a=9
b=4
Rewrite
(4x29x)+(4x+9)
x(4x9)(4x9)
(4x9)(x1)
Step 2
c) 3x210x+8
a+b=10
ab=3×8=24
1, 24
2, 12
3, 8
4, 6
124=25
212=14
38=11
46=10
a=6
b=4
Rewrite
(3x26x)+(4x+8)
3x(x2)4(x2)

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more