Factor the following quadratics.

a)$2{x}^{2}+7x+6$

b)$4{x}^{2}-13x+9$

c)$3{x}^{2}-10x+8$

d)$2{x}^{2}-3x-2$

e)$3{x}^{2}+17x+20$

f)$4{x}^{2}-25x+25$

a)

b)

c)

d)

e)

f)

berljivx8
2021-12-16
Answered

Factor the following quadratics.

a)$2{x}^{2}+7x+6$

b)$4{x}^{2}-13x+9$

c)$3{x}^{2}-10x+8$

d)$2{x}^{2}-3x-2$

e)$3{x}^{2}+17x+20$

f)$4{x}^{2}-25x+25$

a)

b)

c)

d)

e)

f)

You can still ask an expert for help

Your answer

Expert Community at Your Service

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

Solve your problem for the price of one coffee

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

Jimmy Macias

Answered 2021-12-17
Author has **30** answers

Step 1

a)$2{x}^{2}+7x+6$

Factor the quadratic$2{x}^{2}+7x+6$

The coefficient of$x}^{2$ 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$2{x}^{2}+7x+6=2{x}^{2}+4x+3x+6$

$=2x(x+2)+3(x+2)$

$=(2x+3)(x+2)$

$\Rightarrow 2{x}^{2}+7x+6=(2x+3)(x+2)$

Step 2

$4{x}^{2}-13x+9$

The coefficient of$x}^{2$ 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$4{x}^{2}-13x+9=4{x}^{2}-9x-4x+9$

$=x(4x-9)-1(4x-9)$

$=(4x-1)(4x-9)$

$\Rightarrow 4{x}^{2}-13x+9=(4x-1)(4x-9)$

Step 3

$3{x}^{2}-10x+8$

The coefficient of$x}^{2$ 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$3{x}^{2}-10x+8=3{x}^{2}-6x-4x+8$

$=3x(x-2)-4(x-2)$

$=(3x-4)(x-2)$

$\Rightarrow 3{x}^{2}-10x+8=(3x-4)(x-2)$

Step 4

$2{x}^{2}-3x-2$

The coefficien of$x}^{2$ 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$2{x}^{2}-3x-2=2{x}^{2}-4x+x-2$

$=2x(x-2)+1(x-2)$

$=(2x+1)(x-2)$

$\Rightarrow 2{x}^{2}-3x-2=(2x+1)(x-2)$

Step 5

$3{x}^{2}+17x+20$

The coefficient of$x}^{2$ 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

a)

Factor the quadratic

The coefficient of

The product of 2 and 6 is 12

The factor of 12 which sum to 7 ae 3 and 4

So

Step 2

The coefficient of

The factors of 36 which sum to -13 are -4 and -9

So

Step 3

The coefficient of

The product o 3 and 8 is 24

The factors a 24 which sm to -10 are -4 and -6

So

Step 4

The coefficien of

The product of 2 and -2 is -4

The factors of -4 which sum to -3 are 1 and -4

So

Step 5

The coefficient of

The product of 3 and 20 is 60

The factors of 60 which sum to 17 are 5 and 12

So

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

aquariump9

Answered 2021-12-18
Author has **40** answers

Step 1

a)$2{x}^{2}+7x+6$

$a+b=7$

$ab=2\times 6=12$
NKS
$1,\text{}12$

$2,\text{}6$

$3,\text{}4$

$1+12=13$

$2+6=8$

$3+4=7$

$a=3$

$b=4$

Rewrite

$(2{x}^{2}+3x)+(4x+6)$

$x(2x+3)+2(2x+3)$

$(2x+3)(x+2)$

b)$4{x}^{2}-13x+9$

$a+b=-13$

$ab=4\times 9=36$

$-1,\text{}-36$

$-2,\text{}-18$

$-3,\text{}-12$

$-4,\text{}-9$

$-6,\text{}-6$

$-1-36=-37$

$-2-18=-20$

$-3-12=-15$

$-4-9=-13$

$-6-6=-12$

$a=-9$

$b=-4$

Rewrite

$(4{x}^{2}-9x)+(-4x+9)$

$x(4x-9)-(4x-9)$

$(4x-9)(x-1)$

Step 2

c)$3{x}^{2}-10x+8$

$a+b=-10$

$ab=3\times 8=24$

$-1,\text{}-24$

$-2,\text{}-12$

$-3,\text{}-8$

$-4,\text{}-6$

$-1-24=-25$

$-2-12=-14$

$-3-8=-11$

$-4-6=-10$

$a=-6$

$b=-4$

Rewrite

$(3{x}^{2}-6x)+(-4x+8)$

$3x(x-2)-4(x-2)$

a)

Rewrite

b)

Rewrite

Step 2

c)

Rewrite

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

asked 2022-04-05

Finding integer a, b such that the roots of

$3{x}^{2}+3(a+b)x+4ab=0$

satisfy

$\alpha (\alpha +1)+\beta (\beta +1)=(\alpha +1)(\beta +1)$

satisfy

See answers (2)

asked 2021-12-03

A ball is thrown upward from the top of a 48-foot-high building. The ball is 64 feet above ground level after 1 second, and it reaches ground level in 3 seconds. The height above ground is a quadratic function of the time after the ball is thrown. Write the equation of this function.

See answers (1)

asked 2022-03-12

Why is the discriminant of quadratic $f,\text{}\mathrm{\Delta}\le 0$ , when $f\left(x\right)\ge 0\mathrm{\forall}x\in \mathbb{R}$ ?

See answers (2)

asked 2021-11-07

Use the quadratic formula to solve for x.

$2{x}^{2}-6x-1=0$

(If there is more than one solution, separate them with commas.)

(If there is more than one solution, separate them with commas.)

See answers (1)

asked 2022-03-15

What is the probability for x to be positive only?

If x, y,$z\in \mathbb{R}$ and $x+y+z=5,,xy+yz+zx=3$ , what is the probability that $x>0$ ?

a)$\frac{3}{16}$

b)$\frac{5}{16}$

c)$\frac{13}{16}$

d)$\frac{15}{16}$

If x, y,

a)

b)

c)

d)

See answers (1)

asked 2022-05-03

Question about the square root of a non-negative quadratic function.

For which values of x does this apply

$\sqrt{{x}^{2}+2x+1}=x+1$

For which values of x does this apply

See answers (2)

asked 2022-03-31

Quadratic Diophantine equation ${x}^{2}+6{y}^{2}-xy=47$ has no solutions.

See answers (1)

Solve your problem for the price of one coffee

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

- Secondary
- Calculus and Analysis
- Algebra
- Algebra I
- Sequences
- Functions
- Quadratic function and equation
- Linear equations and graphs
- Systems of equations
- Exponential growth and decay
- Irrational numbers
- Piecewise-Defined Functions
- Forms of linear equations
- Exponents and radicals
- Algebra foundations
- exponents and radicals
- Polynomial graphs
- Inequalities systems and graphs
- Quadratics
- Equations and inequalities
- Pre-Algebra
- Algebra II
- Geometry
- Statistics and Probability
- Math Word Problem
- Other
- Physics
- Post Secondary

Get answers within minutes and finish your homework faster

Sign in with Apple

Or

Dont have an account? Register

Get answers within minutes and finish your homework faster

Create a free account to see answers

Sign up with Apple

Or
Already have an account? Sign in