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3 years ago

What is the answer for 9x² + 3xy - 12x - 4y

Mathematics

2 answers:

Lostsunrise [7]3 years ago

4 0

Answer:

${ \tt{9 {x}^{2} + 3xy - 12x - 4y }} \\ ={ \tt{x(9x + 3y - 12) - 4y}}$

Sphinxa [80]3 years ago

3 0

Answer:

(3x + y)(3x - 4)

Step-by-step explanation:

9x² + 3xy - 12x - 4y =

There is no common factor in the 4 terms.

Since there are 4 terms, we try factoring by grouping.

Find a common factor in the first two terms, and find a common factor in the last two terms.

= 3x(3x + y) - 4(3x + y)

Now factor out the common factor 3x + y.

= (3x + y)(3x - 4)

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3 years ago

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gladu [14]

Answer:

$\frac{5x+2}{3x^2+4x-4}= \frac{2}{3x-2}+\frac{1}{x+2}$

Step-by-step explanation:

Ooook, step 1: write the denominator as a product, or we're not going anywhere. Can't spot any two factor by staring at it, so quadratic formula it is.

$x= \frac13(-2 \pm \sqrt{4+12})=\frac13(-2\pm4) = -2;\frac23$

We got our toots, let's split the denominator now: $3x^2+4x-4 = (3x-2)(x+2)\\$

Now it's all a matter of writing down what we need:

$\frac{5x-2}{3x^2+4x-4}=\frac{5x-2}{(3x-2)(x+2)} = \frac{A}{3x-2}+\frac{B}{x+2} = \frac{A(x+2)+B(3x-2)}{(3x-2)(x+2)}=\frac{Ax+2A+3Bx-2B}{(3x-2)(x+2)} =\frac{(A+3B)x+(2A-2B)}{(3x-2)(x+2)}$

Here comes the fun part. Two ways: the fast and loose, and the long one.

Fast and loose: let's look only at the numerators of the 3rd to last and first step: $A(x+2)+B(3x-2) = 5x+2$ If we plugged a convenient value, let's say $x=-2$ the coeffcent of A would disappear, and we would be able to find B. Let's do it. $A(-2+2) + B(3(-2)-2) = 5(-2)+2 \rightarrow -8B =-8 B=1$

At this point we have B, let's pick a different value of x, let's say 1, to get A:

$A(3) + 1(1) = 7 \rightarrow 3A=6 \rightarrow A=2$

More traditional: Pick the first and last numerators: $5x+2 = (A+3B)x+(2A-2B)$ . Stare at them long enough and pick your favourite excuse to justify the following system (two polynomials are equal if the coefficents are equal, polynomials create a vector space of base $(1,x,x^2...)$

$\left \{ {A+3B=5} \atop {2A-2B=2}} \right.$

Again, $A=2, B=1$ is a solution.

Either way, the solution is:

$\frac{5x+2}{3x^2+4x-4}= \frac{2}{3x-2}+\frac{1}{x+2}$

6 0

3 years ago

What is the answer for 9x² + 3xy - 12x - 4y ​

What is the answer for 9x² + 3xy - 12x - 4y