4xsquared + 8x - 21?

Question

by 4x squared i mean 4x to the second power

need help factoring

Answer 1

(2x+7)(2x-3)

Answer 2

16xsquared+8x-21

Answer 3

4x^2+8x-21

(2x-3)(2x+7)

Answer 4

4x squared is 16x Or 4x2= 16x

So 16x + 8x = 24x

21-24x= 3x

I am not too sure if you can add two values if one of them has no variable behind it.  If so then the answer is 3x, if not then the answer stands as is.

Answer 5

(2x+7)(2x-3)

make it a good day

Answer 6

Use the grouping method of factorization:

4x^2 + 8x - 21 = 4x^2 + 14x - 6x - 21 = 4x^2 - 6x + 14x - 21 = 2x(2x-3) + 7(2x-3) = (2x-3) (2x+7)

Answer 7

(2x+7) (2x-3)

4x squared- 6x+14x -21

4xsquared + 8x -21

Answer 8

(2x-3)(2x+7) is the correct answer but don't ya think i'd be good if ya knew how to get that answer....

4x^2+8x-21

first step is to multiply the coefficient of the leading term (the term with the highest exponent) by the last term so 4 * -21 = -84

next you find two number that when multiplied = -84 and when added together equal the coefficient of the middle term....so in this example 8

so your number are -6 and 14 because -6 * 14 = -84 and -6 + 14 =8

then you rewrite your expression with those numbers and the variable of the middle term giving you  4x^2-6x+14x-21

then you factor by grouping you can take 2x out of the first set of terms(4x^2-6x) giving you...

2x(2x-3)+14x-21

you can take a 7 out of the second set of terms(14x-21) giving you

7(2x-3) giving you this...

2x(2x-3)+7(2x-3)

at this point you have your two factors, the common term is one factor (2x-3) and what is left is your other factor (2x+7)

this method of factoring a trinomial will always work, if you doubt your answer all you have to do to check is multiply the factors using the FOIL method, the result should  be the original trinomial

hope this is helpful :)

Answer 9

I learned it this way at school.

4x^2+8x-21=0

We have  ax^2+bx+c=0 =>where  a= 4; b=8; c= -21

To find the x(one) and x(two) we need to memorize 2 formulas :)

D= b^2-4ac and  x(one/two)= (-b+/-V D)/ 2a  where VD is the root of D.

you just put the numbers in those formulas

D=8^2 -4*4*(-21)=64-16(-21)=64+336=400

x(one) =( -8+V400) / 2*4 = (-8+20) / 8= 12 /8= 3/2

x(two) = (-8 -V400) / 2*4 = (-8-20) / 8= -28 / 8 = -7/2

you just change -/+ signs and put them in the result.



Answer (x-3/2)(x+7/2)

It might seem a more complicated way but in this case you never have to guess :)

Answer 10

f(x) = (4x)^2 + 8x - 21

(1) First, change variable by defining y = 4x, yielding the new function

F(y) = y^2 + 2y - 21

(2) Next, solving this quadratic produces two solutions:

y = - 1 + sqrt(22) and y = - 1 - sqrt(22)

(3) Hence, F(y) = (y + 1 - sqrt(22)) (y + 1 + sqrt(22))

(4) Finally, reverting back to the variable x, we see that the answer is:

f(x) = (4x + 1 - sqrt(22)) (4x + 1 + sqrt(22))

Answer 11

Begin by looking for what's common for 4x2 and 8x; its 2x.

So, let 2x be y for now and substitute y into the equation.

If 2x is y, then 4x2 is (2x)2 and it will be y2.

Likewise, 8x is 4(2x), so it will be 4y. Now you have:

y2+4y-21

=>y2+7y-3y+21

=>y(y+7)-3(y+7)

=>(y-3)(y+7)

Now put the original value of y back into the equation. That is 2x for y.

=>(2x-3)(2x+7)

Answer 12

21 is probably 3 * 7

So we get to (Ax + 3)(Bx - 7)  or  (Ax -3)(Bx + 7)

Since 7 -3 = 4, we probably want to try 2 for A and B so as to double 4 to 8

(2x + 7)(2x - 3) = 4x^2 + 14x - 6x + 21 = 4x^2 + 8x - 21 (the original equation)

So the answer (2x + 7)(2x - 3) is correct and has been checked.