How would you simplify this? Grade 10 math?

Question

10a^2 + a - 3


also...

50x^2 - 72

Answer 1

The first one is a quadratic equation. If it can be simplified, the factors will look like:

(w*a + x)(y*a + z)

where w*y will equal 10
and x*z will equal -3

and (a bit trickier) w*z + x*y = +1 (the factor of 'a' in the quadratic).

If this is homework, and if there is an answer, then I suspect it should be a relatively easy one and you could try all the integer possibilities (there are not many)

Integer factors of 10 are

10 and 1
5 and 2
(one set would be used for w and y)

Integer factors of -3 are

-3 and 1
3 and -1
one set would be used for x and z

Let's pick
(5 and 2) and (3 and -1)

We need
w*z + x*y = +1

Let's try w=2, z=3, x=-1, y=5
That works

Let's rebuild our factors:
(w*a + x)(y*a + z)
(2a -1)(5a+3)

Check it out by multiplying them out.

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Sounds complicated, but it is not. It is long and tedious, but it always works IF there is a solution.

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The second one is also a quadratic equation, just that the middle factor is 0:

50x^2 - 72 =
50x^2 - 0x -72.

Same thing; find facotrs that produce 50 and factors that produce -72.
Then combine them so that the cross product gives 0.


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PS: nice shortcut abyssworker.

Answer 2

these are factoring polynomials

In the first one you would need the factors of 10 and 3. Since the operation in front of the constant(3) is subtraction, the signs when factoring will be different. (5a +3)(2a - 1).

In the second one, you would need to factor what is in common between 50 and 72 ( this would be 2) This would leave you with 2(25x^2 - 36) This is now the difference of two squares. The square of 5 is 25 and the square of 6 is 36. In the factored form, the answer would be 2(5x - 6)(5x +6)

Answer 3

10a^2-3 = (5a-3)(2a+1)

50x^2-72 = (5x+6)(10x-12)

Answer 4

2(x+a million)(x+2)+3(x+2)(x+3) (x+2)[2(x+a million)+3(x+3)] (x+2)[2x+2+3x+9] (x+2)(5x+11) answer (5x-2)(2x+3)-(3x+4)(3x+4) 10x² + 15x -4x-6 - 9x² -12x- 12x-sixteen x²+(15-4-12-12)x-(6+sixteen) x²-13x-22 use [-b±?(b²-4ac)]/2a to get the roots right here a=a million, b=-13, c=-22 [13±?(169+88)]/2=[13±?257]/2= (13±3.03)/2 so taking approximation sixteen.03/2=8.012=8 and 9.ninety seven/2=4.985=5 (x-8)(x-5)

Answer 5

11a-1
dont know the second one