How do you factor x squared minus 10x minus 24?

Answer 1

10x2 + 3x - 4 = (5x + 4)(2x - 1)
10x2 + 3x - 4
When dealing with quadratic expressions the standard form is ax2 + bx + c.
The factor format is (mx + n)(px + q). In this question a = 10, b = 3, c = -4.
The technicalities can be covered later but basically combine the product of the factors of a with those of c so that the sum generates the value of b.
As a = 10 the factors are 10 x 1 or 5 x 2 (In all cases the reverse signage may apply e.g. -10 x -1 or -5 x -2)

As c = -4 the factors are -4 x 1, -2 x 2 (and reverse signage if relevant)

10 x -4 and 1 x 1 OR 10 x 1 and 1 x -4 do not generate 3.
5 x -4 and 2 x 1 does not provide the solution but 5 x 1 and 2 x -4 does generates -3 which the reverse signage to 3. So by making the calculation 5 x -1 and 2 x 4 the desired result is achieved.
The factors are thus (5x + 4)(2x - 1)...........note that the pairs of numbers in the calculation process separate when placed in the brackets /parentheses.

Answer 2

First take out the common factor of 2:

10x2 + 48x - 10 = 2(5x2 + 24x - 5)

Now considering the quadratic that's left, the factor pairs of the x2 term provide the first term of each bracket:

5x2 = 5x times x → (5x ...)(x ...)

And consider the factors of the last term:

-5 = -1 x 5 or 1 x -5

Which in combination with the coefficients x in the brackets give a total of the coefficient of the x term; possible combinations are:

1. 5x x -1 + x x 5 = 0
2. 5x x 1 + x x -5 = 0
3. 5x x 5 + x x -1 = 24x
4. 5x x -5 + x x 1 = -24x

Of which one (3) gives the required 24x: 5x x 5 + x x -1

So the 5 goes in the x term bracket (so that it multiples by the 5x) and the -1 goes in the 5x bracket to give:

10x2 + 48x - 10 = 2(5x - 1)(x + 5)

Answer 3

Take out the GCF, which is x.

x(3x - 10)

Answer 4

(x + 3)(x + 1)(x - 3)(x -1)

Answer 5

X^2-10x-24

=(x+2)(x-12)

Answer 6

10x2(2x2 - 1)