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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.
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:
- 5x x -1 + x x 5 = 0
- 5x x 1 + x x -5 = 0
- 5x x 5 + x x -1 = 24x
- 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)
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What is a factor of 24 and is a squared number?
The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24. The ones that are squares are 1 and 4.
What is the gratest factor of 24?
The greatest factor of 24 is 24. The greatest factor of a number is the number itself.
Is 24 a factor of 48?
A factor = a number which can be divided into the given number with no remainder so yes 48/24 = 2
What is the greasest common factor of 24 and 72?
Since 24 is a factor of 72, it is automatically the GCF.
Why is 24 not a factor of 12?
That simply means that there is no integer solution to:24n = 12 For comparison, 4 IS a factor; so the equation: 4n = 12 DOES have an integer solution.
What are the factors of x squared minus 10x minus 24?
x2-10x-24 = (x+2)(x-12) when factored
How do you factor 6x squared minus 7x minus 24?
It is: (2x+3)(3x-8) when factored
Who can solve the quadratic equation 2x squared plus 8x minus 2 equals 22?
2x+8x-2=22 10x-2=22 10x+2=+2 10x=24 10/10=24/10 x=2.4
How do you factor 3x squared plus 10x minus 8?
3x2 + 10x - 8The auxiliary equation is 3x2 + 10x - 24 [because 8*3 = 24] Two factors of -24 which sum to 10 are 12 and -2. So the factorisation of the auxillary is (3x + 12)*(3x - 2) = 3*(x + 4)*(3x - 2) Dividing by the 3 used to create the auxiliary gives the solution as (x + 4)*(3x - 2).
Factor the polynomial expression x2 plus 10x - 24?
x2+10x-24 = (x-2)(x+12)
How do you factor x squared plus 5x minus 24?
x2+5x-24=0(x+8)(x-3)=0x=-8 x=3
Factor x2 - 10x plus 24?
-8x+24 {This answer may be wrong: I think the question was intended to read, "Factor x2 - 10x + 24?" If so, the factors are (x - 6) and (x - 4)}
How do you factor x2 minus 10x plus 24?
what two numbers multiply to 24 and add to -10? -4 and -6 look good, so: (x - 4)(x - 6) x = 4 or 6
Factor x2 - 10x - 24?
(x + 2)(x - 12)
What is 2x squared plus 2x minus 24 in factored form?
Factor out a 22(X2 + X - 12)2(X - 3)(X + 4)===========
How do you factor x2-10x equals -24?
x^2 - 10x + 24 You're looking for two factors of 24 that equal 10 (x - 6)(x - 4)
What is the factorization to 3x squared minus 14x minus 24?
3x2 -14x -24 can be factored as (3x + 4)(x - 6).
