So the questions was-->Factor the following algebraic equation and describe the process by which it is done: x²+ 3x – 10 = ?

I solved the questions correctly but my teacher said I need to show it algebraically not arithmetically. & she said that I need to show how I arrived with the factors (x+5)(x-2) = ?

factors of 10

(10,1,2,5)

since you get 5-2 = 3...you would use 5,2

(x +5)*(x-2) = foil

x^2 +(-2x)+5x-10 =

x^2 + 3x - 10

Make a list of factors for both the coefficient of the x^2 term and the constant. In this case, 1 and 10. so 1X1 and then 1X10 and 2X5. Also, the fact that the constant is a negative 10, that means one of the 2 binomials

must be negative. Then you look for the combination of the sets of factors that when put together with FOIL, you get the middle term, in this case, 3x.

Thank you both!!

To factor the algebraic equation x² + 3x – 10, we need to find two binomials that, when multiplied, give us the original equation.

Step 1: Write down the equation:
x² + 3x – 10

Step 2: Look for pairs of numbers whose product is the product of the coefficient of x² (which is 1) and the constant term (which is -10). In this case, the product is -10. We need to find two numbers whose product is -10 and whose sum is the coefficient of x (which is 3). The numbers that fit these criteria are 5 and -2.

Step 3: Rewrite the middle term (3x) using the two numbers you found in Step 2 (5 and -2). The goal is to decompose the middle term into two terms so that we can group them and factor them separately. We do this by splitting the middle term 3x into 5x and -2x:
x² + 5x - 2x – 10

Step 4: Group the terms into pairs:
(x² + 5x) - (2x + 10)

Step 5: Factor out the common factors from each pair:
x(x + 5) - 2(x + 5)

Step 6: Notice that both expressions now have a common factor of (x + 5), so we can factor it out:
(x + 5)(x - 2)

So the factored form of the equation x² + 3x – 10 is (x + 5)(x - 2).