1) 5x2+3x+2=? Find the factor
Answers
Answer:
Step by step solution :
Step 1 :
Equation at the end of step 1 :
(5x2 - 3x) - 2 = 0
Step 2 :
Trying to factor by splitting the middle term
2.1 Factoring 5x2-3x-2
The first term is, 5x2 its coefficient is 5 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 5 • -2 = -10
Step-2 : Find two factors of -10 whose sum equals the coefficient of the middle term, which is -3 .
-10 + 1 = -9
-5 + 2 = -3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 2
5x2 - 5x + 2x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
5x • (x-1)
Add up the last 2 terms, pulling out common factors :
2 • (x-1)
Step-5 : Add up the four terms of step 4 :
(5x+2) • (x-1)
Which is the desired factorization
Equation at the end of step 2 :
(x - 1) • (5x + 2) = 0
Step 3 :
Theory - Roots of a product :
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation :
3.2 Solve : x-1 = 0
Add 1 to both sides of the equation :
x = 1
Solving a Single Variable Equation :
3.3 Solve : 5x+2 = 0
Subtract 2 from both sides of the equation :
5x = -2
Divide both sides of the equation by 5:
x = -2/5 = -0.400
Supplement : Solving Quadratic Equation Directly
Solving 5x2-3x-2 = 0 directly
Step-by-step explanation: