factorise a square+2a-3
Answers
Answer:
Factoring a2+2a-3
The first term is, a2 its coefficient is 1 .
The middle term is, +2a its coefficient is 2 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 1 • -3 = -3
Step-2 : Find two factors of -3 whose sum equals the coefficient of the middle term, which is 2 .
-3 + 1 = -2
-1 + 3 = 2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -1 and 3
a2 - 1a + 3a - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
a • (a-1)
Add up the last 2 terms, pulling out common factors :
3 • (a-1)
Step-5 : Add up the four terms of step 4 :
(a+3) • (a-1)
Which is the desired factorization
Equation at the end of step
1
:
(a + 3) • (a - 1) = 0
STEP
2
:
Theory - Roots of a product
2.1 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:
2.2 Solve : a+3 = 0
Subtract 3 from both sides of the equation :
a = -3
Solving a Single Variable Equation:
2.3 Solve : a-1 = 0
Add 1 to both sides of the equation :
a = 1
Supplement : Solving Quadratic Equation Directly
Solving a2+2a-3 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Answer:
(a + 3) (a - 1)
Step-by-step explanation:
a² + 2a - 3
= a² -a + 3a - 3
= a(a - 1) +3(a - 1)
= (a + 3) (a - 1)
Hope it helps you.
Thanks :)