b²+7b-30 factorise the alagebraic expression
Answers
Answer:
b²+7b-30
b²+10b-3b-30
b(b+10) -3(b+10)
(b+10) (b-3)
b= -10 and 3
Trying to factor by splitting the middle term
1.1 Factoring b2-7b-30
The first term is, b2 its coefficient is 1 .
The middle term is, -7b its coefficient is -7 .
The last term, "the constant", is -30
Step-1 : Multiply the coefficient of the first term by the constant 1 • -30 = -30
Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -7 .
-30 + 1 = -29
-15 + 2 = -13
-10 + 3 = -7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 3
b2 - 10b + 3b - 30
Step-4 : Add up the first 2 terms, pulling out like factors :
b • (b-10)
Add up the last 2 terms, pulling out common factors :
3 • (b-10)
Step-5 : Add up the four terms of step 4 :
(b+3) • (b-10)
Which is the desired factorization
Equation at the end of step
1
:
(b + 3) • (b - 10) = 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 : b+3 = 0
Subtract 3 from both sides of the equation :
b = -3
Solving a Single Variable Equation:
2.3 Solve : b-10 = 0
Add 10 to both sides of the equation :
b = 10