(z²+7z+10)÷(z+3) divide polynomial
Answers
Answer:
Step-by-step explanation:
Answer:
The first term is, z2 its coefficient is 1 .
The middle term is, +7z its coefficient is 7 .
The last term, "the constant", is +10
Step-1 : Multiply the coefficient of the first term by the constant 1 • 10 = 10
Step-2 : Find two factors of 10 whose sum equals the coefficient of the middle term, which is 7 .
-10 + -1 = -11 -5 + -2 = -7 -2 + -5 = -7 -1 + -10 = -11 1 + 10 = 11 2 + 5 = 7 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 2 and 5
z2 + 2z + 5z + 10
Step-4 : Add up the first 2 terms, pulling out like factors :
z • (z+2)
Add up the last 2 terms, pulling out common factors :
5 • (z+2)
Step-5 : Add up the four terms of step 4 :
(z+5) • (z+2)
Which is the desired factorization
Equation at the end of step1:
(z + 5) • (z + 2) = 0
STEP2: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 : z+5 = 0
Subtract 5 from both sides of the equation :
z = -5
Solving a Single Variable Equation:
2.3 Solve : z+2 = 0
Subtract 2 from both sides of the equation :
z = -2
Step-by-step explanation:
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