factorize the following expressions y² +9y+ 20
Answers
Answer:
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.The first term is, y2 its coefficient is 1 .
The middle term is, -9y its coefficient is -9 .
The last term, "the constant", is +20
Step-1 : Multiply the coefficient of the first term by the constant 1 • 20 = 20
Step-2 : Find two factors of 20 whose sum equals the coefficient of the middle term, which is -9 .
-20 + -1 = -21 -10 + -2 = -12 -5 + -4 = -9 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -4
y2 - 5y - 4y - 20
Step-4 : Add up the first 2 terms, pulling out like factors :
y • (y-5)
Add up the last 2 terms, pulling out common factors :
4 • (y-5)
Step-5 : Add up the four terms of step 4 :
(y-4) • (y-5)
Which is the desired factorization
(y - 4) • (y - 5) = 0Solve : y-4 = 0
Add 4 to both sides of the equation :
y = 4Solve : y-5 = 0
Add 5 to both sides of the equation :
y = 5y2-9y+20 = 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
Step-by-step explanation:
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