factorize by splitting the middle term r^2+5r+4
Answers
Answer:
The first term is, r2 its coefficient is 1 .
The middle term is, -5r its coefficient is -5 .
The last term, "the constant", is -4
Step-1 : Multiply the coefficient of the first term by the constant 1 • -4 = -4
Step-2 : Find two factors of -4 whose sum equals the coefficient of the middle term, which is -5 .
-4 + 1 = -3
-2 + 2 = 0
-1 + 4 = 3
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Answer:
r²+5r+4
Since the product of first and third term is 4r², we have to break the middle term in such a way so that the sum is 5r and product is 4r².
So, We Will Break 5r Like This:
4r and 1r
Product= 4r×1r
= 4r²
Sum= 4r+1r
= 5r
Now, we will substitute the terms in place of 5r.
⇒ r²+4r+1r+4
r(r+4)+1(r+4)
(r+1)(r+4) Ans
VERIFY:
(r+1)(r+4) should be equal to r²+5r+r
⇒ (r+1)(r+4)= r²+5r+4
To solve the LHS, we will use the identity:
(x+a)(x+b)= x²+(a+b)x+ab
x=r
a=1
b=4
⇒ r²+(1+4)r+1×4= r²+5r+4
r²+5r+r= r²+5r+4
LHS=RHS
Hence, verified
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