if (x+1) is factor of x²+5x+6 then remainder will be ________
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if (x+1) is factor of x²+5x+6 then remainder will be ________
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Answer:
We need to factorise the given equation
Given equation
x2 + 5x + 6
Let us try factorizing this polynomial using splitting the middle term method.
Factoring polynomials by splitting the middle term:
We need to find two numbers ‘a’ and ‘b’ such that a + b =5 and ab = 6.
On solving this we obtain, a = 3 and b = 2
Thus, the above expression can be written as:
x2 + 5x + 6
= x2 + 3x + 2x + 6
= x(x + 3) + 2(x + 3)
= (x + 3)(x + 2)
Thus, x+3 and x+2 are the factors of the polynomial x2 + 5x + 6.