Mathematics
Assertion (A) : x2 + 7x + 12
= x2 + (4 + 3)x + 3 x 4
= x2 + 4x + 3x + 3 x 4
= (x + 4)(x + 3)
Reason (R) : To factorise a given trinomial, the product of the first and the last term of the trinomial is always the sum of the two parts when we split the middle term.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Factorisation
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Answer
For a quadratic trinomial of the form :
ax2 + bx + c
To factor using the middle-term splitting method;
Find two numbers that multiply to give ac and add to give b.
So, reason (R) is true.
Given; x2 + 7x + 12
= x2 + (3 + 4)x + 3 x 4
= x2 + 3x + 4x + 3 x 4
= x(x + 3) + 4(x + 3)
= (x + 3)(x + 4)
So, assertion (A) is true and, reason (R) is the correct explanation of assertion (A).
Hence, option 1 is the correct option.
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Related Questions
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