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The algebraic sum of a and b is the coefficient of the middle term - the term for x.
Incidentally, the algebraic sum is the sum of a and b which takes account of their signs.
The constant term of the trinomial
Ax + Bx + C is not a trinomial!
A trinomial is a polynomial that consists of three terms, typically expressed in the form ( ax^2 + bx + c ), where ( a ), ( b ), and ( c ) are constants. An example of a trinomial is ( 2x^2 + 3x - 5 ). Another example is ( x^2 - 4x + 4 ). These expressions can often be factored or used in various algebraic operations.
A trinomial is perfect square if it can be factored into the form (a+b)2 So a2 +2ab+b2 would work.
The answer will depend on what c is!If the trinomial is ax^2 + bx + c then the required value of c is (b^2)/(4a)
The constant term of the trinomial
B. Sum of two numbers
The number represented by B should be viewed as the coefficient of the linear term (x) in the trinomial. This number affects the middle term in the factored form of the trinomial.
A trinomial of the form ax2 + bx + c is a perfect square if (and only if) b2-4ac = 0 and, in that case, it is factored into a*(x + b/2a)2
Ax + Bx + C is not a trinomial!
A trinomial is a polynomial that consists of three terms, typically expressed in the form ( ax^2 + bx + c ), where ( a ), ( b ), and ( c ) are constants. An example of a trinomial is ( 2x^2 + 3x - 5 ). Another example is ( x^2 - 4x + 4 ). These expressions can often be factored or used in various algebraic operations.
A trinomial is perfect square if it can be factored into the form (a+b)2 So a2 +2ab+b2 would work.
No.
Here are the steps to factoring a trinomial of the form x2 + bx + c , with c > 0 . We assume that the coefficients are integers, and that we want to factor into binomials with integer coefficients.Write out all the pairs of numbers which can be multiplied to produce c .Add each pair of numbers to find a pair that produce b when added. Call the numbers in this pair d and e .If b > 0 , then the factored form of the trinomial is (x + d )(x + e) . If b < 0 , then the factored form of the trinomial is (x - d )(x - e) .Check: The binomials, when multiplied, should equal the original trinomial.Note: Some trinomials cannot be factored. If none of the pairs total b , then the trinomial cannot be factored.
The answer will depend on what c is!If the trinomial is ax^2 + bx + c then the required value of c is (b^2)/(4a)
A trinomial is considered perfect if it can be expressed as the square of a binomial. For example, the trinomial (x^2 + 6x + 9) is a perfect square because it can be factored into ((x + 3)^2). Perfect trinomials typically take the form (a^2 + 2ab + b^2) or (a^2 - 2ab + b^2).
The expression (7x^2 + 2x + 1) is not a prime trinomial because it can be factored. To determine if it's prime, we can check for factors of the form ((ax + b)(cx + d)). In this case, it does not factor neatly into integers, but it can be analyzed further. In conclusion, while it may not have simple integer factors, it is not prime in the algebraic sense as it cannot be simplified into a product of polynomials.