The value of t for which the given expression 2x²+tx+10 will be a product of two binomial is 9.
A binomial expression is an expression that has two terms.
In order to get the value of t for which the given expression 2x²+tx+10 will be a product of two binomial. We need to find a number(A) that is when broken into two other numbers(B and C), the sum of these numbers(B and C) is the number itself(A). Also, the product of the two numbers is equal to the product of the rest two terms of the expression(2 and 10).
Therefore, the number that fulfills this condition is 9. Let's check by substituting the value of t as 9.
[tex]2x^2+tx+10\\\\= 2x^2+9x+10 \\\\= 2x^2+5x+4x+10\\\\ = x(2x + 5)+2(2x+5)\\\\= (x+2)(2x+5)[/tex]
Hence, the value of t for which the given expression 2x²+tx+10 will be a product of two binomial is 9.
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