Fundamental Concepts Test - 1

The given equation is 2(x + 2) = x − 2.

The expression (x + 2) means two more than x.

Thus, 2(x + 2) means the product of two and two more than x.

The expression x − 2 means two less than x

Thus, 2(x + 2) = x − 2 means ‘the product of two and two more than x equals two less than x’.

The product of mx² and x(2 + y + mx) is

mx²{x(2 + y + mx)}

= mx²{2x + xy + mx²}

= 2mx³ + mx³y + m²x⁴

Thus, the required product is 2mx³ + mx³y + m²x⁴.

The numerical factor of a term is said to be its coefficient.

In the expression 8z² + 7yz + 7z –7y, the coefficient of z² is 8, that of yz is 7, and that of y² is 0 (this expression does not contain any term with y²).

Thus, the information in alternative D is incorrectly matched.

A polynomial of degree 1 is known as linear polynomial.

A polynomial of degree 2 is known as quadratic polynomial.

A polynomial of degree 3 is known as cubic polynomial.

A polynomial of degree 0 is known as constant polynomial.

Number 0 is known as zero polynomial.

Since the degree of the polynomial 3y + 3 is 1, it is not a cubic polynomial. It is a linear polynomial.

The expressions 3ab² + c³+ 37b²a + 26a²b² and −2a²b² − 3ab² +32√ 3c³ +13b³a² can be added as follows:

3ab² + c³ + 37b²a + 26a²b² −2a²b² − 3ab² +32√ 3c³ + 13b³a²

= (3ab² − 3ab²) + (26a²b²−2a²b²) + 37b²a + (c³+32√ 3c³) + 13b³a²

= 24a²b² + 37b²a + (32√ 3+1)c³ + 13b³a²