Explanation

The expression 2x² + 3x + 2 has three separate terms: 2x², 3x, and 2.

Terms are separated by plus or minus signs.

Explanation

x²y and xy² have the same variables but with different exponents, so they are not like terms.

Unlike terms cannot be combined through addition or subtraction.

Explanation

x + y is an expression because it shows a combination of variables and operations without an equal sign.

An equation must include an equal sign (e.g., x + y = 5).

Explanation

A fraction of the form P(x)/Q(x), where both P(x) and Q(x) are polynomials and Q(x) ≠ 0, is called a rational function.

This is because it represents the ratio of two polynomials, which defines a rational expression.

Explanation

In direct variation, two variables increase or decrease together, and are related by a = kb, where k is a constant.

If k = 1, then a = b, which expresses direct variation.

Explanation

Let's denote the man's present age as x.

(x + 5) * 3 = 84

x + 5 = 84 / 3

x + 5 = 28

x = 28 - 5

x = 23

Explanation

Logarithm of 0 is undefined because there is no exponent you can raise 5 to that results in 0.

In math, log₅(0) has no real value, as logarithmic functions are only defined for positive real numbers.

Explanation

Given polynomial: p(x) = x² - 4x + 3

Step 1: Factor the polynomial

p(x) = (x - 3)(x - 1)

Step 2: Find the zeros

Zeros are x = 3 and x = 1

Explanation

Given quadratic equation: 9x² - 27x + k = 0

Step 1: Find the sum and product of roots

Sum of roots (α + β) = -(-27)/9 = 3

Product of roots (αβ) = k/9

Step 2: Use the given condition

2α + 5β = 7

We also know α + β = 3

Step 3: Express α in terms of β or vice versa

From α + β = 3, α = 3 - β

Step 4: Substitute α in the given condition

2(3 - β) + 5β = 7

6 - 2β + 5β = 7

3β = 1

β = 1/3

Step 5: Find α

α = 3 - β = 3 - 1/3 = 8/3

Step 6: Find k using the product of roots

αβ = k/9

(8/3)(1/3) = k/9

8/9 = k/9

k = 8

Explanation

Z1Z2 = (2 - i)(3 - i)

= 6 - 2i - 3i + i²

= 6 - 5i - 1 (since i² = -1)

= 5 - 5i