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

HCF = x - 2

LCM = x^3 + 3x^2 - 6x - 8

One polynomial = x^2 - x - 2 = (x - 2)(x + 1)

Factorize LCM:

x^3 + 3x^2 - 6x - 8 = (x - 2)(x^2 + 5x + 4) = (x - 2)(x + 1)(x + 4)

Using HCF × LCM = Product of polynomials:

(x - 2) × (x - 2)(x + 1)(x + 4) = (x - 2)(x + 1) × Second polynomial

Second polynomial = (x - 2)(x + 4) = x^2 + 2x - 8

Explanation

We are asked to find the difference between the largest and smallest 4-digit number.

Step 1: Identify the numbers

Smallest 4-digit number = 1000

Largest 4-digit number = 9999

Step 2: Subtract

9999 − 1000 = 8999

Explanation

Given that the two sides of the isosceles triangle are equal:

3x - 2y + 2 = x - y + 7

This simplifies to:

2x - y = 5

The sum of the two equal sides is 12 cm:

(3x - 2y + 2) + (x - y + 7) = 12

This simplifies to:

4x - 3y = 3

Solving these two equations simultaneously, we find x = 6.

Explanation

Given the calculation:

70 decreased in 2:5

New value = 70 * (2/5)

= 70 * 0.4

= 28

Explanation

A number is divisible by 3 if the sum of its digits is divisible by 3.

2+6+5+9 = 22, which is not divisible by 3, so 2659 is not divisible by 3.

Explanation

To determine the number of significant figures in 0.00253, follow these rules:

• Leading zeros are not significant.
• All non-zero digits are significant.

Breakdown:

0.00253 → The leading zeros (0.00) are not significant.

The digits 2, 5, and 3 are significant.

There are 3 significant figures in 0.00253.

Explanation

Let's check each equation by plugging in a = -5:

(3/5)a + 19 = 16

→ (3/5)(-5) + 19 = -3 + 19 = 16 → True

So, the equation (3/5)a + 19 = 16 has a solution of a = -5

Explanation

Total painted = 25% (blue) + 30% (green) = 55%

Remaining for white = 100% - 55% = 45%

Explanation

Let's calculate what needs to be added:

(7 + 2a - a² + 4a³) - (2a³ + a² - 3a - 1)

= 7 + 2a - a² + 4a³ - 2a³ - a² + 3a + 1

= 2a³ - 2a² + 5a + 8