. I Simplify the following algebraie expressions i. Usc rule of distribution lu expand (14x-5)(3x-4) ii. Use identities rule to the expression (4cdot x)^2 2a^3b^7times 2ab^5 iv. (14x-5)(3x-4) (9x-11)(3x+8) 2. A Polynomial (x) is multiple of x-3 and the remainder when P(x) is divided by x+3 is Determine the remainder when P(x) is divided by x^a-9 is marks) 3 . Applying splitting the middle term method factorise the expression 35x^2-54x+16 (3)marks) (5 marks) 4. Establish relations between log_(a)x=p and a^p=x 5. Use matrix method to solve the system of simultaneous equations below (5 marks) x-4y=3 3x-y=-2 b. State properties of matrix multiplication 7. If A=(} 1&2 -2&3 ) Verify that A(B+C)=AB+AC ifB+C= ) -1&2 4&3 8.Use first principle to differentiate the function y=(1)/(x^3) (5 marks) cs marks)

Question

. I Simplify the following algebraie expressions i. Usc rule of distribution lu expand (14x-5)(3x-4) ii. Use identities rule to the expression (4cdot x)^2 2a^3b^7times 2ab^5 iv. (14x-5)(3x-4) (9x-11)(3x+8) 2. A Polynomial (x) is multiple of x-3 and the remainder when P(x) is divided by x+3 is Determine the remainder when P(x) is divided by x^a-9 is marks) 3 . Applying splitting the middle term method factorise the expression 35x^2-54x+16 (3)marks) (5 marks) 4. Establish relations between log_(a)x=p and a^p=x 5. Use matrix method to solve the system of simultaneous equations below (5 marks) x-4y=3 3x-y=-2 b. State properties of matrix multiplication 7. If A=(} 1&2 -2&3 ) Verify that A(B+C)=AB+AC ifB+C= ) -1&2 4&3 8.Use first principle to differentiate the function y=(1)/(x^3) (5 marks) cs marks)

Answer 1

1. Simplify the following algebraic expressions: i.

- Using the distributive property, we get:

ii.

- Using the power of a product rule, we get:

iii.

- Using the product of powers rule, we get:

iv.

- This is the same as the first expression, so the answer is the same:

v.

- Using the distributive property, we get:

2. A Polynomial

is multiple of

and the remainder when

is divided by

is

. Determine the remainder when

is divided by

. - Since

is a multiple of

, we can write

, where

is some polynomial. - When

is divided by

, the remainder is

, so we can write

, where

is some polynomial. - Since

is a multiple of

, we can write

. - Equating the coefficients of

, we get

. - Substituting

, we get

, which is not possible. - Therefore, the remainder when

is divided by

is

.3. Applying splitting the middle term method factorise the expression

. - We can write the expression as

. - Grouping the terms, we get

. - Factoring out the common factors, we get

. - Rearranging the terms, we get

.4. Establish relations between

and

. - If

, then

. - Conversely, if

, then

.5. Use matrix method to solve the system of simultaneous equations below:

- Representing the system of equations in matrix form, we get:

- Solving the system using the inverse matrix method, we get:

6. State properties of matrix multiplication. - Matrix multiplication is associative:

- Matrix multiplication is not commutative:

- The product of a matrix

Question

Solution

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