Answer:
Part A ----> 2
Part B ----> 2 (2x - 1) (x + 5)
Part C -----> See explanation below
Explanation:
Given expression is
4x² + 18x - 10
Part A
The greatest common factor (GCF) of the terms 4x², 18x and 10 is the largest number that divides into all three numbers without a remainder
To find this
Find the prime factors of each of the terms
4x² = 2 · 2 · x · x
18x = 2 · 3 · 3 · x
10 = 2 · 5
The prime factor common to all 3 is 2
Therefore the GCF of the expression is 2
Part B
The factored expression can be obtained by factoring out the GCF
4x² + 18x - 10 = 2(2x² + 9x - 5)
We can further factor the term in parentheses:
2x² + 9x - 5
To do this,
Break the expression into groups:
= (2x² - x) + (10x - 5)
Factor x from 2x² - x: x(2x - 1)
Factor 5 from 10x - 5: 5(2x - 1)
Therefore
(2x² - x) + (10x - 5) = x(2x - 1) + 5(2x - 1)
Factor out the common term 2x -1 to get
(2x - 1)(x + 5)
Therefore
4x² + 18x + 10 = 2 (2x - 1) (x + 5)
Part C
Checking if factorization is correct
Multiply (2x - 1)(x + 5) using the FOIL method
= 2x ·x + 2x · 5 + (-1) · x + (-1) · 5
= 2x² + 10x -1x -5
= 2x² + 9x - 5
Multiply the whole expression by 2
2 · 2x² + ² · 9x - 2 · 5
= 4x² + 18x + 10
which is the original expression
So the factorization is correct