Question

Use the table to identify the values of pand that should be used to factor x2

+ 3x - 10 as (x + p)(x + 9).
р
1
-1
2.
-2
a
--10
10
-5
5
p+a
-9
9
-3
3
A. -2 and 5
B. -1 and 10
C. 1 and -10
O D. 2 and -5

Answer 1

`p =-2`

`q = 5`

Explanation:

Given

`(x^2 + 3x - 10) = (x + p)(x + q)`

Required

Find p and q

`(x^2 + 3x - 10) = (x + p)(x + q)`

Open brackets

`x^2 + 3x - 10 = (p + q)x + pq`

By comparison

`(p + q)x = 3x`

`pq = -10`

`(p + q)x = 3x` implies that:

`p + q = 3`

From the table, the value of p and q that corresponds to
`p + q = 3` is:

`p =-2`

`q = 5`