Question

Quesuon 10 of 10

Use the table to identify the values of pand q that should be used to factor x2
+ 3x - 10 as (x + p)(x + 9).
р
1
-1
2
-2
q
-10
10
5
5
p+q
9
9
-3
3
A. -2 and 5
B. -1 and 10
C. 1 and -10
D. 2 and -5
.

Answer 1

The values of p and q are D. 2 and -5

To factor the quadratic expression $x^2 + 3x - 10$ as $(x + p)(x + q)$, we need to find the values of $p$ and $q$ such that $p + q = 3$ and $pq = -10$. From the given table, we can see that the only pair of values that satisfy these conditions is $p = 2$ and $q = -5$, since $p + q = 2 + (-5) = -3$ and $pq = 2 \cdot (-5) = -10$. Therefore, we can write:

x²+3x−10=(x+2)(x−5)

To check that this is the correct factorization, we can use the distributive property:

(x+2)(x−5)=x(x−5)+2(x−5) = x²−5x+2x−10=x² −3x−10

which is the original expression. Therefore, the values of $p$ and $q$ that should be used to factor $x^2 + 3x - 10$ as $(x + p)(x + q)$ are $p = 2$ and $q = -5$.

Therefore, the correct answer is: D. 2 and -5

Answer 2

(p, q) is (2, 5)

Explanation:

Given the expression

x^2 + 3x - 10

Factorize;

x^2 + 5x - 2x - 10

x(x+5) - 2(x+5)

(x-2)(x+5)

Comparing with (x + p)(x + 9).

x+2 = x+ p

x-x+2 = p

2 = p

p = 2

Similarly;

x+5 = x+q

x-x+5 = q

5 = q

q= 5

Hence (p, q) is (2, 5)