The product of (x + 4) and (x + k) is x² + 10x + 24. What is k?

The product of $(x + 4)$ and $(x + k)$ is $x^{2} + 10 x + 24$ . What is $k$ ?

Class 8Algebraic Expressions and IdentitiesAlgebra

Step-by-Step Solution

(x + 4) (x + k) = x^{2} + (4 + k) x + 4 k

. Matching the

x

term:

4 + k = 10

, so

k = 6

— and

4 k = 24

matches the constant, confirming it. Copying the constant 24, or reusing the given 4, skips the matching step; 14 comes from adding 10 + 4 instead of subtracting.

Answer: D) 6

Key idea: Why identities matter

Identities save time and reveal structure. Examples of clever uses:

- Compute

10 2^{2}

mentally:

(100 + 2)^{2} = 10 0^{2} + 2 (100) (2) + 2^{2} = 10000 + 400 + 4 = 10404

.
- Compute

99 \times 101 : (100 - 1) (100 + 1) = 10 0^{2} - 1^{2} = 10000 - 1 = 9999

.
- Compute

4 7^{2} - 4 3^{2} : (47 - 43) (47 + 43) = 4 \times 90 = 360

.

Look at any number-pair calculation; if you can rewrite it as one of the three identity forms, the answer falls out.

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The product of (x+4) and (x+k) is x2+10x+24. What is k?

Step-by-Step Solution

Key idea: Why identities matter

Master this chapter in 30 minutes a day.

More Class 8 Algebraic Expressions and Identities practice

The product of $(x + 4)$ and $(x + k)$ is $x^{2} + 10 x + 24$ . What is $k$ ?