Identify Variables: Identify a, b, and c in the quadratic expression x^2 + 4x + 8. Compare x^2 + 4x + 8 with the standard quadratic form ax^2 + bx + c. Here, a = 1, b = 4, and c = 8.Find Product and Sum: Find two numbers that multiply to a*c (which is 1*8 = 8) and add up to b (which is 4). We are looking for two numbers whose product is 8 and whose sum is 4. However, there are no two real numbers that satisfy both of these conditions.Conclusion: Since we cannot find two numbers that satisfy the conditions from Step 2, we conclude that the quadratic expression x^2 + 4x + 8 cannot be factored over the real numbers using integer factors.

Algebra 1

Factor quadratics with leading coefficient 1

Full solution

Q. Factorize.

x^2+4x+8

Identify Variables: Identify $a$ , $b$ , and $c$ in the quadratic expression $x^2 + 4x + 8$ . Compare $x^2 + 4x + 8$ with the standard quadratic form $ax^2 + bx + c$ . Here, $a = 1$ , $b = 4$ , and $c = 8$ .
Find Product and Sum: Find two numbers that multiply to $a*c$ (which is $1*8 = 8$ ) and add up to $b$ (which is $4$ ). $\newline$ We are looking for two numbers whose product is $8$ and whose sum is $4$ . $\newline$ However, there are no two real numbers that satisfy both of these conditions.
Conclusion: Since we cannot find two numbers that satisfy the conditions from Step extbf{ $2$ }, we conclude that the quadratic expression $x^2 + 4x + 8$ cannot be factored over the real numbers using integer factors.