Turn f(x)= x^2+14x+48 into factored form

Answer 1

f(x) = x^2 + 14x + 48 is a quadratic equation. To factor it, we want to put it into the form f(x) = (x+a)(x+b).

To determine a and b, we need to find two numbers that, when added, equal 14, and when multiplied, equal 48.

We can see that 6 + 8 = 14 and 6 * 8 = 48. So we have found that a is 6 and b is 8.

The factored form of the equation is f(x) = (x + 6) (x + 8).

Checking our answer, f(x) = x^2 + 8x + 6x + 48

so f(x) = x^2 + 14x + 48 which is our original equation so we know our answer is correct.😊

Answer 2

(x^2+6x)+(8x+48)

x(x+6)+8(x+6)

(x+6)(x+8)

Answer 3

Turn f(x) = x² + 14x + 48 into factored form

This is a quadratic equation (equation in the form Ax² + Bx + C)

To factor we need to know B and C, then find factors of C (let's call them a and b) that add up to B, then plug those factors into a set factored form (x+a)(x+b)

Here's How:

Here B = 14 (see the +14 in front of the x in original equation)

and C = 48 (see the +48 as the last term in the original equation)

So to factor the equation, we need to know the factors of C (48) that add up to B (14)

Factors of 48 = 1x48, 2x24, 3x16, 4x12, 6x8 all equal 48 (our value for C)

Add each of the factor sets to find one that equals 14 (our value for B)

1 + 48 = 49 nope

2 + 24 = 26 nope

3 + 16 = 19 nope

4 + 12 = 16 nope

6 + 8 = 14 GOT IT

The factored form of the quadratic equation is (x + a)(x + b),

where a and b are the 2 factors we found last step!

Let's say that a = 6 and b = 8

So, the factored form of x² + 14x + 48 is:

(x + 6)(x + 8)

BUT REMEMBER! This is an equation, so we need to have the full function form written:

f(x) = (x + 6)(x + 8)

Answer 4

Want the form, (x+a)(x+b) = x²+14x+48

Need to find factors of 48 that add up to 14

Factors: 1,2,4,6,8,12,24,48

6+8=14

f(x)=(x+6)(x+8)