what is the expression in factored form
X^2+13X+42
SHOW ALL YOUR STEPS
Step 1: This quadratic equation is in the form of ax^2 + bx + c, where a = 1, b = 13, and c = 42.
Step 2: To factor the quadratic equation, we need to find two numbers that multiply to give 'c' (42) and add to give 'b' (13).
Step 3: Determine the two numbers. In this case, they are 6 and 7 because 6 * 7 equals 42 and 6 + 7 equals 13.
Step 4: Now we rewrite the given equation as (x + 6)(x + 7).
So, the factored form of the equation x^2 + 13x + 42 is (x + 6)(x + 7).
To express the expression x^2 + 13x + 42 in factored form, we need to factor it completely.
Step 1: We look for two numbers whose product is equal to the constant term (42) and whose sum is equal to the coefficient of the middle term (13). These two numbers are 6 and 7.
Step 2: We rewrite the middle term (13x) using the two numbers found in Step 1: 6x + 7x.
Step 3: We group the terms and factor by grouping:
x^2 + 6x + 7x + 42
(x^2 + 6x) + (7x + 42)
x(x + 6) + 7(x + 6)
Step 4: We notice that both groups have a common factor of (x + 6), so we can factor it out:
(x + 6)(x + 7)
Therefore, the expression x^2 + 13x + 42 in factored form is (x + 6)(x + 7).
To find the expression in factored form, you need to determine the factors of the quadratic equation.
Step 1: Multiply the coefficient of the x^2 term (which is 1) by the constant term (which is 42).
1 * 42 = 42
Step 2: Look for two numbers whose product is equal to 42 and whose sum is equal to the coefficient of the x term (which is 13).
The numbers 6 and 7 satisfy these conditions since 6 * 7 = 42 and 6 + 7 = 13.
Step 3: Rewrite the quadratic equation using the two numbers as coefficients of the x term (13x).
X^2 + 6x + 7x + 42
Step 4: Group the terms and factor out the common factors from each group.
(X^2 + 6x) + (7x + 42)
x(x + 6) + 7(x + 6)
Step 5: Notice that there is a common factor in both terms, (x + 6), so factor it out.
(x + 6)(x + 7)
Therefore, the expression in factored form is (x + 6)(x + 7).