Express the following as a trinomial: (2x-3)(x+7)
Express the following as the product of two bionomials:
x-squared -5x-24
Explain please...This is review and i don't remember learning it.... Thanks So Mcuh!!!
1. 2x^2+11x-21
This is quadratics. Multiply 2x by x and 7 separatel.Mltiply -3 by x and 7 separately. Add the products and you get a trinomial.
2. (x-8)(x+3) If you don't get this, make sure that you understand the chapter on polynomials/quadratics.
To express the given expression as a trinomial, we can use the distributive property.
Given expression: (2x-3)(x+7)
Step 1: Multiply the first term of the first binomial with each term of the second binomial.
2x * x = 2x^2
2x * 7 = 14x
Step 2: Multiply the second term of the first binomial with each term of the second binomial.
-3 * x = -3x
-3 * 7 = -21
Step 3: Combine the like terms obtained from step 1 and step 2 to get the trinomial form.
(2x^2 + 14x) + (-3x - 21) = 2x^2 + 11x - 21
Therefore, the given expression (2x-3)(x+7) is equal to the trinomial 2x^2 + 11x - 21.
To express the given expression as the product of two binomials, we need to factor it.
Given expression: x^2 - 5x - 24
Step 1: Multiply the coefficient of the x^2 term (1) with the constant term (-24).
1 * -24 = -24
Step 2: Find two numbers whose product is equal to the result from step 1 (-24) and whose sum is equal to the coefficient of the x term (-5).
The numbers -8 and 3 satisfy these conditions (-8 * 3 = -24 and -8 + 3 = -5).
Step 3: Rewrite the given expression using the two numbers found in step 2.
x^2 - 8x + 3x - 24
Step 4: Group the terms in pairs and factor out the greatest common factor from each pair.
x(x - 8) + 3(x - 8)
Step 5: Factor out the common binomial factor from the resulting expression.
(x - 8)(x + 3)
Therefore, the given expression x^2 - 5x - 24 can be expressed as the product of two binomials: (x - 8)(x + 3).