Question

Factor completely. 5x^2+44x-9

Answer 1

To factor the expression 5x^2+44x-9 completely, split the middle term and factor by grouping.

Step-by-step explanation:

To factor the expression 5x^2+44x-9 completely, we need to find two binomials that multiply together to give us the original expression.

We can start by splitting the middle term (44x) into two terms that multiply together to give us the product of the coefficient of x^2 (5) and the constant term (-9). In this case, the terms are -1 and 9.

Next, we can use these terms to rewrite the expression: 5x^2-1x+9x-9.

Now, we can factor by grouping: (5x^2-1x)+(9x-9). Taking out the common factors, we get: x(5x-1)+9(5x-1). Finally, we can factor out the common binomial: (x+9)(5x-1). Therefore, the expression 5x^2+44x-9 factors completely to (x+9)(5x-1).

Answer 2

(x + 9)(5x - 1)

Step-by-step explanation:

Given

5x² + 44x - 9

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 5 × - 9 = - 45 and sum = + 44

The factors are + 45 and - 1

Use these factors to split the x- term

5x² + 45x - x - 9 ( factor the first/second and third/fourth terms )

= 5x(x + 9) - 1(x + 9) ← factor out (x + 9) from each term

= (x + 9)(5x - 1) ← in factored form