Question

What is the quadratic factor of 15x squared +52x+45

Answer 1

The quadratic factors of the given expression are (3x + 5) and (5x + 9).

SOLUTION:

Given, quadratic equation is 15x squared + 52x + 45
`\bold{\rightarrow 15 x^(2)+52 x+45}`

We have to find the quadratic factors for the given quadratic expression.

Now, let us factorize the given expression.

`\begin{array}{l}\bold{\rightarrow 15 x^(2)+52 x+45} \\\\ \bold{\rightarrow 15 x^(2)+25 x+27 x+45} \\\\ \text{ (where 52x can be represented as the sum of 25x and 27x)} \\\\ \text{ Taking the common factors out of the braces } \\\\ \bold{\rightarrow 5 x(3 x+5)+9(3 x+5)} \\\\ \bold{\rightarrow(3 x+5)(5 x+9)}\end{array}`

Hence, the quadratic factors are (3x + 5) and (5x + 9).

Steps to factorise quadratic equation:

With the quadratic equation in this form:
`a x^(2)+b x+c=0`

• Step 1: Find two numbers that multiply to give ac (in other words a times c), and add to give b.

• Step 2: Rewrite the middle with those numbers

• Step 3: Factor the first two and last two terms separately

• Step 4: If we've done this correctly, our two new terms should have a clearly visible common factor.