Factor 20x² + 71x + 62

Here we will show you how to factor the quadratic function 20x² + 71x + 62 using the box method. In other words, we will show you how to factor 20x squared plus 71x plus 62 (20x^2 + 71x + 62) using the box method. It is a 5-step process:

Step 1: The standard form of a quadratic equation is ax² + bx + c. We start by labeling the different parts of our equation 20x² + 71x + 62, like this:

a = 20
b = 71
c = 62

Step 2: Next, we need to draw a box and divide it into four squares:

31	31x	62
20x	20x²	40x
	x	2

We put 20x² (a) in the bottom left square and 62 (c) in the top right square, like this:

31	31x	62
20x	20x²	40x
	x	2

Step 3: In order to fill in the other two squares, we need to do some math. We have to find two numbers that multiply together to give us the product of 20 times 62 (a × c), and add together to equal 71 (b).

More specifically, 20 times 62 is 1240. Therefore, we need to find the two numbers that multiply to equal 1240, and add to equal 71.

? × ? = 1240
? + ? = 71

After looking at this problem, we can see that the two numbers that multiply together to equal 1240, and add together to equal 71, are 31 and 40, as illustrated here:

31 × 40 = 1240
31 + 40 = 71

Now, we can fill in the last two squares in our box with 31x and 40x. Place 31x in the upper left square, and place 40x in the lower right square.

31	31x	62
20x	20x²	40x
	x	2

Step 4: Next, we need to find four final numbers to finish factoring our equation. We can see that our box is a 2 x 2 table made up of rows and columns.

Our goal is to find the numbers that, when multiplied together, result in the products in each square. We can do this by finding the greatest common factor in each row.

Let’s look at the top row. We have the terms 31x and 62. The greatest common factor of 31x and 62 is 31. Therefore, we write 31 to the left of the top row. You can see it here in the color green:

31	31x	62
20x	20x²	40x
	x	2

Next, let’s look at the bottom row. We have the terms 20x² and 40x. The greatest common factor of 20x² and 40x is 20x. Therefore, we write 20x to the left of the bottom row. You can see it here in the color blue:

31	31x	62
20x	20x²	40x
	x	2

To find the values below the table, we first divide 20x² by 20x (labeled in blue). This gives us x.

20x² ÷ 20x = x

You can see this value colored in orange below:

31	31x	62
20x	20x²	40x
	x	2

Next, we divide 40x by 20x (labeled in blue). This gives us 2.

40x ÷ 20x = 2

You can see this value colored in purple below:

31	31x	62
20x	20x²	40x
	x	2

Step 5: Now we have all of the information we need to finish factoring the equation. The values outside of the box are used to factor 20x² + 71x + 62. You simply put the values on the left in one set of parentheses, and the values below in another set of parentheses, to get the answer:

(20x + 31)(x + 2)

That’s it! Now you know how to factor the equation 20x² + 71x + 62.

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Factor 20x² + 71x + 63
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