factoring quadratic expressions
8x^2+32x+14
First take out the common factor 2:
2(4x²+16x+7)
Inspired from 4 of 4x², try:
2(2x&plummn;7)(2x±1)
we figure out that a plus sign in both factor would work to give:
2(2x+7)(2x+1)
Can you help me in factoring polynomials using GCF?
To factor a quadratic expression, such as 8x^2 + 32x + 14, you need to look for two binomials that, when multiplied together, give you the original expression.
The general form of a quadratic expression is ax^2 + bx + c, where a, b, and c are constants.
In this particular example, we have 8x^2 + 32x + 14.
1. Start by multiplying the coefficient of x^2 (which is 8) by the constant term (which is 14). This gives you 8 * 14 = 112.
2. Next, look for two numbers that multiply to give you 112, and also add up to the coefficient of x (which is 32). In this case, the numbers are 8 and 14 because 8 * 14 = 112, and 8 + 14 = 22.
3. Rewrite the middle term (32x) using these two numbers. Instead of 32x, write 8x + 14x.
So, the quadratic expression becomes 8x^2 + 8x + 14x + 14.
4. Now, group the first two terms (8x^2 + 8x) together and the last two terms (14x + 14) together.
5. From these grouped terms, factor out the greatest common factor (GCF) separately.
Factoring out the GCF, we get 8x(x + 1) + 14(x + 1).
6. Notice that we have a common binomial factor of (x + 1) in both terms. We can factor this out.
Factoring out (x + 1), we have (x + 1)(8x + 14).
Therefore, the factored form of the quadratic expression 8x^2 + 32x + 14 is (x + 1)(8x + 14).