factor (5p^2) -31p+30
To factor the expression 5p^2 - 31p + 30, we can use the factoring method.
Step 1: Multiply the coefficient of the quadratic term (5) and the constant term (30): 5 * 30 = 150.
Step 2: Find two numbers that multiply to give 150 and add to give the coefficient of the linear term (-31). The numbers in this case are -1 and -30 since (-1) * (-30) = 30 and (-1) + (-30) = -31.
Step 3: Rewrite the middle term -31p as the sum of the two numbers found in step 2: -1p - 30p.
Step 4: Group the terms in pairs: (5p^2 - p) + (-30p + 30).
Step 5: Factor out the greatest common factor (GCF) from each pair: p(5p - 1) - 30(5p - 1).
Step 6: Notice that you now have a common binomial factor (5p - 1). You can factor it out: (5p - 1)(p - 30).
So, the factored form of the expression 5p^2 - 31p + 30 is (5p - 1)(p - 30).
To factor the quadratic expression 5p^2 - 31p + 30, we need to find two binomials whose multiplication gives us this expression.
Let's break down the steps to factor this quadratic expression:
Step 1: Multiply the coefficient of the quadratic term (5) by the constant term (30). In this case, 5 * 30 = 150.
Step 2: Look for two numbers that multiply to give us 150 and add up to the coefficient of the linear term (-31). In this case, the numbers are -6 and -25 since -6 * -25 = 150, and -6 + (-25) = -31.
Step 3: Rewrite the middle term (-31p) using the two numbers (-6 and -25) we found in the previous step. So instead of -31p, we can write -6p - 25p.
Now, let's factor the expression using these steps:
Factorization: 5p^2 - 31p + 30
= 5p^2 - 6p - 25p + 30 (Rewriting the middle term)
= (5p^2 - 6p) + (-25p + 30)
Now, we can factor by grouping:
= p(5p - 6) - 5(5p - 6)
= (p - 5)(5p - 6)
Therefore, the factored form of the expression 5p^2 - 31p + 30 is (p - 5)(5p - 6).
To factor the expression 5p^2 - 31p + 30, we can look for two numbers that multiply to give the constant term (30) and add up to give the coefficient of the middle term (-31).
The possible pairs of numbers that multiply to give 30 are:
1, 30
2, 15
3, 10
5, 6
However, none of these pairs add up to -31. So let's try the pairs with negative numbers:
-1, -30 -> -1 + (-30) = -31 --> This is a match!
Thus, we can split the middle term -31p as -1p - 30p and factor it as follows:
5p^2 - 31p + 30 = 5p^2 - p - 30p + 30
Take out the common factors from the pairs:
= p(5p - 1) - 30(5p - 1)
Now, we can see that we have a common factor of (5p - 1) in both terms, so we can factor it out:
= (5p - 1)(p - 30)
Therefore, the factored form of 5p^2 - 31p + 30 is (5p - 1)(p - 30).