Factorise..2x^-7x+5
You need to proofread before posting. If you mean 2x^2 + 7x + 5, it factors into (2x + 5)(x+1).
Or, as you might have meant,
2x^2 - 7x + 5 = (2x-5)(x-1)
To factorize the expression 2x^2 - 7x + 5, we can use the factoring techniques such as grouping, factoring by grouping, or factoring by using the quadratic formula. Let's go through the factoring by grouping method step by step:
Step 1: Multiply the coefficient of the quadratic term (2) with the constant term (5). In this case, it is 2 * 5 = 10.
Step 2: Look for two numbers that add up to the coefficient of the linear term (-7) and multiply to give the product obtained in Step 1 (10). In this case, the numbers are -2 and -5 because -2 + (-5) = -7 and (-2) * (-5) = 10.
Step 3: Now, rewrite the linear term (-7x) using the two numbers found in Step 2. We have 2x^2 - 2x - 5x + 5.
Step 4: Group the terms and factor out the common factors from each group. In this case, we can group the first two terms and the last two terms: (2x^2 - 2x) + (-5x + 5).
Step 5: Factor out the greatest common factor (GCF) from each group. We can factor out 2x from the first group and -5 from the second group: 2x(x - 1) - 5(x - 1).
Step 6: Notice that (x - 1) is common to both terms. Factor out (x - 1) from the expression: (2x - 5)(x - 1).
Therefore, the factorized form of 2x^2 - 7x + 5 is (2x - 5)(x - 1).