factorise
4x square + 17 multiply +15
Answers
Answer:
STEP 1:
Equation at the end of step 1
(22x2 - 17x) + 15 = 0
STEP 2:
Trying to factor by splitting the middle term
2.1 Factoring 4x2-17x+15
The first term is, 4x2 its coefficient is 4 .
The middle term is, -17x its coefficient is -17 .
The last term, "the constant", is +15
Step-1 : Multiply the coefficient of the first term by the constant 4 • 15 = 60
Step-2 : Find two factors of 60 whose sum equals the coefficient of the middle term, which is -17 .
-60 + -1 = -61
-30 + -2 = -32
-20 + -3 = -23
-15 + -4 = -19
-12 + -5 = -17 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -12 and -5
4x2 - 12x - 5x - 15
Step-4 : Add up the first 2 terms, pulling out like factors :
4x • (x-3)
Add up the last 2 terms, pulling out common factors :
5 • (x-3)
Step-5 : Add up the four terms of step 4 :
(4x-5) • (x-3)
Which is the desired factorization
Equation at the end of step 2
(x - 3) • (4x - 5) = 0
STEP 3
Theory - Roots of a product
3.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.