Question

Factorize :
$4a {}^{2} - 16a + 15$
​

Answer 1

4a2-16a=-15

Two solutions were found :

a = 3/2 = 1.500
a = 5/2 = 2.500
Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

4*a^2-16*a-(-15)=0

Step by step solution :

Step 1 :

Equation at the end of step 1 :

(22a2 - 16a) - -15 = 0
Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring 4a2-16a+15

The first term is, 4a2 its coefficient is 4 .
The middle term is, -16a its coefficient is -16 .
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 -16 .

-60 + -1 = -61
-30 + -2 = -32
-20 + -3 = -23
-15 + -4 = -19
-12 + -5 = -17
-10 + -6 = -16 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and -6
4a2 - 10a - 6a - 15

Step-4 : Add up the first 2 terms, pulling out like factors :
2a • (2a-5)
Add up the last 2 terms, pulling out common factors :
3 • (2a-5)
Step-5 : Add up the four terms of step 4 :
(2a-3) • (2a-5)


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Answer 2

Answer:

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