Factorise 5x^2 + 8x + 3
and can you please show steps in how to solve it. Thanks
It is mostly a trial and error thing..
start with the factors of 5
5,1
(5x ) (x )
next, the factors of 3: 1,3; 3,1
you want the cross factors to add to 8, so 5+3 =8
(5x+1)(x+3) gives 16x as the middle term , so it must be
(5x+3)(x+1)
EXPLANATION:for example x^2 -5x+6 first of al the product =6*x^2=6x^2(first and last term) sum=-5x(2nd term) now find 2 terms dat when u add give -5x and product 6x^2 [(terms ar -3x&-2x)since -*-=+ &-+-=-] now it bcoms x^2-3x-2x+6, factorise=x(x-3)-2(x-3)=(x-2)(x-3) (collectin like terms)
now 5x^2 +8x+3 (product 15x^2 &sum 8x)term 5x&3x (ans=(5x+3)(x+1) same way as the above solution
try this x^2+x+13(it seems the above method don't work, in expresin like this u can use completin the square mtd or form
To factorize the expression 5x^2 + 8x + 3, we need to find two binomial factors that multiply together to give the original expression.
Step 1: Multiply the coefficient of x^2 (5) with the constant term (3). In this case, 5 multiplied by 3 gives 15.
Step 2: Find two numbers that multiply together to give the product from step 1 (15) and add up to the coefficient of x (8). In this case, the numbers are 3 and 5 (3 * 5 = 15 and 3 + 5 = 8).
Step 3: Rewrite the middle term (8x) of the original expression using the two numbers found in step 2. In this case, we rewrite 8x as 3x + 5x.
Therefore, the factored form of the expression 5x^2 + 8x + 3 is:
5x^2 + 3x + 5x + 3
Step 4: Group the terms and factor them separately. In this case, we group the terms as (5x^2 + 3x) + (5x + 3).
Step 5: Factor out the greatest common factor from each group. In the first group, the common factor is x, and in the second group, the common factor is 1.
x(5x + 3) + 1(5x + 3)
Step 6: Notice that both groups have the same binomial factor, which is (5x + 3).
Therefore, the final factored form of the expression 5x^2 + 8x + 3 is:
(5x + 3)(x + 1)