Can anyone help me understand how to do this?
Factoring each polynomial
x^2+5ax+6a^2
and
solve each equation
a^2+a=20
I am so lost with this one I can not grab how you get a number from this.
thanks for trying who ever you may be
X^2+5aX+6a^2
splitting the middle term as
X^2+3ax+2aX+6ax^2
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take common factor from 2 terms,sequentially as
X(X+3a)+2a(X+3a)
(X+2a) (X+3a) answer is x=-2a ;X=-3a
Question 2: a^2+a-20=0
a^2+5a-4a-20=0
a(a+5)-4(a+5)
(a+5) (a-4)=0
or a=-5 ; +4
both are factorised using splitting the middle term method
Of course! I can help you understand how to factor the polynomial and solve the equation.
To factor the polynomial x^2 + 5ax + 6a^2, we can look for two binomials that multiply together to give us the original polynomial.
First, we need to find two numbers that multiply to give us the constant term (6a^2) and add up to give us the coefficient of the middle term (5a). In this case, the numbers are 2a and 3a.
Next, we split the middle term (5ax) using these numbers:
x^2 + 2ax + 3ax + 6a^2
Now, we group the terms into two pairs:
(x^2 + 2ax) + (3ax + 6a^2)
Now, we factor out the greatest common factor from each pair:
x(x + 2a) + 3a(x + 2a)
Finally, we notice that we have a common binomial factor, (x + 2a), and we can factor it out:
(x + 2a)(x + 3a)
So the factored form of the polynomial x^2 + 5ax + 6a^2 is (x + 2a)(x + 3a).
Now let's move on to solving the equation a^2 + a = 20.
To solve this equation, we want to find the values of a that make the equation true.
First, we can rearrange the equation to form a quadratic equation:
a^2 + a - 20 = 0
Now, we can factor the quadratic equation. We need to find two numbers that multiply to give us the constant term (-20) and add up to give us the coefficient of the middle term (1). In this case, the numbers are 5 and -4.
Finally, we rewrite the equation using the factored form:
(a + 5)(a - 4) = 0
Now we can set each factor equal to zero and solve for a:
a + 5 = 0 => a = -5
a - 4 = 0 => a = 4
So the solutions to the equation a^2 + a = 20 are a = -5 and a = 4.
I hope this explanation helps! If you have any further questions, feel free to ask.