Answer:
[12] 7x+5
[13] 72
Step-by-step explanation:
[12] [tex]7x^2+75+50[/tex]
- The first term is, 7x^2 its coefficient is 7 .
- The middle term is, +75x its coefficient is 75 .
- The last term, "the constant", is +50
First, Multiply the coefficient of the first term by the constant 7 × 50 = 350
Then, find two factors of 350 whose sum equals the coefficient of the middle term, which is 75 .
Then, Rewrite the polynomial splitting the middle term using the two factors 5 and 70
7x^2 + 5x + 70x + 50
Add up the first 2 terms, pulling out like factors :
x × (7x+5)
Add up the last 2 terms, pulling out common factors :
10 × (7x+5)
(x+10) • (7x+5)
Hence, Answer = 7x + 5
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
[13]
A perfect square trinomial is a quadratic equation of the form
[tex]ax^2+bx+c=0[/tex]
and a result of squaring a binomial. This means that the first and third term of the trinomial is equal to the square of the first and second term of a binomial. Therefore, in order to determine the value of the third term, we can use the method of completing the square in which the formula is
[tex]c=(\frac{b}{2a})^2[/tex]
where c is the constant and b and a are the coefficients of the first and the second term.
The trinomial 9x^2+72x+144 is a perfect square trinomial, because it's discriminant is equal to zero
Δ=b 2 −4ac=72 2 −4(9)(144)=0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
~Learn with Lenvy~
