Louise begins factoring the polynomial, which has four terms. 4x3 + 12x2 + 5x + 15 4x2(x + 3) + 5(x + 3) which is the completely factored form of her polynomial? 4x2(x + 3)2 x(4x2 + 5) (4x2 + 5) (x + 3) (4x2 + 5) (x + 3)2

Louise wants to factorize completely the given polynomial

Grouping first, second terms together and third, fourth terms together

=

Taking common from first and second terms of the given expression and taking 5 common from the third and fourth terms.

=

Taking (x+3) common from the given expression,

= is the completely factored form.

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1