First, decide which type of factoring to use and then FULLY factor each of the following questions: 35x^2+5x, x^2-16x+63, -2x^3-14x^2+36x, 100-x^2, x^2+8x+16, 3x^2-6x-72
1) 35x^2+5x
First, notice that both terms have a common factor of 5x.
5x(7x+1)
2) x^2-16x+63
This is a trinomial that can be factored into two binomials. The factors of 63 that add up to -16 are -7 and -9.
(x-7)(x-9)
3) -2x^3-14x^2+36x
All three terms have a common factor of -2x.
-2x(x^2+7x-18)
Then, factor the quadratic equation:
-2x(x+9)(x-2)
4) 100-x^2
This is a difference of squares, which can be factored into (a+b)(a-b). In this case, a=10 and b=x.
(10+x)(10-x)
5) x^2+8x+16
This is a perfect square trinomial, which can be factored into (x+a)(x+a), where a is half of the coefficient of the x term, in this case 4.
(x+4)(x+4) or (x+4)^2
6) 3x^2-6x-72
First, factor out the common factor of 3.
3(x^2-2x-24)
Next factor the quadratic equation:
3(x-6)(x+4)