Question

Factor the following completely, full solution each.

1. x² + 3x - 18
2. 3x² - 9x - 12
3. 18x² + 3x - 15
4. 5x² + 32x + 12
5. 3x³ + 24​

Answer 1

1. x² + 3x - 18

= x² + 6x-3x-18

= x(x+6)-3(x+6)

=(x+6)(x-3)

2. 3x² - 9x - 12

= (3x² - 9x - 12)/3

= x²- 3x- 4

= x²-4x+x-4

=x(x-4)+1(x-4)

=(x-4)(x+1)

3. 18x² + 3x - 15

= (18x² + 3x - 15)/3

= 6x²+x-5

= 6x²+6x-5x-5

=6x(x+1)-5(x+1)

=(x+1)(6x-5)

4. 5x² + 32x + 12

= 5x²+30x+2x+12

= 5x(x+6)+2(x+6)

5. 3x³ + 24

= 3(x³+8)

= 3(x³ + 2³)

= 3[ (x+2)(x²-2x+2²)]

=3 [(x+2)(x-2)²]

= [ (3)(x+2)(x-2)(x-2) ]

HOPE THIS WILL HELP YOU!

Answer 2

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1.) x²+3x-18

= x²+6x-3x-18

= x(x-6)-3(x-6)

= (x-6)(x-3)

2.) 3x²-9x-12

= 3x²-3x+12x-12

= 3x(x-1)+12(12-1)

= (x-1)(3x+12)

3.) 18x²+3x-15

= 18x²+18x-15x-15

= 18x(x+1)-15(x+1)

= (x+1)(18x-15)

4.) 5x²+32x+12

= 5x²+30x-2x+12

= 5x(x+6)+2(x+6)

= (x+6)(5x+2)

5.) 3x³ + 24

= 3 (x³+8)

= 3(x³+2³)

= Using identity :- a³-b³ = (a-b)(a²+b²-ab)

= (x-2)(x²+2²-2x)

= 3 (x-2) (x²-2x+4)

✒ Extra Information :-

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form is ax² + bx + c = 0 with a, b, and c being constants, or numerical coefficients, and x is an unknown variable.