Question

Choose all of the equations that are true x2 + 2x − 24 = (x + 6)(x − 4) x2 − 8x + 15 = (x + 5)(x + 3) 3x2 + 4x + 1 = (3x + 1)(x + 1) 5x2 − 2x − 3 = (5x + 3)(x − 1) 4x2 − 49 = (2x − 7)(2x + 7)

Answer 1

Equations 1, 3, and 5 are the right Options.

Explanation:

To find the equations which are true we will factorize all the equations.

1). x²+2x-24 = x²+6x-4x-24 = x(x+6)-4(x+6) = (x-4)(x+6)

2). x²-8x+15 = x²-3x-5x+15 = x(x-3)-5(x-3) = (x-5)(x-3)

3).3x²+4x+1 = 3x²+3x+x+1 = 3x(x+1)+1(x+1) = (x+1)(3x+1)

4).5x²-2x-3 = 5x²-5x+3x-3 = 5x(x-1)+1(x-3) = (x-3)(5x+1)

5). 4x²-49 = (2x+7)(2x-7)

Therefore options 1, option 3, option 5 are the correct options.

Answer 2

Choices 1,3,4 and 5 are true.

Explanation:

We have given equations. we have to factor them.

We use following formulas to solve this.

(a+b)(a-b) = a²-b²

We use method of factorization to find factors.

x²+2x-24 = x²+6x-4x-24 = x(x+6)-4(x+6)

x²+2x-24 = (x+6)(x-4)

x²-8x+15 = x²-5x-3x+15 = x(x-5)-3(x-5)

x²-8x+15 = (x-5)(x-3)

3x²+4x+1 = 3x²+3x+x+3 = 3x(x+1)+1(3x+1)

3x²+4x+1 = (3x+1)(x+1)

5x²-2x-3 = 5x²-5x+3x-3 = 5x(x-1)+3(x-1)

5x²-2x-3 = (5x+3)(x-1)

4x²-49 =(2x)²-(7)²

4x²-49 = (2x-7)(2x+7)