check your understanding\nfactor each of the quadratics completely.\n1. $x^{2}+5x - 36$\n2. $7x^{2}+15x +…

check your understanding\nfactor each of the quadratics completely.\n1. $x^{2}+5x - 36$\n2. $7x^{2}+15x + 2$\n3. $-2x^{2}+4x + 70$\n4. $6x^{2}+11x - 10$

check your understanding\nfactor each of the quadratics completely.\n1. $x^{2}+5x - 36$\n2. $7x^{2}+15x + 2$\n3. $-2x^{2}+4x + 70$\n4. $6x^{2}+11x - 10$

Answer

Explanation:

Step1: For $x^{2}+5x - 36$

Find two numbers that multiply to - 36 and add up to 5. The numbers are 9 and - 4. So $x^{2}+5x - 36=(x + 9)(x - 4)$.

Step2: For $7x^{2}+15x + 2$

We need to find two numbers that multiply to $7\times2 = 14$ and add up to 15. The numbers are 14 and 1. Then $7x^{2}+15x + 2=7x^{2}+14x+x + 2=7x(x + 2)+1(x + 2)=(7x + 1)(x+2)$.

Step3: For $-2x^{2}+4x + 70$

First, factor out - 2: $-2x^{2}+4x + 70=-2(x^{2}-2x - 35)$. Then find two numbers that multiply to - 35 and add up to - 2. The numbers are - 7 and 5. So $-2(x^{2}-2x - 35)=-2(x - 7)(x+5)$.

Step4: For $6x^{2}+11x - 10$

We need to find two numbers that multiply to $6\times(-10)=-60$ and add up to 11. The numbers are 15 and - 4. Then $6x^{2}+11x - 10=6x^{2}+15x-4x - 10=3x(2x + 5)-2(2x + 5)=(3x - 2)(2x + 5)$.

Answer:

  1. $(x + 9)(x - 4)$
  2. $(7x + 1)(x + 2)$
  3. $-2(x - 7)(x + 5)$
  4. $(3x - 2)(2x + 5)$