Question

solve the factorize question ​

Answer 1

Question number 1:-

${p}^{2} + 5p + 6$

$= {p}^{2} + 2p + 3p + 6$

$= p(p + 2) + 3(p + 2)$

$= (p + 3)(p + 2)$

Question number 2:-

${x}^{2} + 2x - 15$

$= {x}^{2} + 5x - 3x - 15$

$= x(x + 5) - 3(x + 5)$

$= (x - 3)(x + 5)$

Question number 3:-

${m}^{2} + 3m - 4$

$= {m}^{2} - m + 4m - 4$

$= m(m - 1) + 4(m - 1)$

$= (m + 4)(m - 1)$

Question number 4:-

${p}^{2} - 10p + 24$

$= {p}^{2} - 4p - 6p + 24$

$= p(p - 4) - 6(p - 4)$

$= (p - 4)(p - 6)$

Question number 5:-

${z}^{2} - z - 2$

$= {z}^{2} - 2z + z - 2$

$= z(z - 2) + 1(z - 2)$

$= (z + 1)(z - 2)$

Question number 6:-

${z}^{2} - 2z - 8$

$= {z}^{2} - 4z + 2z - 8$

$= z(z - 4) + 2(z - 4)$

$= (z + 2)(z - 4)$

Question number 7:-

${x}^{2} - 21x + 110$

$= {x}^{2} - 10x - 11x + 110$

$= x(x - 10) - 11(x - 10)$

$= (x - 10)(x - 11)$

Question number 8:-

${x}^{2} - 21x + 90$

$= {x}^{2} - 15x - 6x + 90$

$= x(x - 15) - 6(x - 15)$

$= (x - 6)(x - 15)$

Question number 9:-

${x}^{2} - 22x + 117$

$= {x}^{2} - 13x - 9x + 117$

$= x(x - 13) - 9(x - 13)$

$= (x - 9)(x - 13)$

Question number 10:-

${x}^{2} - 9x + 20$

$= {x}^{2} - 4x - 5x + 20$

$= x(x - 4) - 5(x - 5)$

$= (x - 4)(x - 5)$