Factor each trinomial completely.
Problem 1 :
x2 + 8x + 7
Problem 2 :
m2 - 11m + 10
Problem 3 :
y2 + y - 90
Problem 4 :
r2 + 4r - 12
Problem 5 :
p2 - 10p + 9
Problem 6 :
z2 + 16z + 64
Problem 7 :
x2 + 2x - 24
Problem 8 :
y2 - 4y - 12
Problem 9 :
a2 - 13a + 40
Problem 10 :
d2 + 11d + 18
Problem 11 :
2x2 + 6x - 108
Problem 12 :
3k2 + 6k - 9
Problem 13 :
5w2 - 30w + 40
Problem 14 :
3x2 - 2x - 5
Problem 15 :
2m2 + 3m - 9
Problem 16 :
9y2 + 66y + 21
1. Answer :
= x2 + 8x + 7
= x2 + 7x + 1x + 7
= x(x + 7) + 1(x + 7)
= (x + 7)(x + 1)
2. Answer :
= m2 - 11m + 10
= m2 - 10m - 1m + 10
= m(m - 10) - 1(m - 10)
= (m - 10)(m - 1)
3. Answer :
= y2 + y - 90
= y2 + 10y - 9y - 90
= y(y + 10) - 9(y + 10)
= (y + 10)(y - 9)
4. Answer :
= r2 + 4r - 12
= r2 + 6r - 2r - 12
= r(r + 6) - 2(r + 6)
= (r + 6)(r - 2)
5. Answer :
= p2 - 10p + 9
= p2 - 9p - 1p + 9
= p(p - 9) - 1(p - 9)
= (p - 9)(p - 1)
6. Answer :
= z2 + 16z + 64
= z2 + 8z + 8z + 64
= z(z + 8) + 8(z + 8)
= (z + 8)(z + 8)
7. Answer :
= x2 + 2x - 24
= x2 + 6x - 4x - 24
= x(x + 6) - 4(x + 6)
= (x + 6)(x - 4)
8. Answer :
= y2 - 4y - 12
= y2 - 6y + 2y - 12
= y(y - 6) + 2(y - 6)
= (y - 6)(y + 2)
9. Answer :
= a2 - 13a + 40
= a2 - 8a - 5a + 40
= a(a - 8) - 5(a - 8)
= (a - 8)(a - 5)
10. Answer :
= d2 + 11d + 18
= d2 + 9d + 2d + 18
= d(d + 9) + 2(d + 9)
= (d + 9)(d + 2)
11. Answer :
= 2x2 + 6x - 108
= 2(x2 + 3x - 54)
= 2(x2 + 9x - 6x - 54)
= 2[x(x + 9) - 6(x + 9)]
= 2(x + 9)(x - 6)
12. Answer :
= 3k2 + 6k - 9
= 3(k2 + 2k - 3)
= 3(k2 + 3k - 1k - 3)
= 3[k(k + 3) - 1(k + 3)]
= 3(k + 3)(k - 1)
13. Answer :
= 5w2 - 30w + 40
= 5(w2 - 6w + 8)
= 5(w2 - 4w - 2w + 8)
= 5[w(w - 4) - 2(w - 4)]
= 5(w - 4)(w - 2)
14. Answer :
= 3x2 - 2x - 5
= 3x2 - 5x + 3x - 5
= x(3x - 5) + 1(3x - 5)
= (3x - 5)(x + 1)
15. Answer :
= 2m2 + 3m - 9
= 2m2 + 6m - 3m - 9
= 2m(m - 3) - 3(m - 3)
= (m - 3)(2m - 3)
16. Answer :
= 9y2 + 66y + 21
= 3(3y2 + 22y + 7)
= 3(3y2 + 21y + 1y + 7)
= 3[(3(y + 7) + 1(y + 7)]
= 3(y + 7)(3y + 1)
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