- 17. Factor -5 - 2*d**2 - m + 0*d**2 - d**2 - 9*d.
-3*(d + 1)*(d + 2)
Let n(t) = -2*t**2 + 17*t - 13. Let z be n(8). Let q be (-40)/(-42)*(-6)/z. Factor 2/7*l**3 + q - 2/7*l**2 - 8/7*l.
2*(l - 2)*(l - 1)*(l + 2)/7
Let i = 42 + -42. Let b be -2 + -3 + 5 + i. Determine a so that 0 + 0*a**2 - 3/4*a**5 - 3/4*a + 3/2*a**3 + b*a**4 = 0.
-1, 0, 1
Factor -2/7*u + 2/7*u**2 - 24/7.
2*(u - 4)*(u + 3)/7
Factor 0 - 1452*i - 44*i**2 - 1/3*i**3.
-i*(i + 66)**2/3
Let v be (-95)/(-50) - 3/(-5). Let r be (-1)/10*(2 - (-22)/(-6)). Factor -v*o - r*o**3 + 7/6*o**2 + 3/2.
-(o - 3)**2*(o - 1)/6
Let g(q) be the third derivative of q**5/105 - 5*q**4/21 + 7*q**2 + 6. Suppose g(z) = 0. What is z?
0, 10
Let o be ((-192)/(-80))/((-2)/10). Let w be (26/o + 1)*16/(-56). Factor 0*p**2 + 0 + 0*p - 1/3*p**5 + w*p**3 + 0*p**4.
-p**3*(p - 1)*(p + 1)/3
Let h(q) be the third derivative of 9*q**8/112 - 267*q**7/35 + 10441*q**6/40 - 3243*q**5 - 5850*q**4 - 4000*q**3 - 5*q**2 + 4. Factor h(o).
3*(o - 20)**3*(3*o + 1)**2
Suppose 0 = 4*b - c - 14 + 2, 2*b - 4 = c. Suppose 20 = -b*q + 9*q. What is h in -h + 2 - h - h + q*h**3 + 4*h**2 - 4*h = 0?
-2, 1/2
Suppose 0 = -h + 6*h + 60. Let k be (16/h)/((-4)/22). Find g such that -10/3*g - 4/3 + k*g**2 + 28/3*g**3 = 0.
-1, -2/7, 1/2
Let w = 36 - 107/3. Suppose -2*z = -5*v - 9, -3*z - 9*v + 10*v + 7 = 0. Factor 4/3 + h - w*h**z.
-(h - 4)*(h + 1)/3
Let u(c) = -c**3 + 3*c**2 + 4*c + 5. Let m be u(4). Suppose -m = -k + 1. Factor -k*n**5 + 3*n**5 + 5*n**5 - 4*n**3 - 2*n**4.
2*n**3*(n - 2)*(n + 1)
Let w(c) be the second derivative of c**4/36 + 23*c**3/3 + 1587*c**2/2 + 6*c - 12. Find o, given that w(o) = 0.
-69
Let t be 14 + (6 - 20) + 3. What is k in -1/6 + 5/12*k + 1/3*k**2 - 1/4*k**t = 0?
-1, 1/3, 2
Suppose 2*v - 4*f = -2, 0 = -v + 5*f - 2 - 2. Let d(n) = -5*n**2 - 10*n - 12. Let t(h) = h**2 - h. Let x(a) = v*d(a) + 2*t(a). Find w, given that x(w) = 0.
-2
Factor -5*q**2 + 4*q**2 + 29 - 59*q + 3*q**2.
(q - 29)*(2*q - 1)
Let b(z) be the second derivative of 15*z + 0 + 5/6*z**3 + 25/12*z**4 + 0*z**2. Factor b(p).
5*p*(5*p + 1)
Let f = -1501 - -1505. Let m(j) be the third derivative of 1/196*j**8 - 2/735*j**7 + 0*j**f + 0*j**5 + 0*j**3 + 0*j - 12*j**2 - 1/105*j**6 + 0. Factor m(o).
4*o**3*(o - 1)*(3*o + 2)/7
Suppose 2 = 4*v - 3*v. Let y be (1/v)/((-5)/(-30)). Let 3*k**2 - 1 + 3*k**4 + 2*k**3 + 9*k**5 - y*k - 8*k**5 - 5*k**2 = 0. Calculate k.
-1, 1
Suppose -c - 67 = -4*x, 4*x - 52 = -3*c + 7*c. Let g be x/40 + 10 + 41/(-4). Find z, given that 0 + 3/5*z**3 - g*z**5 + 2/5*z**2 + 0*z**4 + 0*z = 0.
-1, 0, 2
Let n(p) be the second derivative of 8*p**3 + p**4 - 3*p + 32*p**2 + 1/20*p**5 + 0. Solve n(m) = 0.
-4
Let w = -744824/8211 + 10866/119. Let v = w - 2/69. Factor v*q - 2/7*q**4 + 0 - 10/7*q**2 + 8/7*q**3.
-2*q*(q - 2)*(q - 1)**2/7
Factor 0*z**3 + 23 - 2*z**3 + 8*z - z**2 - 15 - z**2.
-2*(z - 2)*(z + 1)*(z + 2)
Suppose 4*w - 24 = -8*w. Solve 86*a**2 - 9 - 10*a - 43*a**w - 44*a**2 = 0 for a.
-9, -1
Let n = -129014/45 - -2867. Let m(d) be the second derivative of 1/90*d**4 + 0*d**2 + 0 + n*d**3 + d. Solve m(b) = 0 for b.
-1, 0
Let m(b) be the first derivative of -b**5/60 + 2*b**3/3 - 9*b**2/2 + 21. Let j(k) be the second derivative of m(k). Factor j(q).
-(q - 2)*(q + 2)
Let k(z) be the first derivative of -z**6/10 + 3*z**5/5 - 27*z**4/20 + 7*z**3/5 - 3*z**2/5 - 49. Factor k(r).
-3*r*(r - 2)*(r - 1)**3/5
Let b be (222/8)/((-4)/16). Let v = -108 - b. Find j such that 0 - 1/2*j + 3/2*j**2 - 3/2*j**v + 1/2*j**4 = 0.
0, 1
Let o(z) be the third derivative of -z**8/784 + z**7/98 - 3*z**6/140 + 30*z**2. Solve o(j) = 0 for j.
0, 2, 3
Factor 1/2*a + 0 - 1/3*a**2 - 1/6*a**3.
-a*(a - 1)*(a + 3)/6
Let v be (-170)/(-55) - ((-18 - -1) + 20). Determine p so that 2/11 + v*p**2 - 3/11*p = 0.
1, 2
Let f(n) be the third derivative of 0 + 0*n - 1/660*n**6 + 1/330*n**5 + 1/132*n**4 - 1/33*n**3 + n**2. Factor f(c).
-2*(c - 1)**2*(c + 1)/11
Let v(g) be the first derivative of 4 + 2/3*g**3 + 0*g - 1/6*g**4 + 1/60*g**5 + 7/2*g**2. Let a(o) be the second derivative of v(o). Factor a(h).
(h - 2)**2
Solve -42*z - 16/5*z**2 + 2/5*z**3 + 0 = 0.
-7, 0, 15
Suppose -1/5*m**4 + 1/5*m**5 - 7/5*m**3 - 6/5*m + 0 + 13/5*m**2 = 0. What is m?
-3, 0, 1, 2
Let u(h) be the third derivative of h**5/24 + 225*h**4/8 + 30375*h**3/4 - 5*h**2. Factor u(t).
5*(t + 135)**2/2
Let n(q) = -14*q**3 - 274*q**2 - 66*q - 44. Let a(y) = -2*y**3 - 39*y**2 - 9*y - 6. Let z(i) = 44*a(i) - 6*n(i). Factor z(x).
-4*x**2*(x + 18)
Let o(k) be the second derivative of 3*k**5/4 - 115*k**4/12 + 100*k**3/3 + 40*k**2 - 22*k + 3. Factor o(a).
5*(a - 4)**2*(3*a + 1)
Let k(l) be the second derivative of 1/4*l**2 + 0 - 1/16*l**3 + 4*l - 1/96*l**4. Find y, given that k(y) = 0.
-4, 1
Factor 288*h**2 + 2/9*h**4 + 0 + 0*h + 16*h**3.
2*h**2*(h + 36)**2/9
Let b(r) be the second derivative of -1/2*r**3 - 1/42*r**7 - r - 1/6*r**4 + r**2 + 1/5*r**5 + 0*r**6 + 0. Factor b(m).
-(m - 1)**3*(m + 1)*(m + 2)
Let o(m) be the third derivative of -m**8/7560 - m**7/1260 - 5*m**3/3 + 18*m**2. Let g(y) be the first derivative of o(y). Let g(n) = 0. Calculate n.
-3, 0
Let d = 499/112 - -5/112. Solve -15/2*a**3 + 0 - d*a**2 + 3*a = 0 for a.
-1, 0, 2/5
Let q(p) be the second derivative of -5*p - 7/15*p**3 + 0*p**4 + 0 + 1/50*p**5 + 6/5*p**2. Suppose q(n) = 0. Calculate n.
-3, 1, 2
Let i(l) be the third derivative of l**6/6 - 39*l**5/4 - 455*l**4/24 + 25*l**3 - 431*l**2. Factor i(n).
5*(n - 30)*(n + 1)*(4*n - 1)
Suppose 7*h - 34 = 246. Let y be 195/h + 4/(-32) + -4. Suppose -y*t**2 - 3 + 3*t = 0. What is t?
2
Let t be (51/34)/((-105)/(-28)). Factor -2/5*d - t*d**2 + 4/5.
-2*(d - 1)*(d + 2)/5
Let t(p) be the second derivative of 8/3*p**3 + 1/12*p**4 + 28*p + 32*p**2 + 0. Let t(s) = 0. What is s?
-8
Let d(b) = -44*b**2 - 26*b + 57. Let k(i) = 10*i**2 + 6*i - 14. Let m(r) = -2*d(r) - 9*k(r). Suppose m(f) = 0. Calculate f.
-3, 2
Factor -618*g**3 + 4233*g**3 + 5500*g**4 + 3585*g**3 - 625*g**5 + 400*g + 2960*g**2.
-5*g*(g - 10)*(5*g + 2)**3
Suppose 12 = 5*n - 3. Let y(z) = -z + 12. Let k be y(10). Find p such that -n*p**4 - 2*p**2 + 0*p**k + 5*p**2 = 0.
-1, 0, 1
Let l(w) be the second derivative of -w**4/5 - 41*w**3/15 + 7*w**2/5 + 176*w. Factor l(q).
-2*(q + 7)*(6*q - 1)/5
Let s(d) be the first derivative of 20 + 27/5*d**5 + 0*d + 0*d**2 + 2*d**3 - 27/4*d**4. Factor s(g).
3*g**2*(3*g - 2)*(3*g - 1)
Let a(t) be the first derivative of -t**6/2 + 6*t**5/5 - 2*t**3 + 3*t**2/2 - 114. Factor a(c).
-3*c*(c - 1)**3*(c + 1)
Let q(r) = -9*r**5 + 19*r**3 + 6*r**2 + 4*r. Let g(t) = -10*t**5 + 20*t**3 + 5*t**2 + 5*t. Let m(j) = -4*g(j) + 5*q(j). Factor m(f).
-5*f**2*(f - 2)*(f + 1)**2
Suppose -8*k + 17 = -23. Let o(a) be the first derivative of -2/55*a**k - 2 - 4/11*a**2 - 4/11*a**3 - 2/11*a - 2/11*a**4. Factor o(r).
-2*(r + 1)**4/11
Suppose -2*b - 317 = 33. Let v = 177 + b. Factor 7/3*h**v - 16/3*h + 4/3.
(h - 2)*(7*h - 2)/3
Suppose -4*g - 55 = 5*b, -2*b - 16 = 4*g + 18. Let v(p) = -p**3 - 6*p**2 + 8*p + 12. Let n be v(b). Factor 0 - 1/4*q**n - q**4 - 1/2*q**2 - 5/4*q**3 + 0*q.
-q**2*(q + 1)**2*(q + 2)/4
Let i(z) = -16*z**3 + 146*z**2 - 623*z. Let o(v) = 5*v**3 - 49*v**2 + 208*v. Let f(a) = 2*i(a) + 7*o(a). Suppose f(n) = 0. Calculate n.
0, 7, 10
Let s(v) be the first derivative of -v**6/6 + v**5 - 5*v**4/3 + 24*v + 20. Let l(b) be the first derivative of s(b). Factor l(x).
-5*x**2*(x - 2)**2
Let p(o) = -21*o**4 + 0*o - o + 22*o**4 - o**2. Let m(z) = -8*z**4 + 18*z**3 + 18*z**2 - 14*z. Let t(y) = m(y) - 6*p(y). Suppose t(a) = 0. What is a?
-1, 0, 2/7, 2
Let z(c) = -2*c**3 - 139*c**2 + 73*c + 216. Let s be z(-70). Factor s*y**2 + 0 + 2*y + 2*y**4 - 15/2*y**3.
y*(y - 2)**2*(4*y + 1)/2
Suppose 3*x = 9 + 6. Let w(a) = a - 1. Let v be w(x). Factor f**2 + v*f + f - 7 + 9 + f**2.
(f + 2)*(2*f + 1)
Let k(j) be the second derivative of 0*j**3 + 0*j**4 - 11*j - 7/30*j**6 + 0 - 1/20*j**5 + 0*j**2. What is a in k(a) = 0?
-1/7, 0
Let g(w) be the third derivative of -w**7/42 + w**6/8 - w**5/12 - 5*w**4/8 + 5*w**3/3 + 13*w**2 - 4*w. Factor g(k).
-5*(k - 2)*(k - 1)**2*(k + 1)
Let j(o) be the third derivative of 1/24*o**4 + 0 - 1/120*o**5 + 0*o**3 + 0*o + 4*o**2. Determine k, given that j(k) = 0.
0, 2
Let s be (-2)/(-5) + 168/(-20). Let d = s + 10. Factor 3 + 6*k - 3*k**2 + 0*k**d +