i).
-2*(i + 1)*(i + 10)/5
Let m = 59 - 41. Let y be (-2)/(-7) - (-830)/35. What is f in m*f**4 - 3 - 1 - y*f**2 + 14*f**5 + 4 - 80*f**3 = 0?
-3, -2/7, 0, 2
Let m(o) be the second derivative of -o**6/150 - o**5/20 + o**4/10 + 16*o**3/15 - 16*o**2/5 - 7*o - 104. Factor m(t).
-(t - 2)*(t - 1)*(t + 4)**2/5
Let i(r) = r**2 + 22*r. Let q(h) = 13*h**2 - 68*h + 612. Let m(f) = 22*i(f) - 2*q(f). Solve m(c) = 0 for c.
2, 153
Let l = 86565 + -86561. Find g such that 13/9*g**2 + 8/9*g - 4/3 - 1/9*g**l + 1/9*g**5 - g**3 = 0.
-3, -1, 1, 2
Let h(o) be the second derivative of -2/15*o**6 - 392*o**4 - 76832*o**2 + 0 + 56/5*o**5 - o + 21952/3*o**3. Let h(a) = 0. Calculate a.
14
Factor -100/3*w**2 + 248/3*w + 352/3 + 4/3*w**3.
4*(w - 22)*(w - 4)*(w + 1)/3
Let a(m) = -8*m**3 - 134*m**2 - 862*m + 3890. Let g(s) = 2*s**3 + s**2 - s - 1. Let b(i) = a(i) + 2*g(i). What is n in b(n) = 0?
-18, 3
Suppose 11*a + 47 = 13*a + 5*q, 2*a + 23 = 5*q. Let x(i) be the second derivative of -2/9*i**3 + 0 - 2/9*i**4 + 1/15*i**5 + a*i + 4/3*i**2. Factor x(z).
4*(z - 2)*(z - 1)*(z + 1)/3
Let p = -666912 - -7336034/11. Factor -p*m**2 + 0*m + 8/11.
-2*(m - 2)*(m + 2)/11
Let r be (-187)/22*52/(-442) - 1/2. Solve r + 1/6*z - 1/6*z**3 - 1/2*z**2 = 0.
-3, -1, 1
Factor 889/4*k - 1/4*k**3 + 949/4 - 61/4*k**2.
-(k - 13)*(k + 1)*(k + 73)/4
Let u = -1388 - -1388. Let s(q) be the third derivative of 1/10*q**5 + 1/6*q**4 - 19*q**2 + 1/9*q**3 + 0 + u*q. Find i such that s(i) = 0.
-1/3
Suppose 20 - 52 = 2*j - 2*m, m = 4*j + 67. Let u = j + 18. Suppose -60*t**2 + 124*t**3 + 10 + u - 10*t - 2*t - 60*t**4 - 3 = 0. Calculate t.
-1/3, 2/5, 1
Let f(t) be the third derivative of 1/90*t**5 + 16 + 2*t**2 + 1/3*t**4 + 0*t + 4*t**3. Let f(o) = 0. What is o?
-6
Let u(k) be the third derivative of -k**7/3360 + k**6/120 - k**5/10 - 5*k**4/8 + 37*k**2 - 1. Let n(c) be the second derivative of u(c). Factor n(w).
-3*(w - 4)**2/4
Let x = -19/296 - -1279/1480. Let w(u) be the first derivative of -3/10*u**2 - x*u**3 + 9/20*u**4 + 6/5*u - 7. Suppose w(y) = 0. What is y?
-2/3, 1
Let y(h) = h**3 - 44*h**2 + 185*h - 997. Let u be y(40). Factor 3/2 + 1/2*x**u - 5/2*x + 1/2*x**2.
(x - 1)**2*(x + 3)/2
Suppose 10*n - 7*n + d = 4, -n + 6 = -2*d. Factor 62 + 28*q + 0*q**2 + 2*q**n - 63*q - 29*q.
2*(q - 31)*(q - 1)
Let u = -44 + 53. Let f(c) = -c**2 + 10*c - 6. Let p be f(u). Suppose -4*o - 10*o**4 - 28*o**p + 34*o**4 - 12*o**4 + 20*o**2 = 0. Calculate o.
0, 1/3, 1
Let r(g) be the first derivative of 35*g**3 + 471*g**2 + 360*g + 5925. Factor r(x).
3*(5*x + 2)*(7*x + 60)
Let d be 218*2*(4 + -6 + 1). Let m = -3487/8 - d. Let m*n**3 + 0 + 3/8*n**2 + 1/4*n = 0. What is n?
-2, -1, 0
Let z(d) be the second derivative of -d**6/10 + 21*d**5/100 - d**4/10 + 207*d. Factor z(t).
-3*t**2*(t - 1)*(5*t - 2)/5
Let c be -2 + -2 - ((-4 - 1) + -5). Let r be ((-9)/10)/((-36)/60). Suppose 15/2*k - c*k**2 - 3 + r*k**3 = 0. What is k?
1, 2
Let y(n) be the second derivative of -3*n - 5/3*n**3 + 24 - 3/8*n**5 + 0*n**2 - 5/3*n**4. Determine m, given that y(m) = 0.
-2, -2/3, 0
Let o = 209 + -139. Suppose o*z = 61*z + 36. Factor -5/2*d**2 + 1/2*d + 5/2*d**z - 1/2*d**3 + 0.
d*(d - 1)*(d + 1)*(5*d - 1)/2
Suppose 33*b - 34*b + 9 = 0. Let q = b - -17. Factor -6*w**4 + 0*w**5 - 24*w**2 + 2*w**5 + 8*w - 6*w**4 + q*w**3.
2*w*(w - 2)**2*(w - 1)**2
Let d = -122 - -129. Factor -82*g - 35*g - 84*g + 32 - d*g + 338*g**2.
2*(13*g - 4)**2
Let y be 54 + -2 - 37 - (275/20 + -2). Find z, given that 1/4*z + 13/4 - y*z**2 - 1/4*z**3 = 0.
-13, -1, 1
Suppose -2*o - 257 + 267 = 4*t, -2*o + 3*t + 3 = 0. Let y(s) be the second derivative of 0 + s**4 + 0*s**2 + 25*s - 2/3*s**o. Find c, given that y(c) = 0.
0, 1/3
Let a = -990176 + 990176. Let 0 + 12/5*d**3 - 8/5*d**4 + a*d**2 + 1/5*d**5 + 0*d = 0. Calculate d.
0, 2, 6
Let t(n) = 4*n**4 + 1155*n**3 + 86433*n**2 + 168265*n + 13. Let p(u) = -2*u**4 - 578*u**3 - 43216*u**2 - 84130*u - 6. Let y(j) = -13*p(j) - 6*t(j). Factor y(a).
2*a*(a + 2)*(a + 145)**2
Factor 2242 + o**3 - 210*o**2 - 3*o**3 - 412*o - 4491 + 2249.
-2*o*(o + 2)*(o + 103)
Let m(z) = -z + 35. Let x be m(30). Let -48 + 98*h - 48*h - 32 - x*h**2 = 0. What is h?
2, 8
Let s(v) be the third derivative of 0 - 3/4*v**3 + 0*v + 29/32*v**4 - 9/80*v**5 + 120*v**2. Factor s(a).
-3*(a - 3)*(9*a - 2)/4
Let p be ((-14256)/990)/(4/(16/(-12))). Factor -p*q**2 + 39/5*q + 3/5*q**3 - 18/5.
3*(q - 6)*(q - 1)**2/5
Let j(u) be the first derivative of -180 - 3/10*u**2 - 6/5*u + 3/20*u**4 + 2/5*u**3. Factor j(b).
3*(b - 1)*(b + 1)*(b + 2)/5
Let w = -168774 + 168776. Factor 42/13*s + 0 + 2/13*s**w.
2*s*(s + 21)/13
Solve -1/5*m - m**3 + 6/5*m**5 + 0 - 5/2*m**2 + 5/2*m**4 = 0 for m.
-2, -1, -1/12, 0, 1
Suppose 4445 = 1068*l - 895. Let -1/3*j**l + 2/3*j**3 + 0 + 0*j + 0*j**2 + 1/3*j**4 = 0. Calculate j.
-1, 0, 2
Let q(i) be the first derivative of -6 + 0*i + 2/33*i**3 + 2/11*i**2 - 2/55*i**5 - 1/11*i**4. Let q(v) = 0. What is v?
-2, -1, 0, 1
Let t(h) = -h**2 - h. Let m(n) = -8*n**2 - 144*n + 1484. Let r(w) = -m(w) + 10*t(w). What is b in r(b) = 0?
14, 53
Let j(k) be the first derivative of 28/5*k - 3/10*k**4 - 33/5*k**2 - 18 - 2/25*k**5 + 46/15*k**3. What is z in j(z) = 0?
-7, 1, 2
Let n be (-3 - 1) + -1*(75 + 1). Let i = -75 - n. Determine c, given that 0*c**4 + 4 + c**5 + 2*c**2 - 6*c**4 + 7*c + 8*c**3 - i*c - 11*c = 0.
-1, 1, 4
Let n(m) be the third derivative of 1/160*m**6 + 0*m - 21 + 1/40*m**5 + 0*m**3 + 1/32*m**4 + 5*m**2. Factor n(g).
3*g*(g + 1)**2/4
Let l(t) be the first derivative of -t**4/4 - t**3/3 + 3*t**2/2 - t + 45. Let r(y) = -9*y**3 - 13*y**2 + 41*y + 21. Let h(p) = -3*l(p) + r(p). Factor h(f).
-2*(f - 2)*(f + 3)*(3*f + 2)
Let x = 14/128715 + 128687/257430. Find l such that 0*l - 1/2*l**4 + x*l**2 + 0 + 1/2*l**3 - 1/2*l**5 = 0.
-1, 0, 1
Let h(t) be the first derivative of -9*t**3 - 3*t**2/2 + 24*t - 1326. Factor h(s).
-3*(s + 1)*(9*s - 8)
Suppose 5*j - 10 = -4*k, 3*j = 5*j + 5*k - 4. Factor -33*r**2 + 323*r + r**3 + 36*r**j - 323 - 38*r**2 + 34.
(r - 17)**2*(r - 1)
Let x be 4/(-10) + (11016/15)/6. Let h = 125 - x. Find o such that -4*o**4 + 1266 - 16*o + 12*o**h - 1266 = 0.
-1, 0, 2
Let z be 66/44*8*(-5)/(-24). Solve -11/4 + 3*r**2 - z*r - 1/4*r**4 + 5/2*r**3 = 0.
-1, 1, 11
Let r(t) be the second derivative of t**5/20 - 59*t**4/6 - 119*t**3/6 - 81*t + 47. Factor r(c).
c*(c - 119)*(c + 1)
Let a(s) = -6724*s**3 - s**2 + 3*s + 2. Let z be a(-1). What is y in -15*y**3 + 1234 + 1176*y + 8*y**3 - z + 9*y**3 - 84*y**2 = 0?
14
Let -14/17*h + 2/17*h**2 + 0 = 0. What is h?
0, 7
Let t(s) be the second derivative of s**7/420 - 19*s**6/180 + 3*s**5/10 + 131*s**3/6 + 2*s + 5. Let v(g) be the second derivative of t(g). Factor v(r).
2*r*(r - 18)*(r - 1)
Factor -285/4*r + 1/4*r**2 + 0.
r*(r - 285)/4
Let p(o) be the second derivative of -o**6/45 + 28*o**5/5 - 765*o**4/2 - 14450*o**3/9 - 5240*o + 2. Factor p(a).
-2*a*(a - 85)**2*(a + 2)/3
Let o(y) be the second derivative of -y**4/126 + 16*y**3/63 - 13*y**2/7 - 1476*y. Factor o(s).
-2*(s - 13)*(s - 3)/21
Let o(f) = -8*f**2 + 9*f + 560. Let m(x) = -26*x**2 + 26*x + 1702. Let y(s) = -3*m(s) + 10*o(s). Determine q, given that y(q) = 0.
-13, 19
Factor 2/7*o**3 + 0 - 38/7*o - 36/7*o**2.
2*o*(o - 19)*(o + 1)/7
Let u(j) be the third derivative of 1/20*j**5 - 4*j + 0 + 28*j**2 + 0*j**3 + 9/8*j**4. Factor u(w).
3*w*(w + 9)
Let x(n) be the second derivative of -2 - 2331/5*n**5 + 0*n**2 + 7938/5*n**6 + 3*n + 4410*n**7 + 121/3*n**4 - 4/3*n**3. Factor x(h).
4*h*(5*h + 2)*(21*h - 1)**3
Let u = 183914771/74076359 + 15/93649. Let q = 10/113 + u. Determine h, given that -34/7*h + 4/7*h**2 - q = 0.
-1/2, 9
Let i(z) be the second derivative of 0*z**3 + 0 + 0*z**2 + 32/63*z**7 + 0*z**4 - 4/45*z**6 - 1/10*z**5 + 46*z. Factor i(q).
2*q**3*(4*q + 1)*(8*q - 3)/3
Let k = -375114 + 375146. Find x such that k*x + 8*x**2 + 128/3 + 2/3*x**3 = 0.
-4
Let q(t) be the third derivative of -125*t**8/448 + 265*t**7/56 + 317*t**6/32 - 24489*t**5/80 - 4131*t**4/2 - 5832*t**3 + 543*t**2. Factor q(j).
-3*(j - 8)**2*(5*j + 9)**3/4
Factor 769/2*x**2 + 0 - 1/4*x**3 - 591361/4*x.
-x*(x - 769)**2/4
Let f(d) be the first derivative of -15/14*d**2 - 2/7*d**3 + 3/28*d**4 + 18/7*d - 23. Factor f(j).
3*(j - 3)*(j - 1)*(j + 2)/7
Let o(m) = 10*m - 42. Let w be o(8). Let n(a) be the first deriv