en that -1/2 + 3/4*g**2 - 1/4*g**4 + 1/4*g**3 - v*g = 0.
-1, 1, 2
Let v(g) = -g**3 + g**2 + 35. Let z = -12 + 12. Let x be v(z). Factor 205*n + 132*n**3 + 288*n**2 - n**4 + x*n + 48 + 22*n**4.
3*(n + 2)**3*(7*n + 2)
Let j = 66 - 62. Find h such that -j*h**2 - 77*h**4 - 4*h**3 - 2*h**5 + 65*h**4 - 8*h**3 - 2*h**5 = 0.
-1, 0
Let t(q) be the third derivative of 0 + 5/192*q**4 - 1/120*q**5 - 1/960*q**6 - 17*q**2 + 0*q**3 + 0*q. Let t(i) = 0. Calculate i.
-5, 0, 1
Let w(q) = -4*q**2 + 4*q + 3. Let p be w(-3). Let l = 73 + p. Factor 2*c**4 - c + l*c**2 + 6*c**3 + 5*c - 2*c - 22*c**2.
2*c*(c + 1)**3
Let t = -579/1606 - 50/73. Let u = -6/11 - t. Factor x**4 + 0 - 1/2*x**3 + 0*x - u*x**5 + 0*x**2.
-x**3*(x - 1)**2/2
Let -3/2*l**4 - 63/2*l**3 + 3/2*l**2 + 3/2*l**5 + 0 + 30*l = 0. What is l?
-4, -1, 0, 1, 5
Let v(g) be the first derivative of g**7/1680 + g**6/720 - g**5/120 - 7*g**3/3 + 9. Let k(u) be the third derivative of v(u). Suppose k(o) = 0. Calculate o.
-2, 0, 1
Let d(w) be the first derivative of -1/15*w**5 - 1/3*w + 0*w**4 + 10 + 2/9*w**3 + 0*w**2. Factor d(c).
-(c - 1)**2*(c + 1)**2/3
Suppose 0 = 2*x - 10 - 0. Suppose -4*v = -0 - 8. Let w(m) = m**3 - m**2 - m + 11. Let q(c) = -c**3 + c**2 + c - 5. Let h(z) = v*w(z) + x*q(z). Factor h(r).
-3*(r - 1)**2*(r + 1)
Let h(s) be the third derivative of 2*s**7/35 + s**6/30 - 14*s**5/15 - 2*s**4/3 + 16*s**3/3 - s**2 + 23. Solve h(a) = 0.
-2, -1, 2/3, 2
Factor 4*c**4 - 173*c**2 + 24*c**3 + 374*c**2 - 20 + c - 25*c - 185*c**2.
4*(c - 1)*(c + 1)**2*(c + 5)
Let z(j) be the second derivative of 8*j - 1/20*j**5 + 3*j**2 - 1/6*j**4 + 5/6*j**3 + 0. Suppose z(k) = 0. Calculate k.
-3, -1, 2
Let z be 380/(-57)*(-6)/4. Solve 22*r**2 - 11*r**2 - z*r**2 = 0.
0
Let o(h) be the second derivative of h**7/252 + h**6/180 - h**5/10 + h**4/18 + 4*h**3/9 - 68*h. Find y, given that o(y) = 0.
-4, -1, 0, 2
Let w(c) = -2*c**4 + 4*c**3 + c. Let v(l) = 24*l**4 - 255*l**3 + 144*l**2 - 18*l. Let q(z) = v(z) + 18*w(z). Find i, given that q(i) = 0.
-16, 0, 3/4
Let p(w) = 2*w - 25. Let s be p(14). Suppose -s*o - 9*o + 24*o**2 - 19*o**2 + 4 = 0. What is o?
2/5, 2
Let g = 3/67 + 451/402. Let o(w) be the first derivative of -22/9*w**3 + 4/3*w + g*w**4 + 6/5*w**5 - 7/3*w**2 + 3. Determine h, given that o(h) = 0.
-1, 2/9, 1
Let a be 2/(-4)*(3*348/180 - 7). Suppose a*k**2 - 12/5*k + 9/5 = 0. What is k?
1, 3
Suppose 0*c = c - 5. Suppose -6*s + 27 - 3 = 0. Find k, given that 3*k**c + 5*k**2 - k**3 - 2*k**3 - 8*k**2 + 5*k**s - 2*k**4 = 0.
-1, 0, 1
Let z(f) be the first derivative of 4*f**3/3 - 10*f**2 + 16*f + 87. Factor z(t).
4*(t - 4)*(t - 1)
Suppose -3*s = 5*h - 11, 3*s - 24*h - 3 = -21*h. Let -3*y**3 + 0*y**s + 0*y + 3/2*y**4 + 0 = 0. What is y?
0, 2
Let u(j) be the second derivative of -j**7/21 - 2*j**6/15 + j**5/5 + 2*j**4/3 - j**3/3 - 2*j**2 + 112*j. Solve u(o) = 0 for o.
-2, -1, 1
Let h(z) be the first derivative of 0*z + 5*z**2 + 10 - 5/3*z**3 - 5/4*z**4. Determine c so that h(c) = 0.
-2, 0, 1
Suppose 4*v + 23 = 2*v + 5*y, v + 4*y = 21. Let m(a) = -a**2 + a + 1. Let d(b) = -20*b**2 - 5*b + 15. Let u(c) = v*d(c) - 15*m(c). Find n such that u(n) = 0.
-4, 0
Let v be (-6)/(-27) - (-3)/(81/75). Let k be (1 - 48/15) + 3. Determine g so that -5*g**4 + 0*g + 0 - k*g**2 + 4*g**v = 0.
0, 2/5
Let i(c) be the third derivative of 1/30*c**5 + 0 + 5*c**2 + 0*c + 1/27*c**3 + 1/18*c**4. Factor i(s).
2*(3*s + 1)**2/9
Let r(h) = -h**2 + 30*h + 64. Let q be r(32). Suppose 11/4*c**2 + q - 1/2*c + 7/4*c**4 - 4*c**3 = 0. What is c?
0, 2/7, 1
Let c(y) be the second derivative of 7/4*y**4 - 2*y**3 + 3/2*y**5 - 8*y + 3/10*y**6 - 6*y**2 + 0. Let c(w) = 0. What is w?
-2, -1, 2/3
Suppose 4970*t = 4956*t + 28. Factor 2*k**t + 10/11*k + 14/11*k**3 + 2/11*k**4 + 0.
2*k*(k + 1)**2*(k + 5)/11
Let g be 2/(-3) - 414/(-324). Let n = g - 1/9. Factor -1/4*p**2 + n*p - 1/4.
-(p - 1)**2/4
Let z be 4/(-16) - 105/(-100). Let v(j) be the first derivative of 8/15*j**3 + z*j**4 - 5 + 0*j + 0*j**2 + 1/15*j**6 + 2/5*j**5. Factor v(g).
2*g**2*(g + 1)*(g + 2)**2/5
Let f(m) be the first derivative of -75*m**4/4 - 51*m**3 - 81*m**2/2 - 3*m + 15. Suppose f(o) = 0. What is o?
-1, -1/25
Let s(h) = h**2 - 9*h + 12. Let n be s(8). Suppose -v + 2 = -n. Factor 2*d - 2*d**3 + 10*d**2 + v*d**4 + 0*d**2 - 11*d**2 - 5*d**2.
2*d*(d - 1)*(d + 1)*(3*d - 1)
Let l(x) = 5*x**2 + 100*x - 2212. Let a(h) = -7*h**2 - 102*h + 2213. Let m(n) = 3*a(n) + 4*l(n). Factor m(q).
-(q - 47)**2
Let h(m) be the first derivative of 5*m**6/6 - 5*m**5 - 15*m**4/4 + 65*m**3/3 + 25*m**2 + 242. Factor h(j).
5*j*(j - 5)*(j - 2)*(j + 1)**2
Let r = 86/7 - 151/14. Factor -1/2*s**5 + 3/2*s - s**3 + 1/2 - r*s**4 + s**2.
-(s - 1)*(s + 1)**4/2
Let b(p) be the third derivative of p**7/2520 - p**6/720 - 7*p**4/24 + 10*p**2. Let s(d) be the second derivative of b(d). Factor s(o).
o*(o - 1)
Let j(t) be the third derivative of -t**8/448 - t**7/140 + 3*t**6/32 + t**5/2 - t**4/8 - 6*t**3 + 10*t**2 - 1. Find z, given that j(z) = 0.
-3, -2, 1, 4
Suppose 2*n + w + 4*w = 24, -5*n + 14 = w. Let t be 2/(-6) + 30/9. Find l such that 2*l**2 + 2*l**t + 3*l - 2 + 3*l - 8*l**n = 0.
1
Let f be (0/(-1))/((-4)/24*-6). Suppose q - 5 + 3 = f. Factor -4/9*h + 0 - 2/9*h**q.
-2*h*(h + 2)/9
Let s(d) be the second derivative of d**6/24 - 5*d**5/16 - 15*d**4/16 + 135*d**3/8 - 135*d**2/2 - 973*d. Let s(o) = 0. Calculate o.
-4, 3
Let y(l) be the first derivative of -3*l**5/5 + 15*l**4/2 - 17*l**3 + 12*l**2 + 97. Determine h so that y(h) = 0.
0, 1, 8
Let t(p) = 17*p + 88. Let u be t(-5). Let c(m) be the second derivative of -1/24*m**u + 0 + 1/48*m**4 + 0*m**2 - 4*m. Factor c(b).
b*(b - 1)/4
Factor 4232/3 + 1/6*m**2 - 92/3*m.
(m - 92)**2/6
Determine q so that 2/21*q**3 + 56*q + 784/3 + 4*q**2 = 0.
-14
Suppose 4*d - a + 1 = 26, 4*a = 5*d - 45. Let i be (4 + 0)/(-4 + 1 + d). What is w in -18/17*w**5 + 108/17*w**i - 24/17*w**4 + 16/17 + 46/17*w**3 + 72/17*w = 0?
-1, -2/3, 2
Let b(z) be the second derivative of z**7/70 - 4*z**6/75 + z**5/25 + 39*z. Determine i, given that b(i) = 0.
0, 2/3, 2
Let n be (((-27)/(-14))/3)/((-3)/(-18)) - 3. Factor -6/7*z**2 + 3/7*z + n - 3/7*z**3.
-3*(z - 1)*(z + 1)*(z + 2)/7
Let q(w) = 21*w**2 + 60*w - 6. Let z(x) = -3*x**2 - x + 1. Let u(d) = -q(d) - 6*z(d). Factor u(p).
-3*p*(p + 18)
Let n(x) = 11*x**2 + 25*x - 4. Let j(k) = -26*k**2 - 50*k + 9. Let f(h) = -4*j(h) - 9*n(h). Solve f(w) = 0.
0, 5
Suppose -t + 2 = -1. What is w in 4*w - 22*w**3 + 10*w**3 + 4*w**t + 4*w**5 = 0?
-1, 0, 1
Let h(n) be the second derivative of n**6/60 + n**5/20 - n**3/6 - n**2/4 - 5*n - 12. Suppose h(s) = 0. What is s?
-1, 1
Let c(f) be the first derivative of 12*f**5/5 - 2*f**4 - 12*f**3 + 16*f - 9. Determine j so that c(j) = 0.
-1, 2/3, 2
Let u be (25 - 23) + 0/(-2 - -1). Suppose 0 = u*o - 7*o. Factor o*p**2 - 2/5*p**3 - 1/5 + 2/5*p + 1/5*p**4.
(p - 1)**3*(p + 1)/5
Suppose 3*f + 14 = -5*k, 2*f - 7*f + 4*k + 26 = 0. Factor 53*h**3 - 4*h - 2*h**f + h**4 - 49*h**3 + h**4.
2*h*(h - 1)*(h + 1)*(h + 2)
Let b(p) = -p**3 - 7*p**2 - 7*p + 4. Let r be b(-6). Factor -1 - r*o**3 + 8*o**3 + 1.
-2*o**3
Let a be (-4)/(-1*6/9). Factor -2*b + 41 - 4*b**2 + a*b - 17.
-4*(b - 3)*(b + 2)
Let j(k) = -3*k**3 - 3*k**2 - 10*k - 11. Let q be j(-6). Factor -35*v - 589 - 5*v**2 + q.
-5*v*(v + 7)
Let -4 - 4*g**4 - 3*g + 23*g**3 + 12*g**2 - 7*g - 10*g**5 + 7*g**3 - 10*g**3 - 4*g**2 = 0. What is g?
-1, -2/5, 1
Let w be (4*2)/((6 - 4) + 0). Let i be (-80)/(-84) - w/14. Factor 0 - i*s - 1/3*s**2.
-s*(s + 2)/3
Let j(s) be the first derivative of -s**8/4480 + s**6/320 - s**5/160 - 3*s**3 - 10. Let h(c) be the third derivative of j(c). Factor h(o).
-3*o*(o - 1)**2*(o + 2)/8
Let s(r) be the first derivative of -4*r**5/5 + 4*r**4 + 76*r**3/3 - 92*r**2 + 96*r - 12. Factor s(y).
-4*(y - 6)*(y - 1)**2*(y + 4)
Factor 136/3*i + 1/3*i**2 + 4624/3.
(i + 68)**2/3
Let x = 626/35 - 114/7. Find w, given that -8/5*w + 2/5*w**4 + 8/5*w**3 - x + 6/5*w**2 = 0.
-2, -1, 1
Let p be (0 - 2/(-6))/(2/(-182)). Let s = -619/21 - p. Determine d, given that s + 8/7*d + 2/7*d**2 = 0.
-3, -1
Let t(y) be the third derivative of 3*y**5/70 - 89*y**4/168 - 5*y**3/42 + 703*y**2. Determine l, given that t(l) = 0.
-1/18, 5
Let k(h) = -h**3 + 2*h + 2. Let g(c) = -26*c**3 + 756*c**2 - 7934*c + 27787. Let t(m) = g(m) - 2*k(m). 