r -1/4*c + i*c**3 + 1/2 - n*c**2 + 1/4*c**4.
(c - 1)**2*(c + 1)*(c + 2)/4
Let c(a) = -a**2 - 1. Let q(n) = n**2 + 20*n + 21. Let k(w) = w**3 - 11*w**2 - 1. Let f be k(11). Let x(d) = f*q(d) + 3*c(d). Factor x(y).
-4*(y + 2)*(y + 3)
Let s(j) = -j**3 + 13*j**2 - 9*j + 6. Let d be s(12). Suppose 9*g = -15 + d. Let 1/2 + 0*v**2 + v - v**g - 1/2*v**4 = 0. What is v?
-1, 1
Let g = -26 - -14. Let p = g - -14. Factor -v**p - 12*v**2 + 14*v**3 - 4*v + 3*v**2.
2*v*(v - 1)*(7*v + 2)
Let h(r) be the third derivative of r**7/350 - r**6/10 + 77*r**5/100 + 121*r**4/20 + 3*r**2 - 17. Find m such that h(m) = 0.
-2, 0, 11
Let n(g) = 8*g - 5 - 1 + 3 + 2*g**2 - 9*g. Let c(a) = a**2 - 2*a - 2. Let q(u) = 3*c(u) - 2*n(u). Solve q(v) = 0.
-4, 0
Let p be (8/10)/((-4)/70*-1). Let v be p/35*10/6. Factor v*k**3 + 1/3*k**2 + 0 + 1/3*k**4 + 0*k.
k**2*(k + 1)**2/3
Let b be ((-18)/10)/((-3)/5). Let d(y) be the first derivative of -2 + 0*y + 0*y**2 - 2/15*y**b - 1/5*y**4 - 2/25*y**5. Solve d(q) = 0.
-1, 0
Let n = -48 + 51. Find p, given that p**3 + 4*p**n + 5*p**3 - 6*p**3 - 4*p**2 = 0.
0, 1
Let y(b) = b**2 - b - 3. Let n be y(-3). Factor n*f**2 + 6*f**2 + 103*f + 15 - 53*f.
5*(f + 3)*(3*f + 1)
Suppose 0 = -4*h + 17*w - 16*w + 13, -h = -2*w - 5. Find r, given that -2/9*r**h + 0*r**2 + 0 + 0*r = 0.
0
Let d(r) = -5*r**2 + 24*r - 9. Let l(t) = -10*t**2 + 50*t - 15. Let x(j) = 5*d(j) - 2*l(j). Suppose x(h) = 0. Calculate h.
1, 3
Let n be -1 - (2 + -2 + -3). Suppose -c + n*c = 0. What is i in -4*i**2 + 0*i**4 - 2*i**3 + c*i**3 + i**4 + 5*i**4 = 0?
-2/3, 0, 1
Suppose 4 - 10 = z. Let u(i) = i + 8. Let w be u(z). Factor 3*j**3 + 15*j**2 - 3*j**5 - 15*j**w.
-3*j**3*(j - 1)*(j + 1)
Let q = 1049/5 + -207. Factor 2/5*i**3 + q*i + 6/5 + 2*i**2.
2*(i + 1)**2*(i + 3)/5
Let n(u) be the first derivative of -7*u**5/20 - 5*u**4/4 - 3*u**3/2 + 17*u**2 - 9. Let b(m) be the second derivative of n(m). Let b(z) = 0. What is z?
-1, -3/7
Let m(q) be the second derivative of q**6/1800 + q**5/100 + 3*q**4/40 + q**3/6 - 11*q**2/2 - 3*q + 3. Let h(a) be the second derivative of m(a). Solve h(w) = 0.
-3
Let t(u) be the second derivative of -u**4/84 + u**3/42 + 6*u**2/7 - 14*u. Find o, given that t(o) = 0.
-3, 4
Let h = -3 - 7. Let y(p) = -p**2 - 16*p. Let w(j) = 2*j**2 + 48*j. Let t(d) = h*y(d) - 3*w(d). Solve t(m) = 0.
-4, 0
Suppose -165 = -69*q - 27. Let m(d) be the third derivative of 0 - 12*d**q + 5/6*d**4 - 4/3*d**3 + 7/15*d**5 + 0*d. Factor m(w).
4*(w + 1)*(7*w - 2)
Let t(w) be the third derivative of -w**6/30 - 2*w**5/15 - w**4/6 + 20*w**2. What is z in t(z) = 0?
-1, 0
Suppose 148*i**2 + 394*i**3 - 2*i**5 + 20*i + 30*i**5 + 276*i**2 - 56 + 272*i**4 + 198*i**3 = 0. Calculate i.
-7, -1, 2/7
Let i(f) = f**3 + 64*f**2 + 120*f - 243. Let y be i(-62). What is g in -108*g**3 + 162/7*g**y + 0 - 162/7*g**4 - 144/7*g - 600/7*g**2 = 0?
-2/3, 0, 3
Suppose -3 + 17 = -7*a. Let s(j) = j**2 + 1. Let x(c) = 3*c**2 - 32*c - 123. Let y(i) = a*x(i) + 10*s(i). Factor y(u).
4*(u + 8)**2
Factor -4*y**2 - 20 - 40 + y + 15*y - 80*y.
-4*(y + 1)*(y + 15)
Let n(x) be the second derivative of x**6/165 - 16*x**5/55 + 64*x**4/11 - 2048*x**3/33 + 4096*x**2/11 - 19*x + 2. Factor n(b).
2*(b - 8)**4/11
Let l(b) = b**3 - 4*b**2 - 15*b + 20. Let u be l(6). Let q be (u - 4) + 60/27. Factor q*w**2 - 2/3*w**3 - 4/9 + 2/3*w + 2/9*w**4.
2*(w - 2)*(w - 1)**2*(w + 1)/9
Let t(l) = -l**2 + 5*l - 1. Let h(v) = 12*v**2 - 12*v - 6. Let d(y) = -h(y) - 2*t(y). Let d(x) = 0. What is x?
-4/5, 1
Let u(p) be the third derivative of p**5/300 - p**4/15 - 2*p**3/3 - 24*p**2 + 3*p. Factor u(q).
(q - 10)*(q + 2)/5
Factor -2/11*s**2 + 12/11*s - 16/11.
-2*(s - 4)*(s - 2)/11
Let f(h) be the third derivative of h**8/168 - h**7/7 - h**6/20 + 47*h**5/30 - 5*h**4/2 - 477*h**2. Determine n so that f(n) = 0.
-2, 0, 1, 15
Let h(f) = -60*f - 897. Let w be h(-15). Factor -2/11*q**4 + 0*q + 0 + 8/11*q**w - 6/11*q**2.
-2*q**2*(q - 3)*(q - 1)/11
Let v(x) = 19*x**3 - 15*x**2 + 4*x - 2. Let q(k) = -4*k**3 + k**2 - k + 1. Let b(c) = 2*q(c) + v(c). Factor b(a).
a*(a - 1)*(11*a - 2)
Let v(x) be the second derivative of x**5/110 + x**4/33 - 5*x**3/33 - 6*x**2/11 + 125*x. Suppose v(h) = 0. What is h?
-3, -1, 2
Factor -2/21*y - 4/21*y**2 + 0.
-2*y*(2*y + 1)/21
Factor -15*y - 3/7*y**2 + 108/7.
-3*(y - 1)*(y + 36)/7
Let v(q) = q**2 + 2. Let x be v(-1). Let r(g) be the first derivative of 0*g**2 + 0*g**4 + 1/15*g**6 + 0*g**x + 0*g - 2/25*g**5 + 5. Factor r(s).
2*s**4*(s - 1)/5
Let b be ((-2)/4)/(49/(-196)). Determine s so that -5/4*s**4 - 1/4*s**5 - s**b + 0*s - 2*s**3 + 0 = 0.
-2, -1, 0
Let s(r) be the second derivative of r**5/20 + r**4/4 - 13*r**3/6 - 15*r**2/2 - 2*r + 28. What is z in s(z) = 0?
-5, -1, 3
Let k(y) be the third derivative of -y**6/840 + 3*y**5/70 - 5*y**4/56 - 17*y**3/21 - 365*y**2. Solve k(t) = 0.
-1, 2, 17
Let b = -4600 + 4604. What is s in -1/4*s**5 - 1/4 - 1/2*s**3 - 1/2*s**2 + 3/4*s + 3/4*s**b = 0?
-1, 1
Let b(h) = -h**3 + 12*h**2 - 17*h - 16. Let j be b(10). Let k be (-1)/(j*(-2)/16). Factor -k*w**3 + 2/7 + 0*w**2 - 2/7*w**4 + 4/7*w.
-2*(w - 1)*(w + 1)**3/7
Let w be (-4)/26 + (1 - (-544)/(-182)). Let h = w - -89/35. Factor 4/5 + h*g**2 + 6/5*g.
2*(g + 1)*(g + 2)/5
Let x be 9 + -9 + 5 + -1. Let h(m) be the third derivative of 0 - 2*m**2 + 0*m - 3/8*m**x - 1/20*m**5 - m**3. Determine j so that h(j) = 0.
-2, -1
Let o(k) be the first derivative of -k**5/20 - 5*k**4/16 + 7*k**3/12 + 5*k**2/8 - 3*k/2 - 317. Factor o(w).
-(w - 1)**2*(w + 1)*(w + 6)/4
Solve -23/6*c**3 - 25/6*c - 47/6*c**2 - 1/6 = 0.
-1, -1/23
Suppose -10 = -2*l, 4*l - 31 = 4*g - 19. Determine d so that 6/19*d**g - 18/19*d**5 - 42/19*d**3 + 0 + 50/19*d**4 + 4/19*d = 0.
-2/9, 0, 1
Let a(m) be the first derivative of -4/27*m**3 + 27 - 4/9*m**2 + 1/9*m**4 + 0*m. Factor a(q).
4*q*(q - 2)*(q + 1)/9
Let i(t) be the third derivative of t**9/22680 - t**8/4480 + t**7/2520 - t**6/4320 - t**4/2 + 13*t**2. Let y(q) be the second derivative of i(q). Factor y(p).
p*(p - 1)**2*(4*p - 1)/6
Let a(m) be the first derivative of 4/3*m**5 + 7/27*m**6 + 5 + 16/9*m**3 + 43/18*m**4 + 0*m + 4/9*m**2. Determine d, given that a(d) = 0.
-2, -1, -2/7, 0
Let n(m) be the third derivative of -m**6/120 + m**5/6 + 11*m**4/24 + 2*m**3/3 - 25*m**2. Let l be n(11). Factor -2*v**3 + 0 - 5/2*v**2 - 1/2*v**l - v.
-v*(v + 1)**2*(v + 2)/2
Let w(p) = -p**3 + p**2 - 2*p. Let q(b) = -5*b**3 + 5*b**2 - 9*b. Let s(m) = 4*q(m) - 18*w(m). Factor s(x).
-2*x**2*(x - 1)
Let 185*t**3 + 208*t**2 + 8*t**4 + 41*t**4 - 40*t + 12*t**4 - 475*t**3 - 11*t**4 = 0. What is t?
0, 2/5, 5
Let a(t) be the first derivative of -3*t**5/25 - 51*t**4/20 - 56*t**3/5 - 78*t**2/5 + 190. Factor a(z).
-3*z*(z + 2)**2*(z + 13)/5
Factor 64*s**4 - 29*s**2 + 39*s**3 - 91*s**4 + 36*s**4 + 5*s.
s*(s + 5)*(3*s - 1)**2
Let v(k) = 8*k**3 - 9*k**2 - 15*k + 9. Let l(d) = -7*d**3 + 8*d**2 + 13*d - 8. Let w(a) = 7*l(a) + 6*v(a). Suppose w(h) = 0. Calculate h.
-1, 1, 2
Let l(u) = u**2 + 211*u + 210. Let g be l(-1). Let 0*i**3 + 4/3*i**2 - 4/3*i**4 + g - 2/3*i**5 + 2/3*i = 0. Calculate i.
-1, 0, 1
Factor 9*p**5 + 8*p**4 - 30 - 175*p**3 - 170 + p**5 - 396*p**2 + 7*p**4 - 660*p - 214*p**2.
5*(p - 5)*(p + 2)**3*(2*p + 1)
Let t(f) be the third derivative of 0 + 8*f**2 - 1/48*f**4 - 1/240*f**6 + 0*f + 0*f**3 + 1/60*f**5. Determine s so that t(s) = 0.
0, 1
Let s be (-6 - (-2 - 2))*-2. Let -s*p**3 + 16*p**3 + 14*p**4 - 8*p**3 = 0. What is p?
-2/7, 0
Let x be 46/10 + (-2 - (-77)/55). Let p(f) be the first derivative of 7 - 4*f**3 - 2*f**2 + 8*f + 4/5*f**5 + f**x. Solve p(j) = 0 for j.
-2, -1, 1
Let l(i) be the third derivative of -i**6/360 - i**5/180 + 5*i**4/72 - i**3/6 + 579*i**2. Solve l(x) = 0 for x.
-3, 1
Let o(q) be the first derivative of -4*q**3/3 - 2*q**2 + 120*q + 643. Factor o(j).
-4*(j - 5)*(j + 6)
Let s = 313 - 309. Suppose -4*h - 5*a = -16 - 7, 4*a - 4 = s*h. Factor -6/5*o - 3/5*o**h + 0.
-3*o*(o + 2)/5
Let x be (-66)/(-36) + 1/6. Factor 22*g - 51*g + 2*g**x + 32 + 13*g.
2*(g - 4)**2
Let s = 14/5 + -13/5. Let x(y) be the second derivative of -y**3 + 2*y + 1/5*y**6 - y**2 + 1/21*y**7 + s*y**5 - 1/3*y**4 + 0. Factor x(m).
2*(m - 1)*(m + 1)**4
Let b(l) be the first derivative of -7 + 4/7*l**3 - 6/7*l**2 - 3/28*l**4 + 0*l. Find y, given that b(y) = 0.
0, 2
Let a = -8/711 + -130342/71