r + 7*r**2 - 17*r**2 + 20*r**3 - 5*r**2 - 40 + 5*r**4 = 0.
-4, -1, 2
Solve -52/5*k + 338/5 + 2/5*k**2 = 0 for k.
13
Let m be (-9)/(-21) - 30/(-126). Factor -m*o + 2/3 + 2/3*o**3 - 2/3*o**2.
2*(o - 1)**2*(o + 1)/3
Factor 128/7 + 2/7*k**3 + 24/7*k**2 + 96/7*k.
2*(k + 4)**3/7
Let l(d) be the second derivative of d**7/105 + d**6/15 + 4*d**5/25 + 2*d**4/15 + 8*d. Factor l(r).
2*r**2*(r + 1)*(r + 2)**2/5
Let h = 35 - 32. Let z(g) be the second derivative of 1/18*g**4 - 1/18*g**3 + 0 - h*g + 0*g**2. Find c, given that z(c) = 0.
0, 1/2
Let z(j) be the first derivative of 1 - 1/3*j**4 - 2*j**2 + 1/6*j**5 + 0*j + 4/15*j**3. Let s(f) be the second derivative of z(f). Let s(o) = 0. Calculate o.
2/5
Factor -64/15 - 32/3*j**2 - 16/3*j**3 - 2/15*j**5 - 4/3*j**4 - 32/3*j.
-2*(j + 2)**5/15
Let x be 36/20 + 5/25. Find k, given that 2*k - 1/2*k**2 - x = 0.
2
Let g = 174 - 170. Suppose 70*a**g - 152/5*a + 516/5*a**2 + 16/5 - 146*a**3 = 0. Calculate a.
2/7, 2/5, 1
Let w(o) be the second derivative of 1/12*o**4 + o - 1/20*o**5 + 0*o**3 + 0 + 0*o**2. Let w(r) = 0. What is r?
0, 1
Let q(t) be the first derivative of 0*t + 5 + 1/5*t**3 + 0*t**2 + 3/20*t**4. Factor q(x).
3*x**2*(x + 1)/5
Let q = -4 + -2. Let a(x) = -1 + 1 - x**2 - x. Let b(w) = -4*w**2 - 8*w - 4. Let y(t) = q*a(t) + b(t). Factor y(h).
2*(h - 2)*(h + 1)
Determine h, given that -10/9*h**2 + 0 + 10/9*h**4 - 2/9*h**3 + 2/9*h = 0.
-1, 0, 1/5, 1
Let y(c) be the second derivative of c**6/1440 - c**5/480 - 5*c**3/6 - 6*c. Let r(o) be the second derivative of y(o). Determine l so that r(l) = 0.
0, 1
Let k(a) be the third derivative of a**7/189 + 7*a**6/135 + 11*a**5/90 - a**4/6 - 20*a**2. Factor k(h).
2*h*(h + 3)**2*(5*h - 2)/9
Factor -3/5*f**2 + 6/5 - 3/5*f.
-3*(f - 1)*(f + 2)/5
Factor 0*n**2 - 2*n**3 + 0*n - 1/2*n**5 - 2*n**4 + 0.
-n**3*(n + 2)**2/2
Let o(a) be the first derivative of -a**5/60 - a**4/24 + a**2 + 3. Let g(k) be the second derivative of o(k). Suppose g(x) = 0. What is x?
-1, 0
Suppose -4/7*g**3 + 0*g + 0 - 2/7*g**2 - 2/7*g**4 = 0. What is g?
-1, 0
Determine q, given that -47*q**3 + 47*q**3 - 4*q**4 = 0.
0
Suppose 0 = -0*f - 4*f. Suppose f*y - 4*y = -8. Factor 0*q**3 + 6*q**3 + y*q**5 + 2*q**2 + 0*q**3 + 6*q**4.
2*q**2*(q + 1)**3
Let n(d) be the first derivative of 2*d**3/9 - 4*d**2/3 + 2*d + 8. Solve n(m) = 0.
1, 3
Let n = 53 - 53. Factor 2/3*v**2 - 1/3*v + n - 1/3*v**3.
-v*(v - 1)**2/3
Suppose 4*o = j + 19, -4*o = -4*j + 2*j - 18. Suppose -7 = -2*h - 0*p + 3*p, -o*p - 7 = -h. Suppose -32/7*s**h - 4/7 - 22/7*s - 2*s**3 = 0. What is s?
-1, -2/7
Suppose 8 - 23 = -5*n. Let x(b) be the third derivative of -1/90*b**5 + 1/9*b**n + 0*b + b**2 + 7/360*b**6 + 0 - 7/72*b**4. Factor x(v).
(v - 1)*(v + 1)*(7*v - 2)/3
What is a in -a + 1/3*a**2 + 2/3 = 0?
1, 2
Let u(i) = -i**3 + 6*i**2 - 6*i + 7. Let c be u(5). Suppose -c*y + 0 = -8. Factor -l**2 + y*l - 6*l + l.
-l*(l + 1)
Let o(r) be the third derivative of r**5/195 - r**4/156 - r**3/39 + 6*r**2. Factor o(m).
2*(m - 1)*(2*m + 1)/13
Let w(h) be the second derivative of 0 + 0*h**2 - 1/42*h**4 + 2*h - 2/21*h**3. Find o such that w(o) = 0.
-2, 0
Suppose o - 5 = -1. Factor -2*h + h - 6*h + o*h + 6 - 3*h**2.
-3*(h - 1)*(h + 2)
Let s(z) = 20*z**2 - 6. Let m = 20 + -34. Let c(i) = 7*i**2 - 2. Let w(d) = m*c(d) + 5*s(d). Factor w(x).
2*(x - 1)*(x + 1)
Solve 9*z**4 - 17*z**4 + 2*z**2 - 13*z**4 - z**3 = 0.
-1/3, 0, 2/7
Let d be 3/(-3)*(-1)/4. Let d*s**2 - s + 1 = 0. What is s?
2
Let z be (3/(-2))/(6/(-8)). What is p in 25*p**5 - 4*p**3 - p**3 - 80*p**z - 16*p - 91*p**3 + 20*p**4 = 0?
-2, -2/5, 0, 2
Let m(h) = -20*h**3 - 76*h**2 - 60*h - 4. Let g(k) = 4*k**3 + 15*k**2 + 12*k + 1. Let u(p) = 16*g(p) + 3*m(p). Factor u(n).
4*(n + 1)**3
Let p(h) = h**3 - h - 1. Let s(v) = -12*v**3 + 8*v**2 - 16*v - 16. Let z = 13 + -12. Let q(w) = z*s(w) - 16*p(w). Suppose q(d) = 0. What is d?
0, 2/7
Let g = 6 - 4. Let m = -77 + 387/5. What is c in 4/5 - m*c**3 + 6/5*c + 0*c**g = 0?
-1, 2
Let u(y) be the third derivative of -y**5/300 - y**4/15 - 8*y**3/15 - 20*y**2. Factor u(x).
-(x + 4)**2/5
Let q be ((-10)/12)/(10/(-8)). Factor q*g**2 - 2/3 + 2/3*g - 2/3*g**3.
-2*(g - 1)**2*(g + 1)/3
Let u(r) = r + 1. Let m be u(1). Factor 4/7*d**3 - 2/7 + 2/7*d**4 + 0*d**m - 4/7*d.
2*(d - 1)*(d + 1)**3/7
Let g = -274/7 - -286/7. Find r, given that -4/7*r**2 - 8/7*r + g = 0.
-3, 1
Let z(o) be the first derivative of o**9/3024 + o**8/840 - o**6/180 - o**5/120 + o**3/3 + 2. Let l(g) be the third derivative of z(g). Factor l(r).
r*(r - 1)*(r + 1)**3
Let k = 2 + 2. What is g in 10*g**5 + 26*g + 104*g**3 + 93*g**2 - 29*g**2 - 16*g**3 + k + 44*g**4 - 12*g**3 = 0?
-1, -2/5
Let f(i) = 2*i**2 - 65*i + 93. Let n be f(31). Find z, given that 2/5*z**2 + n + 2/5*z = 0.
-1, 0
Let w(j) be the first derivative of 0*j + 0*j**2 - 1/18*j**4 - 2 + 2/27*j**3 - 2/45*j**5 + 1/27*j**6. Find g such that w(g) = 0.
-1, 0, 1
Suppose 0 = -3*u + 19 - 1. Suppose 10 = 5*z - 2*c + u*c, -4*c - 8 = -4*z. Suppose -3*l**2 + 3*l**z + l**2 = 0. What is l?
0
Factor 24/7*v + 8/7 + 8/7*v**3 - 30/7*v**2.
2*(v - 2)**2*(4*v + 1)/7
Let q(f) be the first derivative of f**6/48 - f**4/16 + f**2/16 + 12. Solve q(u) = 0.
-1, 0, 1
Let u(x) = -5*x**3 + 5*x**2 + 21*x - 11. Let h(s) = -s**3 + s**2 + 4*s - 2. Let c(d) = -11*h(d) + 2*u(d). Factor c(g).
g*(g - 2)*(g + 1)
Let k(f) = -f**2 - 1. Let v(l) = 14*l - 2 - 15*l - 3*l**2 - 2*l**2. Let m(p) = -4*k(p) + v(p). Find b, given that m(b) = 0.
-2, 1
Suppose 12*g = 7*g + 10. Factor -a**2 - 2*a**2 - 9 + 2*a**2 - 2*a**g + 12*a.
-3*(a - 3)*(a - 1)
Let q = -11 - -19. Let s be ((-5)/10)/((-2)/q). What is y in 15*y**3 + 2 + 25/2*y**4 - 6*y - 11/2*y**s = 0?
-1, 2/5
Let k(w) = -3*w**3 - 3*w + 2*w + 2*w**3 + 2*w. Let a be k(1). Solve -1/4*p**3 + 0*p - 1/4*p**5 - 1/2*p**4 + 0 + a*p**2 = 0.
-1, 0
Let n(a) be the first derivative of 1/8*a**4 + 1/6*a**6 - 1/12*a**3 + 0*a - 2 + 0*a**2 + 7/20*a**5. Let n(m) = 0. Calculate m.
-1, 0, 1/4
Let w(c) = -c**3 - c**2 - c - 1. Let m(b) = -b**5 + 3*b**4 + 10*b**3 + 6*b**2 + b + 1. Let v(n) = 4*m(n) + 4*w(n). Suppose v(t) = 0. What is t?
-1, 0, 5
Let d(g) be the second derivative of -g + 0*g**2 + 1/84*g**7 + 3/20*g**5 + 1/12*g**3 - 1/15*g**6 - 1/6*g**4 + 0. Find u such that d(u) = 0.
0, 1
Let q be (-12)/9*(-3)/2. Let j(d) = -d**2 - 1. Let a(n) = 4*n**2 - 3*n + 3. Let p(v) = q*a(v) + 10*j(v). Factor p(r).
-2*(r + 1)*(r + 2)
Factor 39/4*u - 9/4 - 3*u**2.
-3*(u - 3)*(4*u - 1)/4
Factor -6 + 16*i + 3*i**2 + 6*i - 6 - 13*i.
3*(i - 1)*(i + 4)
Let t(q) = q**2 + 1. Suppose 0 = -4*m + 6 - 2. Let a(i) = -i**3 - 2*i**2 - 2*i + 1. Let o(x) = m*a(x) - t(x). Find b, given that o(b) = 0.
-2, -1, 0
Let s(k) = k**2 + 2*k + 1. Let b(o) = -4*o**2 + o + 5. Let w(j) = j**2 - 1. Let d(m) = -4*b(m) - 18*w(m). Let u(q) = 6*d(q) + 11*s(q). Solve u(f) = 0 for f.
-1
Let m(t) be the first derivative of t**5/210 + t**4/42 + t**3/21 - 3*t**2/2 - 1. Let v(w) be the second derivative of m(w). Factor v(k).
2*(k + 1)**2/7
Let i(x) be the first derivative of -5*x**6/7 + 38*x**5/35 - 8*x**3/21 + 32. Suppose i(f) = 0. What is f?
-2/5, 0, 2/3, 1
Let a(d) be the third derivative of -d**8/504 - d**7/315 + d**6/180 + d**5/90 - 13*d**2. Determine c, given that a(c) = 0.
-1, 0, 1
Let x(m) be the second derivative of -3*m**5/160 + m**4/16 - 3*m. Factor x(y).
-3*y**2*(y - 2)/8
Let u(r) be the first derivative of -2*r**3/3 + 3*r**2 - 4*r - 8. Factor u(b).
-2*(b - 2)*(b - 1)
Suppose 5*j + 21 = 12*j. Let p(v) be the first derivative of -1/4*v**3 - j + 0*v - 3/4*v**2. Solve p(u) = 0.
-2, 0
Let g(j) be the first derivative of 1/10*j**5 + 1/8*j**4 + 3/2*j**2 + 2 - j**3 + 0*j - 1/40*j**6. Let o(b) be the second derivative of g(b). Factor o(t).
-3*(t - 2)*(t - 1)*(t + 1)
Let q(r) be the second derivative of r**5/80 + r**4/8 - r**3/24 - 3*r**2/4 - 24*r. Determine p, given that q(p) = 0.
-6, -1, 1
Let u(g) be the second derivative of g**4/4 + g**3/2 - 3*g**2 + 15*g. Factor u(b).
3*(b - 1)*(b + 2)
Let v(h) be the first derivative of h**6/180 + h**5/90 + h**4/144 - h**2 - 3. Let g(n) be the second derivative of v(n). Find r such that g(r) = 0.
-1/2, 0
Let v(x) = 6*x**3 + 2*x**2 + 7*x. Let b(d) be the third derivative of d**6/120 + d**4/24 - 3*d**2. Let s(t) = -14*b(t) + 2*v(t). Factor s(a).
-2*a**2*(a - 2)
Let x(b) be the first derivativ