 v**5 = 0. What is v?
-1, 0, 1
Let o(p) be the second derivative of p**6/540 - p**5/90 - 3*p**3/2 - 3*p. Let r(k) be the second derivative of o(k). Factor r(u).
2*u*(u - 2)/3
Let x be (-4)/6 + 88/24. Factor 2*m + 2 - m**2 + x*m**2 + 4*m**3 - 4*m**2 - 6*m**3.
-2*(m - 1)*(m + 1)**2
Let 12*t**4 + 4*t**3 - 3*t**5 - 2*t**5 + 0*t**3 - 12*t**2 + t**5 = 0. What is t?
-1, 0, 1, 3
Let c = 2/53 - -194/477. Let t(k) = -k**3 - 2*k**2 - 2*k - 2. Let d be t(-2). Determine w, given that -14/9*w**d + c*w + 0 = 0.
0, 2/7
Let o = -45 - -49. Let y(r) be the second derivative of 1/70*r**5 + 0*r**2 - 2*r - 1/147*r**7 + 1/42*r**o + 0*r**3 - 1/105*r**6 + 0. Factor y(a).
-2*a**2*(a - 1)*(a + 1)**2/7
Let g(t) be the second derivative of 0*t**2 - 1/2*t**4 - 3/20*t**5 - 2*t + 0 - 1/2*t**3. Factor g(b).
-3*b*(b + 1)**2
Let k(i) be the first derivative of -4/7*i - 1/7*i**2 - 5/14*i**4 - 3 + 16/21*i**3. Factor k(d).
-2*(d - 1)**2*(5*d + 2)/7
Let o(h) = -h**3 - 5*h**2 - 7*h - 6. Let c be o(-4). Factor -p**3 + 2*p**3 - c*p**2 + 4*p + 2*p**2.
p*(p - 2)**2
Suppose 2*q - 69 = -5*s, 87 = 5*s - 4*q - 0*q. Let j = s + -12. Factor 0 + 1/3*b - 1/3*b**2 - 1/3*b**j + 1/3*b**4.
b*(b - 1)**2*(b + 1)/3
Factor 34*r + 4*r**2 - 109*r - 9*r**2 + 20 - 15*r**2.
-5*(r + 4)*(4*r - 1)
Let s(q) be the first derivative of -7*q**6/6 - 37*q**5/5 - 73*q**4/4 - 67*q**3/3 - 14*q**2 - 4*q - 2. Solve s(m) = 0 for m.
-2, -1, -2/7
Find c such that 5/9*c**3 - 5/9*c - 1/9 - 1/3*c**2 + 4/9*c**4 = 0.
-1, -1/4, 1
Let a(o) = -o**2 - o. Let z(g) = 8*g**2 + 8*g. Let i(t) = 10*a(t) + z(t). Factor i(w).
-2*w*(w + 1)
Suppose 4*i - 4*o = -2*o + 62, -14 = -3*i - 5*o. Let l = i - 11. Solve 5/4*a**3 + 0*a + 1/4*a**l + a**4 + 0 = 0.
-1, -1/4, 0
Let p = 87/460 - -1/92. Factor 0*t + 0*t**2 - p*t**3 + 0.
-t**3/5
Let t(r) be the third derivative of -r**6/360 - r**5/36 - 7*r**4/72 - r**3/6 + 12*r**2. Factor t(z).
-(z + 1)**2*(z + 3)/3
Let y(k) be the second derivative of 1/18*k**4 + 1/6*k**2 - 1/6*k**3 + 0 + 2*k. Factor y(b).
(b - 1)*(2*b - 1)/3
Find f such that -f**2 + 0*f**3 - 1/2*f**5 + 1/2*f + 0 + f**4 = 0.
-1, 0, 1
Factor -1/2*t**3 + t - 1/2*t**2 + 0.
-t*(t - 1)*(t + 2)/2
Suppose -4 = -4*k - 2*d + 14, 4*k = -5*d + 15. Factor 6*v**2 - v**3 + 2 - k*v + v**2 - 3*v**2.
-(v - 2)*(v - 1)**2
Let j(v) = -v**2 + 6*v - 4. Let r be j(4). Suppose 0 = -r*b + 8. Factor -2*m + 2*m**b + 0*m**2 + 0*m**2.
2*m*(m - 1)
What is c in 6*c**4 - 440*c**2 + 10*c**3 - 40*c - c**4 + 420*c**2 = 0?
-2, 0, 2
Let a be (-4)/(-10) + (-12)/30. Let r(k) be the second derivative of k + 0 - 1/6*k**4 + a*k**3 + 0*k**2 + 1/10*k**5. Factor r(l).
2*l**2*(l - 1)
Let i(x) be the third derivative of -x**8/2352 - x**7/1470 + x**6/840 + x**5/420 - 16*x**2. Factor i(h).
-h**2*(h - 1)*(h + 1)**2/7
Let m(l) = -l + 8. Let o = -8 - -14. Let b be m(o). Factor 40/3*g - 50/3*g**b - 8/3.
-2*(5*g - 2)**2/3
Let m(n) be the third derivative of n**7/14 - 11*n**6/20 + 33*n**5/20 - 5*n**4/2 + 2*n**3 + 11*n**2. Determine o so that m(o) = 0.
2/5, 1, 2
Let p(n) be the second derivative of 0 + 1/9*n**3 + n + 1/30*n**5 + 0*n**2 + 1/9*n**4. Factor p(v).
2*v*(v + 1)**2/3
Let u(o) be the third derivative of -o**6/900 + o**4/60 - o**3/3 - 2*o**2. Let q(w) be the first derivative of u(w). Factor q(z).
-2*(z - 1)*(z + 1)/5
Let a be (-42)/(-20)*(-10)/(-12). Let x = -5/4 + a. Factor -1/2*s**2 - x - s.
-(s + 1)**2/2
Suppose 2*x + 2 = 3*x. Factor -1 - 3*u**2 + 2*u - 3*u**2 + 4*u**2 + u**x.
-(u - 1)**2
Solve 0*l**2 + 53*l - 3*l**2 - 52*l - l**4 + 3*l**3 = 0 for l.
0, 1
Let h = 45 - 43. Suppose 4*v - 3*q = 20, -5*v - q + 4 + 2 = 0. Find c such that 0*c**2 - v*c - c**2 - c + 4*c**h = 0.
0, 1
Let -23*c + 2*c**2 + 22*c - 1 + 2 - 2 = 0. What is c?
-1/2, 1
Let y(u) = u**5 - u**4 + u**3 + u**2 - u - 1. Let c(s) = -11*s**5 + 25*s**4 + 3*s**3 - 17*s**2. Let f(m) = -5*c(m) + 20*y(m). Suppose f(t) = 0. What is t?
-2/3, -2/5, 1
Factor -2*y**3 + y**2 + 4*y - 2*y + 3*y**3 - 2*y**3.
-y*(y - 2)*(y + 1)
Let m be 2/8*8/12. Let f(w) be the second derivative of m*w**4 - w**2 - 7/20*w**5 - w + 0 + 7/6*w**3. Factor f(y).
-(y - 1)*(y + 1)*(7*y - 2)
Let s(v) = -v**4 - v. Let u(f) be the third derivative of -f**7/70 - f**6/40 + f**5/60 - f**4/24 - f**3/3 - 3*f**2. Let r(m) = 4*s(m) - u(m). Factor r(n).
-(n - 2)*(n - 1)**2*(n + 1)
Let g(k) be the third derivative of -k**6/100 + k**5/25 + 3*k**4/20 + 42*k**2. Solve g(c) = 0.
-1, 0, 3
Suppose 0 + 1/4*h**2 + 0*h = 0. Calculate h.
0
Let y be 11/13 - 10/(-65). Let h be -1 - (-5)/y - 2. Factor -1/4*k**3 + 0 + 1/4*k**h + 0*k.
-k**2*(k - 1)/4
Factor -12*g**2 - 11*g - 56 + 0*g**2 + 103*g.
-4*(g - 7)*(3*g - 2)
Let s(t) be the second derivative of t**5/240 + t**4/24 + t**3/6 + t**2/2 - 3*t. Let h(p) be the first derivative of s(p). Factor h(z).
(z + 2)**2/4
Let i(z) be the first derivative of 0*z**3 - 1/30*z**4 + 1/5*z**2 - 1 - 2*z. Let q(g) be the first derivative of i(g). Determine r, given that q(r) = 0.
-1, 1
Find z, given that 36*z**2 - 1 - 4*z**2 - 14*z**2 + 3 - 20*z = 0.
1/9, 1
Let o = 3/4 - -7/12. Factor o*w**2 + 0 + 4/3*w**3 + 1/3*w**4 + 0*w.
w**2*(w + 2)**2/3
Let f(y) be the first derivative of y**6/8 - 10. Factor f(p).
3*p**5/4
Let m(k) be the first derivative of 490*k**5/9 - 280*k**4/3 + 1712*k**3/27 - 64*k**2/3 + 32*k/9 + 8. Factor m(u).
2*(5*u - 2)**2*(7*u - 2)**2/9
Let t(i) be the first derivative of -i**6/135 + i**5/90 - 2*i + 7. Let m(f) be the first derivative of t(f). Factor m(g).
-2*g**3*(g - 1)/9
Let f(p) be the third derivative of p**7/11340 + p**6/1080 + p**5/270 - p**4/12 - 2*p**2. Let n(t) be the second derivative of f(t). Factor n(j).
2*(j + 1)*(j + 2)/9
Let z(b) be the third derivative of b**7/2940 - b**6/1260 - b**5/420 + b**4/84 + b**3/2 + 3*b**2. Let s(g) be the first derivative of z(g). Factor s(t).
2*(t - 1)**2*(t + 1)/7
Let n(c) be the first derivative of 4 - 2/3*c + 7/6*c**2 + 5/12*c**4 - c**3 - 1/15*c**5. Find o such that n(o) = 0.
1, 2
Let l = -2147/780 - -36/13. Let n(u) be the third derivative of 0*u + 3*u**2 + l*u**4 + 1/30*u**3 + 0 + 1/300*u**5. Factor n(s).
(s + 1)**2/5
Let i(t) be the first derivative of 7 + 9*t + 1/3*t**3 + 3*t**2. Factor i(a).
(a + 3)**2
Let 4/15*t**5 - 6/5*t**4 + 28/15*t**2 - 16/15*t**3 - 2/3 + 4/5*t = 0. What is t?
-1, 1/2, 1, 5
Let s(y) = y + 1. Let v(r) = 6*r - 4 + 2*r**2 - 4*r**2 + 5 + 6. Let c(t) = 14*s(t) - 2*v(t). Factor c(f).
2*f*(2*f + 1)
Let t(i) be the first derivative of i**5/15 - i**4/12 - i**3/9 + i**2/6 + 5. Factor t(q).
q*(q - 1)**2*(q + 1)/3
Let d(l) be the first derivative of -7*l**5/20 + 19*l**4/12 - 4*l**3/3 - 2*l**2 - 2*l + 3. Let q(t) be the first derivative of d(t). Solve q(a) = 0.
-2/7, 1, 2
Suppose 5*g - 17 = -4*h, -4*h - 3*g + 12 = g. Let b be h/(-6) - (-4)/(-12). Determine i, given that -2*i**2 + 4*i**3 - 2*i**4 + b + 0 = 0.
0, 1
Solve -2/7*j - 2/7*j**2 + 4/7 = 0 for j.
-2, 1
Let 138*t**2 + 3 - 4*t**3 + 4*t**4 + 5 - 150*t**2 + 4*t = 0. Calculate t.
-1, 1, 2
Let q(s) be the first derivative of 4*s**3/3 + 2*s**2 - 8*s - 7. Factor q(t).
4*(t - 1)*(t + 2)
Let f(n) be the first derivative of -2/25*n**5 + 1 + 0*n - 2/5*n**2 + 2/5*n**3 + 0*n**4. Find x such that f(x) = 0.
-2, 0, 1
Let b(t) = -t**2 - 1. Let p(s) = 6*s**2 - 6*s - 2. Suppose 4*a + 7 = -3*w, -3*a + 2*a = 5*w + 6. Let l(u) = w*p(u) + 3*b(u). Suppose l(x) = 0. What is x?
1/3
Let r(t) = -6*t**3 - 7*t**2 - 13*t + 13. Let x(h) = h**3 + h**2 + 2*h - 2. Suppose 0*y = y - 6. Let i(v) = y*r(v) + 39*x(v). Find a such that i(a) = 0.
0, 1
Let x(w) = -6*w**4 - 2*w**3 + 14*w**2 + 2*w - 6. Let z(d) = 7*d**4 + d**3 - 15*d**2 - d + 5. Let g(l) = 3*x(l) + 2*z(l). Factor g(f).
-4*(f - 1)**2*(f + 1)*(f + 2)
Factor -2*l + 0 - 2/3*l**2.
-2*l*(l + 3)/3
Let u(d) be the second derivative of -5*d**7/63 + 14*d**6/15 - 21*d**5/5 + 82*d**4/9 - 31*d**3/3 + 6*d**2 + 20*d. Suppose u(a) = 0. Calculate a.
2/5, 1, 3
Let x = 72 - 68. Let v(j) be the third derivative of 0*j + 0*j**3 - 4*j**2 + 0*j**x - 1/150*j**6 + 0 - 1/525*j**7 - 1/150*j**5. Factor v(f).
-2*f**2*(f + 1)**2/5
Factor -11*l**2 - 2*l**4 + l**2 - 3*l**4 + 15*l**3 + 0*l**3.
-5*l**2*(l - 2)*(l - 1)
What is f in -4*f**2 + 22*f**4 + 11*f**4 - 35*f**3 - 85*f - 28*f**4 + 30 + 89*f**2 = 0?
1, 2, 3
Let v(s) be the second derivative of -s**7/840 - s**6/480 + s**5/240 + s**4/96 + s**2/2 - 3*s. Let b(f) be the first deriv