(g + 2)/5
Suppose -4*y = -0*o + 2*o - 12, -y = -4*o + 6. Determine z so that 0*z**y - 4/9*z**3 + 4/9*z - 2/9 + 2/9*z**4 = 0.
-1, 1
Let x be (-3 + -53 - 2)*1. Let q = -172/3 - x. Find l, given that -1/3 - 1/3*l**2 + q*l = 0.
1
Let s(j) be the second derivative of j**5/90 + j**4/18 - j**3/3 + 5*j**2/9 - 27*j. Factor s(g).
2*(g - 1)**2*(g + 5)/9
Suppose -2*l**5 + 0*l**2 - 6*l + 4*l**2 - 4*l**4 + 8*l = 0. What is l?
-1, 0, 1
Suppose 3*x - 18 = -12. Let 1/4*u**x + 1/2*u + 0 = 0. What is u?
-2, 0
Suppose -72*k = -44*k. Factor 0 + k*h**3 + 2/11*h**4 + 0*h - 2/11*h**2.
2*h**2*(h - 1)*(h + 1)/11
Let c(z) be the second derivative of 0*z**3 - 1/9*z**4 + 2/45*z**6 + 0 + 1/9*z**7 + 0*z**2 - 3*z - 7/30*z**5. Solve c(m) = 0.
-1, -2/7, 0, 1
Let h(y) = y**3 - 3*y**2 + 3*y - 1. Let o(p) = -p**3 + 3*p**2 - 3*p + 1. Let g(b) = 4*h(b) + 5*o(b). Factor g(d).
-(d - 1)**3
Suppose 0 = 2*d - 2*o - 26, -d + 22 + 3 = 3*o. Solve -144*u + 16 + d + 86*u**2 + 56*u**3 + 34*u**2 - 84*u**3 = 0 for u.
2/7, 2
Solve -3*f**3 + f**3 + 424*f**2 - 4*f - 418*f**2 = 0 for f.
0, 1, 2
Let q(y) = y**2 + y - 1. Let h be (33/(-15) + 1)*5. Let i(a) = -a + 2 - 11 + 3*a**2 + a. Let s(m) = h*q(m) + i(m). Factor s(g).
-3*(g + 1)**2
Let i be 1*(15 + -1 + -1). Find u, given that -14*u**2 + i*u**2 + 4 - 6 - 3*u = 0.
-2, -1
Let t(c) be the first derivative of c**6/180 - c**5/120 - c**4/24 - c**3/3 - 6. Let g(o) be the third derivative of t(o). Factor g(m).
(m - 1)*(2*m + 1)
Let a = 24 - 22. Let p(r) be the second derivative of -1/70*r**5 - 1/7*r**3 - 1/7*r**a - 1/14*r**4 + 0 - r. Factor p(h).
-2*(h + 1)**3/7
Let a be ((-3)/(-2))/(7/140). Let w = a - 59/2. Factor z**3 - w*z**5 + z**2 - 1/2*z**4 - 1/2*z - 1/2.
-(z - 1)**2*(z + 1)**3/2
Let c(s) be the second derivative of 0 - 1/12*s**3 - 1/24*s**4 - 3*s + 1/2*s**2. Determine x, given that c(x) = 0.
-2, 1
Let w(g) be the first derivative of -g**6/39 + 8*g**5/65 - 3*g**4/13 + 8*g**3/39 - g**2/13 - 3. Suppose w(d) = 0. Calculate d.
0, 1
Let x(s) = -25*s**3 - 11*s**2 + 2*s - 4. Let n(h) = -4*h**2 - h. Let a be n(1). Let t(u) = 26*u**3 + 10*u**2 - u + 5. Let l(b) = a*x(b) - 4*t(b). Factor l(q).
3*q*(q + 1)*(7*q - 2)
Suppose -2*z = 5*i + 9, -2*z - 5*i = -z + 12. Suppose 0*d + d - z = 0. Factor -3*r**4 - r**2 - r**4 + r**4 - r**5 - d*r**3.
-r**2*(r + 1)**3
Let k(o) be the second derivative of o**6/10 - o**4/4 - 2*o. Solve k(m) = 0.
-1, 0, 1
Find n such that 3/4*n**3 + 6 + 9*n + 9/2*n**2 = 0.
-2
Let t be 12/(3 - 1) + -2. Factor -z + 1 - t*z**3 + 3*z**2 + 0*z**3 - 2*z + 3*z**3.
-(z - 1)**3
Let a(l) = l**2 + 14. Let h be a(0). Let v be (-2)/h - (-61)/35. Solve 8/5 - v*z + 2/5*z**2 = 0 for z.
2
Let f be (-7 - 4)/1 + 13. Factor c**3 + 0*c + 0 + 0*c**4 + 2/3*c**f - 1/3*c**5.
-c**2*(c - 2)*(c + 1)**2/3
Let 3/2*k**3 - 1 - 1/2*k + 2*k**2 = 0. Calculate k.
-1, 2/3
Let n be (10 + 2 + -2)/2. Find a such that 2*a**2 + 0*a**5 - 6*a**3 - 2*a**5 + 2*a**2 + 4*a**n = 0.
-2, 0, 1
Let l(z) = z. Let r(a) = a**4 - 8*a**3 + 15*a**2 + 6*a - 16. Let j(n) = 2*l(n) + r(n). Factor j(v).
(v - 4)**2*(v - 1)*(v + 1)
Solve -9/4 - 21/8*x + 39/8*x**2 = 0.
-6/13, 1
Factor 0 + 3/8*o**3 + 1/8*o**2 + 1/4*o**4 + 0*o.
o**2*(o + 1)*(2*o + 1)/8
Let c(m) = 5*m**3 - 8*m**2 + 8*m + 3. Suppose 4*o = 12, -2*o = 3*k + 4 - 31. Let a(n) = 11*n**3 - 16*n**2 + 16*n + 7. Let h(u) = k*c(u) - 3*a(u). Factor h(r).
2*r*(r - 2)**2
Let n = 10 - 8. Factor p**n + 7 - 7.
p**2
Factor 1 + 0 - y**2 + 0 - 4 + 4*y.
-(y - 3)*(y - 1)
Let w be 1 - 4/40*6. Let t(m) be the first derivative of -2 + 0*m + 0*m**4 - 1/3*m**6 + 0*m**2 + w*m**5 + 0*m**3. Factor t(h).
-2*h**4*(h - 1)
Factor 2/5*g + 2/5*g**2 + 0.
2*g*(g + 1)/5
Let i = 1/104 + 3/1040. Let j(f) be the second derivative of f + 0*f**2 + 1/48*f**4 + 0*f**3 + 0 - i*f**5. Let j(u) = 0. Calculate u.
0, 1
Factor 2*h + 15*h**2 + 12*h**3 - 6*h - 6 - 17*h.
3*(h - 1)*(h + 2)*(4*h + 1)
Let v(a) be the first derivative of -2*a**6/3 - 8*a**5/5 + 8*a**3/3 + 2*a**2 + 7. Factor v(m).
-4*m*(m - 1)*(m + 1)**3
Let c(x) be the second derivative of x**7/147 - 2*x**6/105 - 15*x. Suppose c(g) = 0. Calculate g.
0, 2
Let z(s) = s - 1. Let a(p) = p**4 + 2*p**3 + p**2 - 4*p + 4. Let g be 45/12 - (-12)/(-16). Let t(o) = g*a(o) + 12*z(o). Factor t(d).
3*d**2*(d + 1)**2
Let k(q) be the first derivative of -2/25*q**5 + 5 - 4/5*q**4 - 44/15*q**3 - 24/5*q**2 - 18/5*q. Solve k(m) = 0 for m.
-3, -1
Let s(w) = 10*w**2 - 11*w + 12. Let n(x) = 3*x**2 - 4*x + 4. Let b(v) = -7*n(v) + 2*s(v). Let m be b(4). Factor 5*t**4 - 4*t**2 + 0*t**m + 2 - 3*t**4 + 0.
2*(t - 1)**2*(t + 1)**2
Let v(b) be the second derivative of 5*b**6/24 + b**5/4 - 7*b**4/16 - 5*b**3/6 - b**2/2 - 6*b. Find q, given that v(q) = 0.
-1, -2/5, 1
Let c(a) = -a**5 - a**4 - a**3 + a. Let d(w) = -6*w**5 - 2*w**4 + 2*w**3 + 2*w. Let h(t) = -2*c(t) + d(t). Solve h(y) = 0.
-1, 0, 1
Let r(s) = -s**4 - 29*s**3 - 30*s**2 - 7*s + 5. Let t(b) = 2*b**4 + 43*b**3 + 45*b**2 + 11*b - 7. Let j(f) = -7*r(f) - 5*t(f). Let j(l) = 0. What is l?
-2, -1, 0
Let j = 14 - 14. Let z(p) be the first derivative of -2*p**3 + p**2 + 2 - 2/5*p**5 + 3/2*p**4 + j*p. Solve z(s) = 0.
0, 1
Let d(p) be the first derivative of p**3/9 + p**2/2 + 2*p/3 + 3. Factor d(r).
(r + 1)*(r + 2)/3
Let u = -9/4 - -49/20. Let f(h) be the first derivative of -6/5*h - u*h**3 - 9/10*h**2 + 2. Let f(l) = 0. What is l?
-2, -1
Let w = 147 + -147. Let 1/4*r**2 + w + 0*r = 0. What is r?
0
Let z(r) be the first derivative of 7 - 9*r - 1/3*r**3 + 3*r**2. Factor z(u).
-(u - 3)**2
Let s(x) be the first derivative of 0*x + 1/4*x**4 - 1/2*x**2 - 1/5*x**5 + 1/3*x**3 + 3. Factor s(r).
-r*(r - 1)**2*(r + 1)
Let y(q) be the first derivative of q**3/3 - 4*q + 9. Factor y(t).
(t - 2)*(t + 2)
Let m(n) be the third derivative of n**5/30 - 2*n**4/3 + 16*n**3/3 - 3*n**2. Let m(c) = 0. Calculate c.
4
Suppose -3*s - 5*b - 21 = -s, 5*s + 2*b = 0. Let c(l) be the second derivative of -s*l + 1/6*l**4 + 0*l**2 + 0*l**3 + 0. Factor c(v).
2*v**2
Suppose -m + 5*o - 4 = -2, -m = 3*o - 6. Solve -20*r + m*r**5 - 3*r**3 + 23*r - 3*r**3 = 0.
-1, 0, 1
Suppose 3*d - 7 + 1 = 0. Suppose 10 = -d*a + 38. Factor 6*y - 4*y**2 - 2*y - a*y**2 + 14*y**3.
2*y*(y - 1)*(7*y - 2)
Let l(d) = -d**3 + 5*d**2 - 6*d + 6. Let p be l(4). Let w = 6 + p. Factor -18*c**2 - 5*c**4 + c + 3*c - c**w + 24*c**3 - 4*c**4.
-2*c*(c - 1)**2*(5*c - 2)
Let x(s) be the first derivative of s**5/20 - s**4/8 + s**2/4 - s/4 + 9. Factor x(b).
(b - 1)**3*(b + 1)/4
Let o(b) = -b**3 + 4*b**2 - 2*b + 2. Let f be o(3). Suppose -8*j**2 - 5*j**2 + 2*j + 4*j**3 + 2*j + f*j**2 = 0. What is j?
0, 1
Let c(b) be the second derivative of 3*b**5/80 + b**4/16 - b**3/8 - 3*b**2/8 + 3*b. Determine h so that c(h) = 0.
-1, 1
Let l(w) be the second derivative of 0 + 1/4*w**4 + 4*w + 1/60*w**6 + 1/4*w**2 - 1/3*w**3 - 1/10*w**5. Let l(t) = 0. What is t?
1
Let y be (-4)/64*42/(-7). Let d(m) be the second derivative of y*m**4 - 1/40*m**5 + 0 + m + 27/4*m**2 - 9/4*m**3. Factor d(v).
-(v - 3)**3/2
Let p(u) = -10*u**4 + 14*u**3 - 8*u**2 + 4*u. Let v(t) = -t**5 - 31*t**4 + 43*t**3 - 24*t**2 + 13*t. Let k(o) = 7*p(o) - 2*v(o). Let k(g) = 0. Calculate g.
0, 1
Let k be (-37)/117 - (-5 + 4). Let n = k + -6/13. Determine t, given that -4/9*t - n*t**2 - 2/9 = 0.
-1
Let c(l) be the third derivative of -l**6/60 + l**5/30 + 5*l**2. Factor c(x).
-2*x**2*(x - 1)
Let o be (-8)/(-14) + ((-5)/21 - -1). Factor 2/3*f + 2/3*f**2 - o.
2*(f - 1)*(f + 2)/3
Let n(g) be the first derivative of 0*g + 1 + 0*g**3 + 1/14*g**4 - 1/7*g**2. Find s such that n(s) = 0.
-1, 0, 1
Factor 4/7*c**3 + 0 - 1/7*c**4 + 2/7*c - 5/7*c**2.
-c*(c - 2)*(c - 1)**2/7
Let i be (15*2/3)/2. Factor -5*q**3 + i*q**3 + 4*q - 6*q**3 - 2*q**2.
-2*q*(q + 1)*(3*q - 2)
Let u(s) = -8*s**2 + 15*s - 16. Let p(z) = -7*z**2 + 14*z - 16. Let c = 4 - -3. Let h(t) = c*p(t) - 6*u(t). Factor h(i).
-(i - 4)**2
Let p(i) be the third derivative of i**7/140 - i**5/20 + i**3/4 + 11*i**2. Find r such that p(r) = 0.
-1, 1
Factor 2/9*n**4 - 2/9*n**2 - 2/9*n + 0 + 2/9*n**3.
2*n*(n - 1)*(n + 1)**2/9
Suppose 6 + 10 + 32*p**2 + 16*p - 4*p**3 - 36*p**2 = 0. What is p?
-2, -1, 2
Let h(w) = 56*w**3 + 32*w**2 - 21*w - 5. Let d(v) = 37*v**3 + 21*v**2 - 14*v - 3. Let o(c) = -8*d(c) + 5*h(c). What is a in o(a) = 0?
-1, 1/4
Let m(y) be the third derivative of y**8/1008 + y**7/630 - y**6