 5*b**3 - 9*b**2 + 9*b - 5. Let s(x) = o*w(x) - y(x). Determine m, given that s(m) = 0.
1
Let l(b) be the first derivative of 84*b**4 + 72*b**3 + 45*b**2/2 + 3*b - 37. Solve l(y) = 0 for y.
-1/4, -1/7
Suppose 3 = 5*h - 7. Suppose j**2 + j**4 - 5*j**2 + 5*j**2 + 0*j**4 + h*j**3 = 0. What is j?
-1, 0
Factor 2/7 + 2/7*n**3 - 2/7*n - 2/7*n**2.
2*(n - 1)**2*(n + 1)/7
Let x = 3 - -1. Factor -c**4 + x*c - 4 + 3*c**2 + 0 + 4*c**3 - 6*c**3.
-(c - 1)**2*(c + 2)**2
Let a = 38 - 36. Suppose -5*h = -10*h. Suppose 4/7*f**3 - 2/7*f**4 + 0 - 2/7*f**a + h*f = 0. What is f?
0, 1
Let v(x) be the second derivative of -1/8*x**4 - 1/18*x**3 + 7/60*x**6 - 1/120*x**5 + 6*x + 0 - 1/28*x**7 + 0*x**2. Find g, given that v(g) = 0.
-1/3, 0, 1, 2
Let x be 14/6 - (-1)/(-3). Factor -110*q**x - 3*q**3 + 106*q**2 - q**3.
-4*q**2*(q + 1)
Let w be (-1)/(-4) + (-60)/(-16). Suppose -4*c - 10 = -5*x - 0, -2*x = -w*c - 4. What is t in 1/2 - t**3 - 1/2*t**4 + t + 0*t**x = 0?
-1, 1
Let g = 21 - 6. Factor -d**2 + 10*d**4 - g*d**4 + 6*d**4.
d**2*(d - 1)*(d + 1)
Find j such that -25/3*j**3 + 5/3*j**2 + 4/3 + 16/3*j = 0.
-2/5, 1
Factor -3/2*k**2 - 27/4*k + 15/4.
-3*(k + 5)*(2*k - 1)/4
Let x(r) be the second derivative of -2*r**7/189 + 2*r**6/45 - 2*r**5/45 - 2*r**4/27 + 2*r**3/9 - 2*r**2/9 - 7*r. Factor x(u).
-4*(u - 1)**4*(u + 1)/9
Let x(g) be the second derivative of -g**8/3360 - g**7/1260 - g**4/6 - g. Let u(q) be the third derivative of x(q). Let u(j) = 0. Calculate j.
-1, 0
Let t(y) be the first derivative of -3 - 2/5*y**5 + 0*y**2 + 0*y - 1/9*y**6 - 1/2*y**4 - 2/9*y**3. Suppose t(q) = 0. Calculate q.
-1, 0
Let r be 2 - (3 + -4 - 2). Suppose -2*s = -3*v + v, 2*v = -5*s. Suppose 1/4*m**3 - 1/2*m**4 + 0*m**2 + 0*m + v + 1/4*m**r = 0. Calculate m.
0, 1
Let g be (-6)/(-4) + (-10)/(-4). Find q, given that -g + 4 + 2*q**2 = 0.
0
Let j be ((-4)/14)/(3/(-21)). Factor 68*l**5 - l**2 + l**j + 2*l**3 - l - 69*l**5.
-l*(l - 1)**2*(l + 1)**2
Find q such that 4/5*q**4 + 4/5*q**2 - 6/5*q**3 - 1/5*q - 1/5*q**5 + 0 = 0.
0, 1
Suppose -4*w + 14 = 2*a, 14 = -2*w + a + 19. Solve 1/2*o**4 - o + 0 - 1/2*o**2 + o**w = 0.
-2, -1, 0, 1
Let b(q) be the third derivative of -q**5/180 + q**4/24 - 4*q**2. Determine u so that b(u) = 0.
0, 3
Let y(z) be the third derivative of z**8/90720 + z**7/5670 + z**6/1080 - z**5/10 - 7*z**2. Let t(b) be the third derivative of y(b). Factor t(o).
2*(o + 1)*(o + 3)/9
Factor -12/7*d**3 - 8/7*d**2 + 4/7*d**4 + 48/7*d - 32/7.
4*(d - 2)**2*(d - 1)*(d + 2)/7
Solve -4/5*y - 2/5*y**5 - 2/5*y**2 + 0 + 6/5*y**3 + 2/5*y**4 = 0 for y.
-1, 0, 1, 2
Suppose 4*v - 856 = -844. Solve 36/5*r**2 + 6/5 + v*r**3 + 27/5*r = 0.
-1, -2/5
Suppose k - 36 = -5*a, -a + 2*a = -3*k + 10. Let -a*n + 4 + 11*n**2 + n - 9*n**2 = 0. Calculate n.
1, 2
Factor -5*a**4 + 2*a**4 - 2*a**4 + 15*a**3 - 10*a**2.
-5*a**2*(a - 2)*(a - 1)
Let u = -10 + 12. Find f, given that 4/3*f + 0 - 2*f**u + 2/3*f**3 = 0.
0, 1, 2
Suppose 0 = -11*h + 6*h + 10. Suppose 11*p**2 + 42*p**4 + 21*p**2 - 10*p**2 - 9*p**5 - 12*p - 69*p**3 + 26*p**h = 0. Calculate p.
0, 2/3, 1, 2
Let a(q) be the second derivative of -q**4/30 + 13*q. Factor a(c).
-2*c**2/5
Let j be (-160)/(-420)*3/4. Factor 0 - j*a**5 + 0*a + 2/7*a**4 + 2/7*a**3 - 2/7*a**2.
-2*a**2*(a - 1)**2*(a + 1)/7
Let m(r) = 5*r + 39. Let h be m(-7). Let l(b) be the second derivative of 1/6*b**3 + 1/12*b**h - b + 0*b**2 + 0. Suppose l(z) = 0. What is z?
-1, 0
Suppose 0 = 4*v + 4*h - 12, -15 = 4*v - 8*h + 3*h. Find r such that 2/11*r**3 + 0 - 6/11*r**2 + v*r = 0.
0, 3
Factor -2/23*r**2 + 0 + 20/23*r.
-2*r*(r - 10)/23
Let x(s) be the first derivative of -s**6/2 - 3*s**5/5 + 3*s**4/4 + s**3 - 11. Factor x(u).
-3*u**2*(u - 1)*(u + 1)**2
Suppose -3*g = -58 + 19. Let q = -9 + g. Solve 2 - u**2 + 2*u + 2*u**3 - u**2 - q*u = 0.
-1, 1
Let o(z) be the second derivative of z**7/455 - z**6/156 + z**5/390 + z**4/156 + 5*z**2/2 + 2*z. Let u(i) be the first derivative of o(i). Factor u(v).
2*v*(v - 1)**2*(3*v + 1)/13
Let i(o) = 2*o**3 - 4*o**2 + 3*o - 2. Let z be i(2). Let d = z - 2. Factor -m**2 + 2*m**d - 12*m**2 + 2*m.
-m*(11*m - 2)
Let k(w) be the first derivative of 1/7*w**2 - 2/35*w**5 + 7 + 2/21*w**3 + 0*w - 1/14*w**4. Suppose k(v) = 0. Calculate v.
-1, 0, 1
Factor -1/2*d - 1/4*d**2 + 3/4.
-(d - 1)*(d + 3)/4
Factor 36/5*w**2 + 4/5*w**4 - 24/5*w**3 - 16/5*w + 0.
4*w*(w - 4)*(w - 1)**2/5
Suppose 3*y + 1 = 4*p, -4*p - 2*y = -y - 5. Suppose u + 7 = 9. Solve -4*s**3 - 3*s + 3*s**3 - s**u + 4*s + p = 0.
-1, 1
Let o(p) be the first derivative of -p**6/15 + p**5/10 + p**4/6 - p**3/3 + 2*p + 3. Let m(j) be the first derivative of o(j). Factor m(n).
-2*n*(n - 1)**2*(n + 1)
Let 0 + 28/17*i**2 + 98/17*i + 2/17*i**3 = 0. Calculate i.
-7, 0
Suppose 0*o = -5*o + 30. Suppose 0 = -5*a + h + 7, 14 = a + 2*h + o. Factor a*i**2 + 8/7 + 32/7*i.
2*(i + 2)*(7*i + 2)/7
Let r be (-10)/(-30) + (-5)/16. Let o(a) be the second derivative of 0 + r*a**4 + 1/12*a**3 + a + 1/8*a**2. Find j such that o(j) = 0.
-1
Suppose p + 5 = -5*j, -5*j = -p - 3*p - 20. Let u(z) be the second derivative of -1/30*z**4 + 1/5*z**2 - z + j*z**3 + 0. Solve u(d) = 0.
-1, 1
Let s(u) = -5*u**3 - 5*u**2 - 8*u. Let j(n) = -n**3 + n**2. Let p(i) = -3*j(i) + s(i). Find a, given that p(a) = 0.
-2, 0
Let j(n) = 7*n**2 + 2*n - 25. Let r(z) = -z**2 + z. Let m(q) = 5*j(q) + 40*r(q). Determine a, given that m(a) = 0.
5
Let s(l) = -10*l**3 + 89*l**2 - 34*l - 25. Let m(n) = 11*n**3 - 88*n**2 + 35*n + 26. Let h(v) = 5*m(v) + 4*s(v). Factor h(t).
3*(t - 5)*(t - 1)*(5*t + 2)
Let l = 12 + -34/3. Let w = 44/27 + -8/27. Find v, given that l + w*v + 2/3*v**2 = 0.
-1
Suppose 2*q = -5*k + 26, 0 = 2*q + k - 16 + 6. Let n(a) = 7*a**2 - 26*a - 6. Let s be n(4). Find d such that 4/9*d**q + 0*d - 2/9*d**4 + 0 + 0*d**s = 0.
0, 2
Let l(g) be the third derivative of 0*g**5 - 1/42*g**4 - 1/21*g**3 + 0 + 1/210*g**6 + 4*g**2 + 0*g + 1/735*g**7. Factor l(b).
2*(b - 1)*(b + 1)**3/7
Let y(b) = -11*b + 7*b + 6 + 5*b. Let q be y(-6). Factor 0 + 1/3*v**3 + q*v - 1/3*v**2.
v**2*(v - 1)/3
Let m(n) = n + 10. Let c be m(-8). Let u = c - 2. Factor o + 3*o - o**2 - 3*o + u*o**2.
-o*(o - 1)
Factor v**2 + 3*v**2 - v**3 + 0*v**2 - 9*v**2.
-v**2*(v + 5)
Let l = -39 + 60. Suppose -3*x - 4*z + 19 = z, 5*x - l = -3*z. Factor 0*r**2 + 5*r**x - 2*r**5 + 0*r**2 - 3*r**3.
-2*r**3*(r - 1)*(r + 1)
Let v(a) be the first derivative of -1/120*a**6 - 5/24*a**4 - 2 - 1/3*a**3 - 1/15*a**5 - a**2 + 0*a. Let c(u) be the second derivative of v(u). Factor c(b).
-(b + 1)**2*(b + 2)
Let u(l) be the first derivative of l**6/14 + 12*l**5/35 + 3*l**4/14 - 4*l**3/7 - 9*l**2/14 + 41. Suppose u(y) = 0. What is y?
-3, -1, 0, 1
Let k(p) be the first derivative of 20*p**3/3 + 15*p**2/2 - 5*p + 11. Factor k(q).
5*(q + 1)*(4*q - 1)
Let x = 2928/13 + -103533/455. Let g = x - -19/7. Solve -6/5*l + g*l**2 - 2/5 + 6/5*l**3 = 0 for l.
-1, -1/3, 1
Solve -6*f**4 - 4*f**5 + 4*f + 4*f**2 - 2*f**4 + 4*f**2 = 0 for f.
-1, 0, 1
Let i = 0 - -3. Suppose -12 = -b - i*b. Find z such that 30*z**2 - 18*z**5 + 9*z**3 - 8 - b*z**3 - 30*z**4 + 4*z**3 = 0.
-1, 2/3
Let j(f) be the third derivative of f**9/105840 + f**8/35280 - f**5/12 - 3*f**2. Let t(g) be the third derivative of j(g). What is r in t(r) = 0?
-1, 0
Let n(m) = -21*m**2 + 8*m - 15. Let c(v) be the first derivative of 10*v**3/3 - 2*v**2 + 7*v - 2. Let g(h) = -13*c(h) - 6*n(h). Let g(k) = 0. What is k?
1/2
Let g(t) = t**3 - 5*t**2 + 3. Let s be g(5). Factor 0 + 0*k - 10/3*k**s + 4/3*k**2.
-2*k**2*(5*k - 2)/3
Let c(a) be the first derivative of 1/2*a**2 + 0*a + 0*a**4 + 1/90*a**5 + 0*a**3 + 3. Let s(d) be the second derivative of c(d). Suppose s(y) = 0. What is y?
0
Suppose 7 = 5*q + 4*f, 3*q - 5*f - 4 = 5*q. Suppose 11 = 5*s + 4*x, s + x - 1 = 1. Factor -4*p + 6*p**s + 0*p**2 - q*p - 3*p**2 + p + 3*p**4.
3*p*(p - 1)*(p + 1)*(p + 2)
Factor 0 + 8/5*i - 2/5*i**3 + 6/5*i**2.
-2*i*(i - 4)*(i + 1)/5
Let l(o) be the third derivative of 2*o**7/315 - o**6/180 - 2*o**2. Determine n, given that l(n) = 0.
0, 1/2
Suppose -2*t + 6*t = 8. Factor d**2 + 0*d - t*d**3 + d**2 - 2 + 2*d.
-2*(d - 1)**2*(d + 1)
Let w(r) be the third derivative of r**6/48 - r**5/40 - r**4/24 - 6*r**2. Find q such that w(q) = 0.
-2/5, 0, 1
Let u(k) be the second derivative of -3/28*k**4 + 0 + 1/7*k**3 + 0*k**2 + 1/70*k**6 + 0*k**