3*r*(r - 1)*(2*r + 1)
Let p(f) be the first derivative of f**6/12 + 2*f**5/5 + f**4/2 - f**3/3 - 5*f**2/4 - f - 3. Let p(d) = 0. Calculate d.
-2, -1, 1
Let i(c) be the first derivative of -c**6/8 + 9*c**5/20 + 27*c**4/16 + 5*c**3/4 + 8. Solve i(l) = 0.
-1, 0, 5
Suppose -7 = -2*c + 17. Factor 4*z**2 + 6*z + 10*z - c*z - 4*z**3 - 4*z**4.
-4*z*(z - 1)*(z + 1)**2
Let n be 4*(-3 + 21/6). Determine d, given that 5*d**4 - 7*d**4 - 5*d**3 - n*d**2 + d**3 = 0.
-1, 0
Let m(d) be the first derivative of d**4/54 + 2*d**3/27 + d**2/9 - 3*d + 4. Let c(i) be the first derivative of m(i). Factor c(j).
2*(j + 1)**2/9
Find n, given that -2/7*n**2 - 6/7*n - 4/7 = 0.
-2, -1
Let w(x) be the second derivative of x**6/480 - x**4/32 + x**3/2 - 2*x. Let b(f) be the second derivative of w(f). Factor b(j).
3*(j - 1)*(j + 1)/4
Let v(a) = -2*a**4 + 2*a**3 - 95*a**2 - 233*a - 173. Let s(k) = 3*k**4 - 3*k**3 + 96*k**2 + 234*k + 174. Let b(f) = 5*s(f) + 6*v(f). Factor b(o).
3*(o - 7)*(o + 2)**3
Let k(r) be the third derivative of -r**5/30 - 7*r**4/12 - 10*r**3/3 - 42*r**2. Factor k(a).
-2*(a + 2)*(a + 5)
Let s = -10 + 16. Factor 5*c**2 - s*c**3 + 2*c - 1 - 2 + 2.
-(c - 1)*(2*c + 1)*(3*c - 1)
Let c(w) be the first derivative of w**6/14 - 6*w**5/35 - 9*w**4/28 + 4*w**3/7 + 6*w**2/7 + 2. Factor c(f).
3*f*(f - 2)**2*(f + 1)**2/7
Factor 1/2*y**2 - 1/4 + 0*y**3 - 1/4*y**4 + 0*y.
-(y - 1)**2*(y + 1)**2/4
Let t be 123/60 + -5 + 3. Let y(o) be the second derivative of -1/12*o**4 + 1/2*o**2 + 0 + 1/6*o**3 - 3*o - t*o**5. Determine c so that y(c) = 0.
-1, 1
Let n(v) be the third derivative of -v**5/12 - 25*v**4/24 - 10*v**3/3 - 37*v**2 + v. Factor n(q).
-5*(q + 1)*(q + 4)
Determine n so that -8/11*n**2 + 0 - 6/11*n - 2/11*n**3 = 0.
-3, -1, 0
Let a(q) be the second derivative of -7/36*q**4 + 1/9*q**3 + 0*q**2 - 6*q + 0. Factor a(f).
-f*(7*f - 2)/3
Let v(g) be the third derivative of g**7/70 - g**5/10 + g**3/2 - 4*g**2. Determine k so that v(k) = 0.
-1, 1
Let m(p) = p**5 - 12*p**4 + 4*p**3 + 9*p**2 - 5*p - 3. Let j(i) = -12*i**4 + 4*i**3 + 8*i**2 - 4*i - 4. Let c(l) = 3*j(l) - 4*m(l). Find x such that c(x) = 0.
-1, 0, 1, 2
Let h(k) = -k**3 + 3*k**2 - 1. Suppose -5*a + 9 = -1. Let z be h(a). Let y**2 - y**4 + 2*y**3 - 2*y + 3*y**2 - z*y**4 = 0. Calculate y.
-1, 0, 1/2, 1
Let l(b) be the second derivative of -b**5/60 + 13*b**4/36 - 8*b**3/3 + 6*b**2 - 21*b. Factor l(g).
-(g - 6)**2*(g - 1)/3
Let g = 4 - 2. Factor -4*z - 2*z**3 + 4*z + g*z.
-2*z*(z - 1)*(z + 1)
Let n(s) be the first derivative of 75*s**4/4 - 20*s**3/3 - 45*s**2/2 - 10*s - 7. Factor n(c).
5*(c - 1)*(3*c + 1)*(5*c + 2)
Suppose -24 = 2*s - s + 2*t, 3*t - 34 = 2*s. Let o be ((-2)/s)/(6/15). Solve 1/2 - 1/4*h**2 + o*h = 0.
-1, 2
Let n be 2/(-9) + 140/63. Factor 6*m**3 - m**3 + 12*m**2 + m**3 + 4*m**3 + n*m.
2*m*(m + 1)*(5*m + 1)
Determine g so that 1/4*g + 0 - 1/4*g**2 = 0.
0, 1
Suppose 2*x + 3*m = 5, m - 3 = -0*x - x. Find t such that -4*t - t**x - 2*t**2 + 31 + 4*t**3 + 0*t - 28 = 0.
-1, 1, 3
Suppose 4*n - 16 = 2*x + 2*x, 4*x + 10 = 2*n. Determine a, given that a**n + 1/3*a - 4/3*a**2 + 0 = 0.
0, 1/3, 1
Let f(g) be the second derivative of -g**4/66 - g**3/33 + 2*g**2/11 + 28*g. Factor f(n).
-2*(n - 1)*(n + 2)/11
Let g be 1*0/(4 - 9). Let j(q) be the first derivative of g*q**2 + 2 + q - 1/3*q**3. Determine p, given that j(p) = 0.
-1, 1
Factor 2*l - 8*l + 5*l**3 + 3*l - 7*l + 5*l**2.
5*l*(l - 1)*(l + 2)
Let a(d) = -2*d**3 + d**2 + 4*d - 3. Let z(y) = 3*y**3 - 4*y + 4. Let c(k) = -4*a(k) - 3*z(k). Let c(v) = 0. What is v?
-2, 0
Let d(z) be the first derivative of -1/10*z**4 - 2 + 4/15*z**3 + 0*z - 1/5*z**2. Suppose d(a) = 0. What is a?
0, 1
Let c(q) be the second derivative of 0 + 0*q**3 - 1/6*q**4 - 2*q + 0*q**2 + 1/20*q**5. Factor c(h).
h**2*(h - 2)
Let h(n) = -9*n**2 - 6*n. Let m(z) = -z**2 - z. Let j(f) = h(f) - 6*m(f). Suppose j(x) = 0. Calculate x.
0
Let x be 2/(14/33) + (-4)/(-14). Let z(d) be the second derivative of 1/6*d**3 + 23/12*d**4 + 2*d - d**2 + d**x + 0. Factor z(h).
(h + 1)*(4*h - 1)*(5*h + 2)
Let g = 31 - 27. Let s(v) be the second derivative of 0 + 1/2*v**g - 1/20*v**5 - 2*v**3 + 2*v + 4*v**2. Let s(w) = 0. Calculate w.
2
Determine u, given that 4*u**4 - 128 + 128 - 8*u**3 = 0.
0, 2
Let k(g) = g**3 + 7*g**2 + 4*g - 8. Let p be k(-6). Let 4*h - 3*h**4 - 3*h - 9*h**2 - 9*h**3 - p*h = 0. What is h?
-1, 0
Let h(l) be the third derivative of -l**7/1470 - l**6/315 + l**5/210 + l**4/21 - 2*l**3/3 - 8*l**2. Let b(i) be the first derivative of h(i). Factor b(n).
-4*(n - 1)*(n + 1)*(n + 2)/7
Let z(h) be the first derivative of -2*h**3/27 + 2*h**2/9 - 2*h/9 + 1. Factor z(c).
-2*(c - 1)**2/9
Let f be ((-135)/10)/(-3)*(-10)/(-6). Find y, given that -3/2*y**3 - 6*y**2 - f*y - 3 = 0.
-2, -1
Let v(u) = -14*u**2 - 4. Let b(f) = 13*f**2 - f + 3. Let o(t) = -6*b(t) - 5*v(t). What is x in o(x) = 0?
-1/4, 1
Let k(x) be the first derivative of -5 + 0*x**3 + 0*x + 1/6*x**2 - 1/12*x**4. Determine t, given that k(t) = 0.
-1, 0, 1
Let k = 7 - 2. Let a = k - 3. Find p, given that p**2 + p**3 + 4*p**2 + 1 - 2*p**a + 3*p = 0.
-1
Let v(g) be the third derivative of -1/1512*g**8 - 4*g**2 + 0*g + 0*g**5 + 0*g**6 + 0*g**4 + 0*g**3 + 2/945*g**7 + 0. Let v(s) = 0. What is s?
0, 2
Let i = -3 + 4. Suppose i = -2*r + 5. Factor 0*g**r - 1/2*g**5 + 0 + 0*g**3 + 0*g**4 + 0*g.
-g**5/2
Let x(p) = 6*p**4 + 4*p**3 + 5*p. Let t(y) = -5*y**4 - 3*y**3 - 4*y. Let z(s) = 5*t(s) + 4*x(s). Let z(b) = 0. What is b?
0, 1
Let u(v) be the first derivative of 3*v**4/4 - 17*v**3/6 + 11*v**2/4 - v - 12. Factor u(j).
(j - 2)*(2*j - 1)*(3*j - 1)/2
Suppose -5*t = -t + 12. Let a(l) be the second derivative of 7*l**4/12 - l. Let p(h) = 3*h**2. Let w(k) = t*a(k) + 8*p(k). Factor w(f).
3*f**2
Let w = 68/287 - -2/41. Let k be ((-78)/21 - -2) + 2. Find q such that -w*q**2 + k*q + 0 = 0.
0, 1
Let i(x) be the third derivative of 7*x**2 + 0*x**3 + 1/140*x**5 + 0*x**4 + 0*x + 0. Find a, given that i(a) = 0.
0
Let x be (-4)/14*(1 + -8). Let f(g) be the third derivative of 2*g**x + 0*g - 1/9*g**3 + 0*g**4 + 0 + 1/90*g**5. Solve f(w) = 0 for w.
-1, 1
Let n(m) be the second derivative of -m**7/105 + m**5/40 - m**4/48 - 3*m**2 + 8*m. Let t(f) be the first derivative of n(f). Find o, given that t(o) = 0.
-1, 0, 1/2
Suppose -12/7*j**3 + 12/7 - 9/7*j**2 - 3/7*j**4 + 12/7*j = 0. What is j?
-2, -1, 1
Let d be (-6)/27 + 40/(-135)*-3. Factor 1/3*u**2 + u + d.
(u + 1)*(u + 2)/3
Let u(h) be the third derivative of h**8/1008 + h**7/315 - h**5/90 - h**4/72 - 12*h**2. Factor u(y).
y*(y - 1)*(y + 1)**3/3
Let y = -23 - -33. Suppose 4 - y = -2*r. Factor 0 + 0*p + 2/3*p**5 + 2/3*p**4 - 2/3*p**2 - 2/3*p**r.
2*p**2*(p - 1)*(p + 1)**2/3
Let n(u) = u**3 + u**2. Let o(y) = -5*y**2 - 2*y**3 + 0*y - 2*y + y + 2*y**2. Let m(z) = 7*n(z) + 2*o(z). Find f, given that m(f) = 0.
-1, 0, 2/3
Let y = 103/261 + -5/29. Solve 2/9*n**3 + 0*n + 0*n**2 - y*n**4 + 0 = 0 for n.
0, 1
Let z = -2/3 + 7/6. Let g(o) be the second derivative of -2*o + 0 - 1/3*o**3 + 1/12*o**4 + z*o**2. Factor g(i).
(i - 1)**2
Factor 111*r - 28 - 4*r**2 - 33*r - 46*r.
-4*(r - 7)*(r - 1)
Let w be 2/(-13) + (-6)/(-39). Factor 3/4*l**4 + 0*l + 0*l**2 + 3/4*l**3 + w.
3*l**3*(l + 1)/4
Let n(b) = 12*b**2 + 21*b - 8. Let x = 4 - 6. Let h(l) = -48*l**2 - 84*l + 33. Let q(z) = x*h(z) - 9*n(z). Factor q(w).
-3*(w + 2)*(4*w - 1)
Let f be ((-2)/16)/(2/(-4)). Let x = -4/55 - -173/110. Solve 1/4 + d**3 + f*d**4 + x*d**2 + d = 0.
-1
Let u be 8/1 + -3 - 3. Factor -22*q - 2*q**2 + 16*q - 2 - u.
-2*(q + 1)*(q + 2)
Suppose -3*j = 2*n + 11, 30 = 7*n - 2*n - 4*j. Factor 1 + b**3 + 0*b - b**n + 0*b**2 - b.
(b - 1)**2*(b + 1)
Determine d so that 4*d**2 + 3*d + 4*d - 4*d**3 - 3*d - 4*d**4 + 0*d**4 = 0.
-1, 0, 1
What is f in 0*f**2 + 8/3*f**3 + 8/3*f**4 - 2*f**5 + 0*f + 0 = 0?
-2/3, 0, 2
Let p be 214/(-7)*(-20)/5. Let s = p - 122. Suppose 6/7*h - 6/7*h**3 - 2/7*h**2 + s = 0. Calculate h.
-1, -1/3, 1
Let q(z) be the first derivative of 11*z**3 - 27*z**2/2 - 6*z - 5. What is o in q(o) = 0?
-2/11, 1
Let k(z) = z + 1. Let f(l) = 2*l. Let w(a) = 3*f(a) - 4*k(a). Let m be w(3). Factor -h**2 - h + m*h**3 - h**3 + 0*h**2 + h**4.
h*(h - 1)*(h + 1)**2
Factor 4/3*c + 1 + 1/3*c**2.
(c + 1)*(c + 3)/3
Let o(f) be the third derivative of f**5/20 + f**4/4 + f**3/2 + f**2. Factor o(x)