- t**2 + 4*t**4 + 2*t**5 - 3*t**5 + t**3.
-t**2*(t - 1)**2*(t + 1)
Let z(x) be the first derivative of x**8/840 - x**7/105 + x**6/36 - x**5/30 + 5*x**3/3 - 2. Let b(k) be the third derivative of z(k). Let b(r) = 0. Calculate r.
0, 1, 2
Find q, given that 4/3*q**2 + 1/6*q**4 + q - q**3 - 3/2 = 0.
-1, 1, 3
Let f(z) = 12*z**4 + 40*z**3 + 20*z**2 + 4. Let p(l) = 13*l**4 + 39*l**3 + 21*l**2 + l + 3. Let m(k) = 3*f(k) - 4*p(k). Factor m(h).
-4*h*(h + 1)**2*(4*h + 1)
Let m be (-31)/(-14) - 6/(-21). Let t = -2 + m. Factor -j - 1/2*j**2 - t.
-(j + 1)**2/2
Let h(f) be the first derivative of 2*f**5/35 - f**4/14 - 2*f**3/7 + 5*f**2/7 - 4*f/7 + 9. Factor h(x).
2*(x - 1)**3*(x + 2)/7
Let c(p) be the third derivative of -p**8/672 - p**7/140 - p**6/80 - p**5/120 + 10*p**2. Solve c(j) = 0 for j.
-1, 0
Let d = -8335/7 + 8073/7. Let c = d + 38. Suppose 10/7*i**5 + c*i**4 - 8/7*i**2 + 10/7*i - 20/7*i**3 + 4/7 = 0. What is i?
-1, -2/5, 1
Let u = 10 + -9. Let w(i) be the first derivative of -1/4*i**4 + 0*i**3 - 1/6*i**6 - 2/5*i**5 + u + 0*i**2 + 0*i. Factor w(v).
-v**3*(v + 1)**2
Let t(z) = 2*z - 6. Let s(a) = -a + 5. Let h(r) = -5*s(r) - 4*t(r). Let u be h(-1). Find p, given that -10*p - 21/2*p**u + 25/2*p**4 + 10*p**3 - 2 = 0.
-1, -2/5, 1
Let x(t) = -4*t**5 + 13*t**4 - 7*t**3 + t**2 - 3*t. Let v(l) = 3*l**5 - 9*l**4 + 5*l**3 - l**2 + 2*l. Let w(i) = -7*v(i) - 5*x(i). Let w(p) = 0. What is p?
-1, 0, 1
Let m(i) be the first derivative of -i**5/10 + i**4/3 - i**3/3 - 8*i - 2. Let n(q) be the first derivative of m(q). Suppose n(p) = 0. What is p?
0, 1
Let l be 2/(-4)*0/(-1). Let a be 3/9*l + 1. Factor -8*g + a - 1 + 16*g**4 - 1 + 8*g**3 - 15*g**2.
(g - 1)*(g + 1)*(4*g + 1)**2
Let b(w) be the third derivative of -w**8/112 + 3*w**7/35 - 13*w**6/40 + 3*w**5/5 - w**4/2 - 26*w**2. Solve b(x) = 0.
0, 1, 2
Let u(p) be the third derivative of p**9/68040 + p**8/15120 + p**4/8 + 8*p**2. Let c(d) be the second derivative of u(d). Find m such that c(m) = 0.
-2, 0
Let m = 19/37 + -1/74. Let d be ((-4)/7)/(8/(-28)). Factor -1/2*u + 0 - m*u**d.
-u*(u + 1)/2
Let g(i) = i**5 - 15*i**4 + 76*i**3 - 156*i**2 + 252. Let v(a) = -2*a**5 + 30*a**4 - 153*a**3 + 313*a**2 - 505. Let m(r) = 7*g(r) + 4*v(r). Factor m(w).
-(w - 4)**4*(w + 1)
Let w(v) be the second derivative of -v**8/84 - 4*v**7/105 - v**6/30 - 5*v**2/2 - 2*v. Let u(b) be the first derivative of w(b). Find j such that u(j) = 0.
-1, 0
Let g(h) = -h**2 + h. Let n(j) = -3*j**3 + 6*j**2 - 3. Let o(r) = -3*g(r) - n(r). Suppose o(z) = 0. What is z?
-1, 1
Let q(k) be the third derivative of 0 + 0*k**3 + 1/20*k**6 + 0*k**4 + 0*k - 9/70*k**7 + 4*k**2 + 0*k**5 + 1/16*k**8. Factor q(i).
3*i**3*(i - 1)*(7*i - 2)
Find r, given that 16*r**2 - 79*r - 1 - 97 + 411*r + 14 = 0.
-21, 1/4
Let j = 580 + -1732/3. Find h, given that 9*h**4 - 23/3*h**2 + j*h + 4/3 + 9*h**5 - 9*h**3 = 0.
-1, -1/3, 2/3
Find v such that v + 14*v**2 - 16*v - 4*v + 4 + v = 0.
2/7, 1
Let p(k) = -k**4 - k - 1. Let d(h) = h**2 + 3*h**4 - 9*h**2 + 3 - 4*h**3 + 2*h**2. Let q(r) = -d(r) - 4*p(r). Factor q(n).
(n + 1)**4
Let f(s) = 5*s + 5. Let w be f(-3). Let r be (8/(-10))/(2/w). Factor 0*o + 0*o**3 - 1/3*o**r + 0 + 1/3*o**2.
-o**2*(o - 1)*(o + 1)/3
Let w(o) be the second derivative of -o**6/60 - o**5/15 - o**2 - 4*o. Let g(p) be the first derivative of w(p). Factor g(k).
-2*k**2*(k + 2)
Let r(c) be the first derivative of 5*c**3 + 10*c**2 - 20*c + 15. Factor r(v).
5*(v + 2)*(3*v - 2)
Let z be ((-24)/30)/(54/15915). Let x = 236 + z. Determine k, given that 0 + x*k**2 - 2/9*k = 0.
0, 1
Let m = -6 + 18. Let p be (-3)/(-6)*m/3. Solve 6*r**4 - 4*r**4 + p*r**3 - 3*r**4 = 0 for r.
0, 2
Find t, given that 0 + 76/9*t**4 + 20/9*t**2 - 28/3*t**3 + 0*t - 4/3*t**5 = 0.
0, 1/3, 1, 5
Determine j, given that 1/2*j**5 + 0 + 0*j**2 + 0*j + 0*j**4 - 1/2*j**3 = 0.
-1, 0, 1
Factor 4 + 6*u**2 + u + 15*u + 7*u**2 + 3*u**2.
4*(2*u + 1)**2
Solve 1/2*f**3 + 7/2 + 5/2*f**2 - 13/2*f = 0 for f.
-7, 1
Let f(p) = -2*p**2 - 4*p + 7. Let v(w) = -3*w**2 - 8*w + 13. Let c(i) = 5*f(i) - 3*v(i). Let c(m) = 0. Calculate m.
2
Let l = -191/4 + 48. Let p(m) be the first derivative of m**3 - 3/2*m**2 - 2 + m - l*m**4. Solve p(v) = 0.
1
Let b(o) be the third derivative of -o**7/3780 + o**6/1080 - o**4/12 + 2*o**2. Let j(u) be the second derivative of b(u). Determine x so that j(x) = 0.
0, 1
Suppose 3*q - 3*m + 24 = 0, -3*m = -8*m + 15. Let o = 7 + q. Factor 4*n + 2 + 3*n + 2*n**3 + n + 6*n**2 - o*n.
2*(n + 1)**3
Let r(w) be the third derivative of w**5/80 + w**4/32 - w**3/4 + w**2. Determine h, given that r(h) = 0.
-2, 1
Suppose 0 = -3*l - l. Let d(m) be the first derivative of -2/5*m**5 + 0*m**2 - 1 + l*m - 2/3*m**3 + m**4. Factor d(f).
-2*f**2*(f - 1)**2
Let h(r) be the second derivative of r**4/48 - r**3/12 + 17*r. Suppose h(k) = 0. Calculate k.
0, 2
Factor -157/3*w**3 + 0 - 27*w**5 - 4/3*w + 44/3*w**2 + 66*w**4.
-w*(w - 1)**2*(9*w - 2)**2/3
Let n = 59/2 - 29. Suppose -2*d + 1 + 2 = 3*x, 0 = 2*x - 2. Determine t, given that d + 0*t + n*t**2 = 0.
0
Let o(p) be the third derivative of -p**6/20 + p**5/15 + 7*p**4/12 + 2*p**3/3 - 5*p**2. Factor o(x).
-2*(x - 2)*(x + 1)*(3*x + 1)
Let h = -3 + 9. Let p(s) be the third derivative of -2/21*s**3 + 0 + 5/84*s**4 - 1/420*s**h + 0*s - s**2 - 1/70*s**5 + 1/735*s**7. Find l such that p(l) = 0.
-2, 1
Let z(s) be the second derivative of s**9/15120 - s**7/840 - s**6/360 + s**4/4 + s. Let t(m) be the third derivative of z(m). Factor t(i).
i*(i - 2)*(i + 1)**2
Suppose -a + 0*a = 5*w + 2, -8 = -2*a + 2*w. Let y be 1*(2/2)/a. Find t such that -y*t + 1/3*t**3 + 0*t**2 + 0 = 0.
-1, 0, 1
Suppose -2/7 + 0*p + 0*p**3 - 2/7*p**4 + 4/7*p**2 = 0. Calculate p.
-1, 1
Let x be 14/(-105) + 14/60. Let n = x + 7/30. Find f, given that n*f**2 + 1/3 + 2/3*f = 0.
-1
Let a(b) be the second derivative of b**7/14 - 9*b**5/20 + b**4/2 - 20*b. Factor a(g).
3*g**2*(g - 1)**2*(g + 2)
Suppose -2*w**3 + 2*w**4 - 3*w**5 - 3*w**3 - 8*w**4 + 2*w**3 = 0. Calculate w.
-1, 0
Let r be (-8)/60*(-1)/2. Let x(p) be the second derivative of -r*p**6 + 1/21*p**7 + 0*p**4 + 0*p**2 - 2*p + 0*p**3 + 0*p**5 + 0. Factor x(o).
2*o**4*(o - 1)
Suppose -5*r = 5*h + 50, 4*h + 0*h = 4*r. Let y(m) = 12*m**2 - 4*m + 7. Let t(g) = 8*g**2 - 3*g + 5. Let q(j) = r*y(j) + 7*t(j). Factor q(a).
-a*(4*a + 1)
Let v(n) be the second derivative of 0*n**4 + 0*n**2 + 0*n**3 + 3/20*n**5 + 1/10*n**6 - 2*n + 0. Factor v(y).
3*y**3*(y + 1)
Factor -44*f**5 + f**3 + 6*f**4 + 8*f**3 + 41*f**5.
-3*f**3*(f - 3)*(f + 1)
Suppose 5*d + 3*f - 99 = 0, 4*d = -2*f + 40 + 40. Let b = -13 + d. Solve 3*x - b*x**2 + 8*x**4 + 2*x**3 - 4*x - x = 0.
-1, -1/4, 0, 1
Let b(p) be the third derivative of p**6/24 + 17*p**5/40 + 3*p**4/4 + 7*p**3/6 - 8*p**2. Let y(r) be the first derivative of b(r). Factor y(u).
3*(u + 3)*(5*u + 2)
Let -2/7*y - 2/7*y**3 + 4/7*y**2 + 0 = 0. Calculate y.
0, 1
Let b(p) = -p**2 + 14*p - 41. Let n be b(9). Let z(m) be the first derivative of 0*m**2 + 1/3*m**3 - 1/10*m**5 + 2 + 0*m - 1/8*m**n. Factor z(i).
-i**2*(i - 1)*(i + 2)/2
Factor -10/7*t**3 - 2*t - 18/7*t**2 - 4/7 - 2/7*t**4.
-2*(t + 1)**3*(t + 2)/7
Let k = -599 - -9587/16. Let u(x) be the first derivative of 2 + 0*x + k*x**4 - 3/8*x**2 + 0*x**3. Factor u(o).
3*o*(o - 1)*(o + 1)/4
Suppose 2*i - 4*r - 16 = 0, 6*i - r - 9 = 3*i. Let g(a) = -a**2 + 11*a - 6. Let w be g(10). Factor 2*u**w + 2*u**i - 3*u**3 - 1/2*u**5 - 1/2*u + 0.
-u*(u - 1)**4/2
Let a(c) be the third derivative of -c**8/26880 - c**4/12 - 4*c**2. Let o(y) be the second derivative of a(y). Let o(q) = 0. Calculate q.
0
Let l = -9 - -24. Factor 3*p + l*p**4 + 9*p**3 - 31*p**4 - 9*p**2 + 13*p**4.
-3*p*(p - 1)**3
Suppose -2*u + 4/3*u**2 + 2/3 = 0. Calculate u.
1/2, 1
What is x in -7 + 3 - 8 - 4*x**2 - 16*x + 0*x = 0?
-3, -1
Let b = -18 - -6. Let k be 0/((b/(-3))/4). Determine i so that -1/2*i**3 - 1/4*i**2 + 0*i + k - 1/4*i**4 = 0.
-1, 0
Suppose -6*x**3 - 3*x**2 - 4*x**3 - 3*x**2 + 7*x**3 = 0. Calculate x.
-2, 0
Factor 62*p**2 - 2*p**3 - 65*p**2 + 6*p + 3*p**5 + 3*p**4 - 7*p**3.
3*p*(p - 1)**2*(p + 1)*(p + 2)
Let j(s) be the second derivative of -1/4*s**4 + 0 + 3*s**2 - 8*s + 1/2*s**3. Factor j(w).
-3*(w - 2)*(w + 1)
Let w be (-2 - (2 + -1)) + 10. Factor 24*u + w*u**2 + 3*u**3 + 14*u**2 - 6*u**2 + 12.
3*(u + 1)*(u + 2)**2
Let m(s) be