 4/5*x**3.
4*x**2*(x + 1)/5
Let h(t) be the second derivative of t**6/15 + 8*t**5/35 + 11*t**4/42 + 2*t**3/21 + 7*t. Suppose h(x) = 0. Calculate x.
-1, -2/7, 0
Let t(q) = 4*q**4 - 44*q**3 + 3*q**2 + 44*q + 12. Let m(o) = -o**4 + 15*o**3 - o**2 - 15*o - 4. Let n(g) = 8*m(g) + 3*t(g). Let n(v) = 0. Calculate v.
-1/2, 2
Let j = -2/15 + 4/5. Suppose -5*l = 3*o + 2, -3*l - 4*o = -0*l + 10. Factor 0*k + 0 - 2/3*k**4 - 2/3*k**5 + j*k**l + 2/3*k**3.
-2*k**2*(k - 1)*(k + 1)**2/3
Let i(p) = -8*p**3 + 8*p**2 + 12*p - 6. Let q(r) = 7*r**3 - 9*r**2 - 13*r + 6. Let o(b) = 3*i(b) + 2*q(b). Factor o(j).
-2*(j - 1)*(j + 1)*(5*j - 3)
What is v in 4 + 0*v + v + 2 + 8*v + 3*v**2 = 0?
-2, -1
Find v such that -3*v**2 + 7*v**2 - 4*v**4 + 2*v**2 + 10*v**2 = 0.
-2, 0, 2
Suppose i = -4*i - 20. Let b be (i/(-3))/((-2)/(-3)). Find s such that -3*s + 2*s**b - 6*s**2 - 1 - s**3 + s**2 = 0.
-1
Let p(v) be the first derivative of 9*v**5/80 - 5*v**4/16 + v**3/8 + 3*v**2/8 + v - 5. Let a(f) be the first derivative of p(f). Factor a(q).
3*(q - 1)**2*(3*q + 1)/4
Let x be 936/405 - 2/(-15). Factor x*j**3 + 0 + 0*j + 4/9*j**2 + 2*j**4.
2*j**2*(j + 1)*(9*j + 2)/9
Let j = 1 + 2. Suppose -3*p - 3 = -3*m, p - j*p = -5*m + 14. Factor 2/3*q**2 + 0 - 2/3*q**p + 0*q.
-2*q**2*(q - 1)/3
Let j be ((-3)/(-2))/(21/56). Let o = -2 + j. Factor 1/2*y**5 + 3*y**3 + 0 + o*y**4 + 1/2*y + 2*y**2.
y*(y + 1)**4/2
Let z be (6/(-10))/(810/(-300)). Factor -z*k - 2/9*k**2 + 4/9.
-2*(k - 1)*(k + 2)/9
Let z = 28 + -32. Let h = z - -6. Solve 4/3*a**h + 5/3*a + 1/3*a**3 + 2/3 = 0 for a.
-2, -1
Let t(l) be the first derivative of l**6/3 - 6*l**5/5 + 3*l**4/2 - 2*l**3/3 + 11. Find w such that t(w) = 0.
0, 1
Let h(x) be the third derivative of -2*x**7/105 + x**6/5 + x**5/15 - x**4 + 39*x**2. Suppose h(w) = 0. Calculate w.
-1, 0, 1, 6
Suppose 0 = -z - 4 + 12. Let -3*r + 12*r**3 + z*r**2 - 2*r + r = 0. What is r?
-1, 0, 1/3
Suppose -96/5*v**2 - 12*v - 8/5 - 44/5*v**3 = 0. What is v?
-1, -2/11
Let r(l) = l**4 - l**2 - l - 1. Let j(n) = 6*n**4 + 9*n**3 + 3*n**2 - 3*n - 3. Let h(x) = j(x) - 3*r(x). Find u such that h(u) = 0.
-2, -1, 0
Let k = 10 - 1. Find q, given that 7 + k + 2*q**2 - 12*q + 2 = 0.
3
Let t(l) be the second derivative of l**6/300 + 2*l**5/75 + l**4/12 + 2*l**3/15 + l**2 + 3*l. Let k(x) be the first derivative of t(x). Factor k(j).
2*(j + 1)**2*(j + 2)/5
Let o be 21/(-77) + 210/528. Find l, given that -o*l - 3/8*l**3 + 3/8*l**2 + 1/8*l**4 + 0 = 0.
0, 1
Let n(w) be the second derivative of -7/6*w**4 + 0 - 2*w - 4/7*w**2 + 4/3*w**3. Solve n(x) = 0 for x.
2/7
Let 4*x**3 + 3*x**2 + 4*x**3 + x**3 = 0. Calculate x.
-1/3, 0
Suppose 4*b = b + 12. Let c(l) = -l + 4. Let n be c(b). Factor 1/2*k**2 + 1/2*k**4 + n*k + 0 - k**3.
k**2*(k - 1)**2/2
Determine u so that -2/3*u**3 - 14/3*u**2 + 0*u + 8/3 + 2*u**4 + 2/3*u**5 = 0.
-2, -1, 1
Factor 2*p**4 - 2*p + 2*p + 2*p**3 - 2*p**2 - 2*p.
2*p*(p - 1)*(p + 1)**2
Let p(a) be the first derivative of -a**5/5 + a**4/4 + 7*a**3/3 - a**2/2 - 6*a + 36. Find k, given that p(k) = 0.
-2, -1, 1, 3
Let y = 784 + -8616/11. Suppose 8/11*n**3 + y*n**4 - 4/11*n + 2/11 - 6/11*n**2 = 0. Calculate n.
-1, 1/2
Let m(u) be the third derivative of u**8/2240 - u**7/168 + u**6/80 + 9*u**5/40 + 5*u**4/24 - 8*u**2. Let a(n) be the second derivative of m(n). Factor a(f).
3*(f - 3)**2*(f + 1)
Suppose 2*c = 3*j - 15, -c - 15 = -j + 3*c. Let z(a) be the second derivative of -1/42*a**4 + 4/21*a**j - 2*a - 4/7*a**2 + 0. Find v, given that z(v) = 0.
2
Let n(v) = -v**2 + 6*v - 4. Let x(j) = 6*j**2 - 42*j + 27. Let g(t) = -27*n(t) - 4*x(t). Factor g(d).
3*d*(d + 2)
Suppose 2 + 1 = k. Suppose 2*s + 2*n = n + 3, -k*n = -9. Find m, given that 2/7*m**4 + 2/7*m**3 - 2/7*m**2 + 0 - 2/7*m**5 + s*m = 0.
-1, 0, 1
Factor -4/13 - 22/13*o - 4*o**3 - 28/13*o**4 - 48/13*o**2 - 6/13*o**5.
-2*(o + 1)**4*(3*o + 2)/13
Let h be 5 - ((-30)/(-5) + -1). Factor -6/5*t**3 + h*t - 3/5*t**2 - 3/5*t**4 + 0.
-3*t**2*(t + 1)**2/5
Let x(o) be the first derivative of 0*o - o**2 - 7/6*o**6 + 23/5*o**5 + 13/3*o**3 + 3 - 27/4*o**4. Solve x(z) = 0 for z.
0, 2/7, 1
Let t be (-3)/7 + (-20)/35. Let l be (-4 + 11/3)/t. Factor 0 + q**4 - l*q**2 + 4/3*q**3 - 2/3*q.
q*(q + 1)**2*(3*q - 2)/3
Let r(o) = 15*o**2 - 54*o + 294. Let l(n) = 17*n**2 - 53*n + 293. Let t(a) = 6*l(a) - 7*r(a). Factor t(u).
-3*(u - 10)**2
Let f(r) be the third derivative of -r**5/330 + r**4/22 + 38*r**2. Solve f(k) = 0.
0, 6
Let v(r) be the third derivative of -1/60*r**4 + 2*r**2 + 1/900*r**6 + 1/3*r**3 + 0*r + 0 + 0*r**5. Let c(g) be the first derivative of v(g). Factor c(s).
2*(s - 1)*(s + 1)/5
Suppose 0 = 5*f - 4*f - 3. Factor 9*l**3 + 2*l - 2*l**5 - 10*l**f - 3*l**4 + l**5 + 3*l**2.
-l*(l - 1)*(l + 1)**2*(l + 2)
Let c(y) = y**3 + 3*y**2 - 4*y + 2. Let b be c(-4). Solve 4*i**2 + i - 4*i - b*i**3 + i = 0.
0, 1
Let z(v) = v - 1. Let s be z(3). Suppose -4 = x - 2*m, 6*m = s*m + 12. Factor 4/7*o - 2/7 - 2/7*o**x.
-2*(o - 1)**2/7
Suppose 6 = 2*s - s. Let g = 8 - s. Factor -4 + g*f**3 + 32*f**5 + 16*f**4 + 4.
2*f**3*(4*f + 1)**2
Let j(y) be the third derivative of y**9/52920 - y**8/7840 + y**7/2940 - y**6/2520 + y**4/24 - 3*y**2. Let b(t) be the second derivative of j(t). Factor b(f).
2*f*(f - 1)**3/7
Let n be (4/(-26))/1 - (-147)/195. Factor -2/5 - n*x - 1/5*x**2.
-(x + 1)*(x + 2)/5
Let u(w) be the second derivative of -1/60*w**5 + 0 + w + 1/36*w**4 + 0*w**3 + 0*w**2. Let u(j) = 0. Calculate j.
0, 1
Let -8*p + 2*p - 3*p**4 - 38*p**3 + 3*p**2 + 44*p**3 = 0. Calculate p.
-1, 0, 1, 2
Suppose -o + 0*o = 0. Let g(a) be the first derivative of o*a**2 - 1 - 1/3*a**3 + a. Suppose g(w) = 0. Calculate w.
-1, 1
Let a(v) be the third derivative of 0*v + 1/100*v**6 + v**2 + 1/50*v**5 + 1/525*v**7 + 0 + 1/60*v**4 + 0*v**3. Factor a(s).
2*s*(s + 1)**3/5
Let x(q) = 2*q**4 - 16*q**3 + 14*q. Let t(b) = 4*b**4 - 32*b**3 + b**2 + 27*b. Let m(i) = 2*t(i) - 5*x(i). Factor m(w).
-2*w*(w - 8)*(w - 1)*(w + 1)
What is h in -12*h + 22*h - 6*h - 16*h**2 + 4*h**5 - 3*h**3 + 11*h**4 = 0?
-2, 0, 1/4, 1
Let r(n) be the second derivative of n**7/231 + 2*n**6/165 - n**4/33 - n**3/33 - 2*n. Factor r(z).
2*z*(z - 1)*(z + 1)**3/11
Suppose 5 = 5*b, -4*j - 2*b - b = -15. Determine x, given that 12 - 3*x**3 - 20*x**2 + 11*x**2 + 6*x**j = 0.
-1, 2
Let d(s) = -4*s**2 + 16*s - 7. Let h(p) = 4*p**2 - 16*p + 6. Let u(o) = 6*d(o) + 5*h(o). Solve u(q) = 0 for q.
1, 3
Let p(r) be the third derivative of -r**7/945 + r**6/540 + r**5/90 - r**4/108 - 2*r**3/27 - r**2 - 20*r. Let p(n) = 0. Calculate n.
-1, 1, 2
Let l(x) = -7*x**3 + 5*x**2 - 5. Let k = -5 + 2. Let h(g) = 4*g**3 - 3*g**2 + 3. Let q(u) = k*l(u) - 5*h(u). Factor q(j).
j**3
Solve 47*j**2 - 3*j**2 - 39*j**3 - 49*j - 13*j**3 + 20*j**4 + 37*j = 0.
0, 3/5, 1
Let x(f) = f**2 - 3*f. Let l be x(3). Let w(r) be the second derivative of l*r**2 - 3*r + 0*r**4 + 0 + 1/40*r**5 - 1/12*r**3. Suppose w(u) = 0. What is u?
-1, 0, 1
Factor 7/2*j - j**2 + 1 - 7/2*j**3.
-(j - 1)*(j + 1)*(7*j + 2)/2
Determine b so that -1/2*b**5 + b**3 - b**2 - 1/2*b + 1/2*b**4 + 1/2 = 0.
-1, 1
Let y be 0/(2/(-4)*-4). Suppose 5*w - 8*w = y. Factor 1 + 3*a**2 + w - 4*a**2.
-(a - 1)*(a + 1)
Let x(a) be the third derivative of a**5/80 + a**4/8 - 14*a**2. What is n in x(n) = 0?
-4, 0
Let g(u) be the first derivative of -2/21*u**3 + 4 + 2/7*u + 1/14*u**4 - 1/7*u**2. Suppose g(s) = 0. What is s?
-1, 1
Suppose -5*v = -2 + 2. Factor -2*y**2 + v - 4/3*y + 10/3*y**3.
2*y*(y - 1)*(5*y + 2)/3
Let v(d) be the first derivative of -d**6/2 + 6*d**5/5 + 3*d**4 - 8*d**3 - 44. Factor v(m).
-3*m**2*(m - 2)**2*(m + 2)
Let v(j) be the third derivative of j**8/6720 - j**6/1440 - 2*j**3/3 - 4*j**2. Let a(i) be the first derivative of v(i). Factor a(g).
g**2*(g - 1)*(g + 1)/4
Let g(u) be the third derivative of u**8/504 + 2*u**7/105 + 7*u**6/90 + 8*u**5/45 + u**4/4 + 2*u**3/9 + 3*u**2. Factor g(n).
2*(n + 1)**4*(n + 2)/3
Let q(x) = -x**2 - 9*x - 10. Let u be q(-7). Suppose -u*s + 24 = 8. Factor -2 - s*l**4 - 6*l**3 - 10*l + 0*l**3 + 0*l**4 - 8*l**3 - 18*l**2.
-2*(l + 1)**3*(2*l + 1)
Let c(n) be the first derivative of -n**5/80 - n**4/24 - n**3/24 - 3*n + 3. Let p(b) be the first derivative of c(b). Factor p(r).
-r*(r + 1)**2/4
Let j = 4 + 13. Suppose -k + j = -3*h, -4*h - 14 = 5*k - 4. What is a in 2/5 + 1/5*a - 1/5*a**k = 0