 + 2/5*s**2.
-2*s*(s - 1)**2*(s + 1)/5
Let i(d) be the third derivative of 0 + 0*d + 0*d**3 + 1/240*d**5 + 4*d**2 + 1/48*d**4. Suppose i(f) = 0. Calculate f.
-2, 0
Let f be (-8)/(-14) - 156/910. Solve -2*m**2 + f + 2/5*m + 6/5*m**3 = 0 for m.
-1/3, 1
Let j(t) be the third derivative of 4*t**2 + 0 + 0*t + 0*t**3 + 1/42*t**4 + 1/735*t**7 + 1/42*t**5 + 1/105*t**6. Factor j(h).
2*h*(h + 1)**2*(h + 2)/7
Let g = 4736/9 - 526. Factor 2/9*z**4 - g*z**3 + 2/9*z + 0 - 2/9*z**2.
2*z*(z - 1)**2*(z + 1)/9
Let 4/7*d**3 + 6/7*d**4 + 0 + 2/7*d**5 + 0*d + 0*d**2 = 0. Calculate d.
-2, -1, 0
Suppose m = 4*f - 0*f + 36, 0 = 2*m. Let c be 9/(-3)*4/f. Find k, given that -c*k - 2/3*k**2 + 0 = 0.
-2, 0
Let g(q) be the third derivative of q**5/30 - q**4/6 + 11*q**2. Let g(f) = 0. Calculate f.
0, 2
Let a(f) = -44*f**2 + 4*f + 16. Let r(s) = -9*s**2 + s + 3. Let v(m) = 5*a(m) - 24*r(m). Factor v(d).
-4*(d - 1)*(d + 2)
Let a(g) be the second derivative of -5*g**7/42 + 2*g**6/3 - g**5 - 5*g**4/6 + 25*g**3/6 - 5*g**2 - 2*g. Factor a(b).
-5*(b - 2)*(b - 1)**3*(b + 1)
Let g = 7/3 - 2. Let i(u) be the first derivative of 0*u - 1/9*u**3 - g*u**2 + 5/12*u**4 + 1/15*u**5 + 1 - 1/6*u**6. Determine v so that i(v) = 0.
-1, -2/3, 0, 1
Let z(k) = 2*k**5 - 2*k**3 + 7. Let c(o) = -8 - o**3 + 10 + o**5 + 1. Let w = 10 - 16. Let g(i) = w*z(i) + 14*c(i). Factor g(q).
2*q**3*(q - 1)*(q + 1)
Let n(u) = u**3 - 9*u**2 + 8*u + 6. Let h be n(8). Let d be ((-9)/24)/(h/(-4)). Determine k so that 5/4*k + d + k**2 = 0.
-1, -1/4
Let y(i) = -i**2 + 9*i - 1. Let l be y(8). Let r = l - 3. Solve -4*f**2 + r*f - 4*f + 2*f + 2*f**3 = 0.
0, 1
Let z(h) be the third derivative of -13/132*h**4 - 5*h**2 - 2/165*h**5 + 0 + 0*h + 1/220*h**6 - 2/11*h**3. What is y in z(y) = 0?
-1, -2/3, 3
Let u(z) be the second derivative of -7*z**6/360 - 19*z**5/180 - z**4/9 + 2*z**3/9 - 2*z**2 + 2*z. Let b(x) be the first derivative of u(x). Factor b(a).
-(a + 1)*(a + 2)*(7*a - 2)/3
Let p(s) = s**2. Let a(l) = -l**3 + 5*l**2 - 7*l. Let r(b) = -a(b) - 3*p(b). Let k be r(7). Determine q so that -q**3 - 1/2*q**2 + k*q - 1/2*q**4 + 0 = 0.
-1, 0
Suppose -4*r + 10 = g, 2*g - 8 = -4. Let l(q) be the second derivative of 1/36*q**4 + 0 - 1/30*q**5 + 0*q**3 + 1/90*q**6 - r*q + 0*q**2. What is i in l(i) = 0?
0, 1
Let s(i) = 5*i - 1. Let z be s(1). Let c be 234/135 - 3*6/45. Suppose -c + 14/3*h**z + 38/3*h**3 + 2/3*h + 10*h**2 = 0. Calculate h.
-1, 2/7
Let u(r) = -r**3 + 3*r**2 - r + 2. Let k be u(3). Let s be k/(3 - (-12)/(-2)). Suppose -1/3*d**5 + 1/3*d**3 - 1/3*d**4 + s*d**2 + 0 + 0*d = 0. What is d?
-1, 0, 1
Let u(j) be the third derivative of 2/5*j**5 + 1/10*j**7 + 0*j**3 + 0*j + 1/2*j**4 - 19/40*j**6 + j**2 + 0. Find n such that u(n) = 0.
-2/7, 0, 1, 2
What is j in -4*j + 0*j**3 - 91*j**2 + j**3 + 89*j**2 + 8 = 0?
-2, 2
Suppose 4*q + 0*q = 60. Let h be (4 - q/4)*0. Factor 2/5*v**3 - 1/5*v**4 + 0 - 1/5*v**2 + h*v.
-v**2*(v - 1)**2/5
Factor 0 + 6/11*t**3 + 8/11*t**4 + 0*t**2 + 2/11*t**5 + 0*t.
2*t**3*(t + 1)*(t + 3)/11
Let h = 5 - 2. Factor 4*j**4 - j**5 - h*j - 2*j**2 + 2*j**5 + 2*j - 2*j**4.
j*(j - 1)*(j + 1)**3
Let f(q) = -3*q**3 + 8*q**2 + 10*q + 4. Let u(x) = 5*x**3 - 12*x**2 - 15*x - 6. Let s(a) = 8*f(a) + 5*u(a). Solve s(v) = 0.
-2, -1
Let b be 2/(-19) - 8/(-76). Factor 3/5*c**5 + b*c + 0 + 0*c**3 + 0*c**2 - 9/5*c**4.
3*c**4*(c - 3)/5
Let s(x) = 6*x**3 - 32*x**2 - 8. Let p(r) = 4*r**3 - 21*r**2 - 5. Let b(z) = 8*p(z) - 5*s(z). Factor b(j).
2*j**2*(j - 4)
Factor -98/13*g + 28/13*g**2 + 0 - 2/13*g**3.
-2*g*(g - 7)**2/13
Factor 0*s + s**2 + s**3 + 5*s**2 - 3*s**2 + 2*s.
s*(s + 1)*(s + 2)
Let c be -3 + (-66)/(-54) - -2. Determine y so that -2/3*y**2 - c*y - 2/3*y**3 - 2/9*y**4 + 0 = 0.
-1, 0
Let b(g) = -g**2 - 2*g. Let o be b(-2). Factor 32 + 104*v**2 - 23*v**3 + o*v**3 - 13*v**3 + 16*v**2 - 112*v.
-4*(v - 2)*(3*v - 2)**2
Let w = -7/6 + 61/42. Factor w + 5/7*h + 1/7*h**3 + 4/7*h**2.
(h + 1)**2*(h + 2)/7
Let m(c) be the second derivative of -5*c**4/12 - 15*c**3/2 + 25*c**2 - 10*c. Suppose m(h) = 0. What is h?
-10, 1
Let f(d) = 10*d**4 + d**3 + 9*d**2 - 9*d. Let i(t) = -t**4 - t**2 + t. Let u(b) = 2*f(b) + 18*i(b). Solve u(m) = 0 for m.
-1, 0
Factor -8/9*k**5 + 0*k + 0 + 10/3*k**4 - 8/9*k**2 - 8/3*k**3.
-2*k**2*(k - 2)**2*(4*k + 1)/9
Let m(d) be the second derivative of -5*d**7/42 + d**6/6 + d**5/4 - 5*d**4/12 + 5*d. What is p in m(p) = 0?
-1, 0, 1
Let o be (68/28 - 2) + (-34)/(-14). Factor 0 - o*q**3 + 0*q - 50/7*q**4 - 2/7*q**2.
-2*q**2*(5*q + 1)**2/7
Determine w so that -6/7*w + 4/7 + 0*w**2 + 2/7*w**3 = 0.
-2, 1
Let i = -108/13 + 229/26. Factor -i - 1/2*h + 1/2*h**3 + 1/2*h**2.
(h - 1)*(h + 1)**2/2
Let h(k) be the first derivative of 12*k - 12*k**2 + 5*k**3 - 3/4*k**4 + 4. Factor h(t).
-3*(t - 2)**2*(t - 1)
Let x(a) be the third derivative of 2*a**7/105 + a**6/6 + 7*a**5/15 + a**4/2 + 15*a**2. Find c, given that x(c) = 0.
-3, -1, 0
Solve -9/2*i**5 + 29/2*i**4 + 0*i**2 - 3*i**3 + 0 + 0*i = 0 for i.
0, 2/9, 3
Let k be 2/6 + 11/330*35. Suppose 11/2*j**2 - 3/2 - 5/2*j - k*j**3 = 0. Calculate j.
-1/3, 1, 3
Let p(x) be the third derivative of 0*x**4 - 1/280*x**7 + 0*x**5 + 0*x + 0*x**3 + 0 - 1/80*x**6 - 4*x**2 + 3/448*x**8. Determine v, given that p(v) = 0.
-2/3, 0, 1
Let p(j) = j**3 + 7*j**2 - 18*j + 4. Let l be p(-9). Let w(g) be the second derivative of 0 + 3*g + 1/2*g**4 + 1/10*g**5 + 0*g**3 - l*g**2. Factor w(y).
2*(y - 1)*(y + 2)**2
Factor -3*a**4 + 0*a**3 + 3*a**2 + 0 + 3/2*a**5 - 3/2*a.
3*a*(a - 1)**3*(a + 1)/2
Let x(v) be the second derivative of v**5/195 + v**4/156 - v**3/39 - v**2 - v. Let t(h) be the first derivative of x(h). Find a such that t(a) = 0.
-1, 1/2
Let o(j) be the third derivative of j**6/30 - j**5/5 + j**4/3 + j**2 - 3. Determine s, given that o(s) = 0.
0, 1, 2
Let i = -7 + 10. Let -3*k**3 + 2*k**2 + 0*k + k**3 - 2*k + 4*k**i - 2 = 0. Calculate k.
-1, 1
Let g(l) be the third derivative of -l**6/420 + l**5/30 - 5*l**4/28 + 3*l**3/7 - 6*l**2. What is t in g(t) = 0?
1, 3
Let a = 7/43 - 146/1161. Let p(l) be the first derivative of 2/45*l**5 - a*l**6 + 0*l**2 + 1/18*l**4 + 2 - 2/27*l**3 + 0*l. Factor p(n).
-2*n**2*(n - 1)**2*(n + 1)/9
Let t be (-2)/(-7)*7/40. Let u(p) be the second derivative of -3*p + 1/6*p**3 - t*p**5 + 0*p**4 + 0*p**2 + 0. Find b, given that u(b) = 0.
-1, 0, 1
Let f(w) = -3*w - 3. Let k be f(-3). Factor -2*g**4 - g**3 + k*g**4 + 2*g**5 + 3*g**3.
2*g**3*(g + 1)**2
Suppose 6*o + 4*y = 3*o - 6, 0 = 4*o + 3*y + 1. Let c = 0 + o. Factor -3*x**2 + 0*x**2 + 4*x**c - 6*x + 4 + x**2.
2*(x - 2)*(x - 1)
Let d(z) = -7*z**3 - 8*z**2 + 9*z + 6. Let h(j) = 0 - 12 + 33*j**2 - 12 - 46*j + 10*j + 27*j**3. Let v(i) = -9*d(i) - 2*h(i). Factor v(r).
3*(r - 1)*(r + 1)*(3*r + 2)
Suppose -5*t = -3*g - 7, -3*t - g + 11 = 4*g. What is i in 2*i + 3*i + i + t*i**2 - 2*i = 0?
-2, 0
Let o(d) be the first derivative of 5*d**4 + 40*d**3/3 + 25*d**2/2 + 5*d + 24. Solve o(h) = 0 for h.
-1, -1/2
Solve -62*j**4 + 57*j**2 - 39*j**3 + 11 - 7*j**4 - 7*j + 1 + 67*j - 21*j**5 = 0.
-2, -1, -2/7, 1
Let p(h) = 3*h**4 + 45*h**3 - 69*h**2 - 45*h + 39. Let n(i) = i**4 + 11*i**3 - 17*i**2 - 11*i + 10. Let c(t) = -9*n(t) + 2*p(t). Factor c(u).
-3*(u - 1)**2*(u + 1)*(u + 4)
Let f = -37 - -37. Let l(c) be the second derivative of 0*c**5 + 1/63*c**7 - 1/45*c**6 + f*c**4 + 0*c**3 + 3*c + 0*c**2 + 0. Factor l(t).
2*t**4*(t - 1)/3
Let b = -7/29 + 121/261. Let h(k) be the first derivative of 1/18*k**4 + 1/3*k**2 - 2/9*k**3 + 1 - b*k. Let h(d) = 0. What is d?
1
Let n = -97/1590 + 5/53. Let d(m) be the second derivative of 3*m - 2/15*m**3 + 0 - n*m**4 - 1/5*m**2. Suppose d(l) = 0. What is l?
-1
Factor 48*w**3 + 196 - 395*w + 4*w**4 + 59*w + 71*w**2 + 17*w**2.
4*(w - 1)**2*(w + 7)**2
Suppose 2*j + 5*u = 10, 4*u = 2*j - 0*j - 46. Suppose -j = -6*r + r. Factor 2*v**4 - v**2 + v**2 + v**2 - r*v**4.
-v**2*(v - 1)*(v + 1)
Let v(u) = u - 1. Let i = -4 + 10. Let w be v(i). Factor 5*y**w + 4*y**5 - 6*y**2 + 3*y**4 + 6*y**2.
3*y**4*(3*y + 1)
Let r = 93/2 - 331/6. Let l = r + 9. Find b such that b**4 - b**3 + 0*b + l*b**2 + 0 - 1/3*b**5 = 0.
0, 1
Find h such that 0*h - 1/5*h**4 + 0 + 1/5*h**2 + 0*h**3 = 0.
-1, 0, 1
Let i = 41/48240 - -2/603. Let m(t) be the third derivative of 0 + 0*t**3 + 0*t**5 - i*t**6 + 0*t**4 - 1/420*t**7 + 0*t - t**2. Let m(d) = 0. What