93*o = 0. What is o?
-3, -2, 1/4, 1
Let b(k) = -9*k**2 + 3*k. Let h = 23 + -29. Let p(v) = 8*v**2 - 2*v. Let w(r) = h*p(r) - 5*b(r). Factor w(j).
-3*j*(j + 1)
Let z be 12/4*(-10745)/(-135). Let t = 239 - z. Factor 2/9*c**3 + 0 - t*c + 0*c**2.
2*c*(c - 1)*(c + 1)/9
Let z(w) = -w - 1. Let h(t) = t**3 + 4*t**2 + 5*t + 6. Let g(j) = -h(j) - 3*z(j). Let v be g(-4). Factor 9*m + v*m - 2*m**3 - 2*m**2 - 10*m.
-2*m*(m - 1)*(m + 2)
Let g(f) be the first derivative of f**6/40 - 3*f**5/40 + f**3/4 - 3*f**2/8 + 8*f - 10. Let t(p) be the first derivative of g(p). Solve t(n) = 0.
-1, 1
Let q(u) be the third derivative of u**8/35280 - u**7/17640 + 11*u**5/60 - 13*u**2. Let a(w) be the third derivative of q(w). Factor a(n).
2*n*(2*n - 1)/7
Let j = -9832/3 + 3278. Let m = 6/95 - -136/855. Factor -j*c - m*c**2 - 4/9.
-2*(c + 1)*(c + 2)/9
Let g(b) be the third derivative of -1/1155*b**7 + 0*b**3 + 0*b - 2/55*b**5 + 2/33*b**4 + 1/110*b**6 + 0 - 2*b**2. Find x, given that g(x) = 0.
0, 2
Let m = 38 - 42. Let a(y) = -5*y**4 - 4*y**3 + 2*y**2 - 9. Let l(p) = -p**4 - p**2 - p - 1. Let w(i) = m*l(i) + a(i). What is d in w(d) = 0?
-5, -1, 1
Let d(w) be the third derivative of -2/5*w**4 - 9/5*w**3 + 29*w**2 + 0 + 1/50*w**5 + 0*w. Factor d(t).
6*(t - 9)*(t + 1)/5
Suppose 3*r + 14 = -5*g, -g - 10 = 4*r - 3*g. Let i(l) = 4*l**2 - 3*l - 1. Let u(o) = 20*o**2 - 16*o - 4. Let k(j) = r*u(j) + 16*i(j). Factor k(q).
4*(q - 1)*(q + 1)
Let s(l) be the third derivative of -l**7/105 - 2*l**6/55 - 73*l**2. Find v such that s(v) = 0.
-24/11, 0
Let q(n) be the first derivative of -n**7/42 - n**6/12 - n**5/12 + 5*n**2 - 9. Let w(b) be the second derivative of q(b). Factor w(g).
-5*g**2*(g + 1)**2
Let g(c) = -c**3 - 1. Let m(o) = -5*o**3 - 2*o**5 - 10*o**4 - 20*o + 10*o - 20*o**2 - 13*o**3. Let t(u) = 4*g(u) + 2*m(u). Factor t(k).
-4*(k + 1)**5
Let o(j) be the third derivative of j**8/30240 - j**7/2520 + j**6/540 - j**5/5 + 21*j**2. Let b(y) be the third derivative of o(y). Let b(q) = 0. What is q?
1, 2
Let c(t) = 3*t**2 + 19*t + 2. Let l be c(0). Factor 2/5*p + 0 + 2/15*p**l.
2*p*(p + 3)/15
Let d be (21/28)/(33/16). Suppose 15*z - 84 = -39. Solve d - 2/11*u - 4/11*u**2 + 2/11*u**z = 0.
-1, 1, 2
Let g be (3 - (-90)/(-25)) + 6/10. Let x(a) be the first derivative of -3/8*a**4 + 2 + g*a - a**3 - 3/4*a**2. Find p such that x(p) = 0.
-1, 0
Let a(d) be the third derivative of d**6/15 - 37*d**5/15 + 17*d**4/6 + 12*d**3 - 3*d**2 - 73*d. Factor a(w).
4*(w - 18)*(w - 1)*(2*w + 1)
Let s(x) = -2*x**4 - 9*x**3 + 32*x**2. Let i(r) = 2*r**4 + 10*r**3 - 32*r**2. Let n(o) = -6*i(o) - 4*s(o). Determine k so that n(k) = 0.
-8, 0, 2
Let p be (6 - -2) + (-3)/1. Solve -5*r**3 + p*r - 18 - 10*r**2 + 21 + 7 = 0.
-2, -1, 1
Factor 0 + 26/9*f - 2/9*f**2.
-2*f*(f - 13)/9
Suppose 13 = 2*c - s, 0 = -0*s + s + 3. Let f(b) = b**3 - 5*b**2 + b - 2. Let h be f(c). Solve -2 + a**3 - a + 2*a**2 + a**h - a = 0.
-1, 1
Let q be 5719/1118 + -2*(-5)/(-2). Let z = 37/130 + q. Factor 2/5*g**2 + 2/5*g**3 - 2/5*g**4 - z*g + 0.
-2*g*(g - 1)**2*(g + 1)/5
Let w(f) be the third derivative of -f**7/35 - f**6/60 - f**5/240 - f**4/4 - 7*f**2. Let r(j) be the second derivative of w(j). Factor r(g).
-(12*g + 1)**2/2
Let b(n) = n + 4. Let v be b(8). Let k be 3/v*(11 - -1). Determine f, given that -4*f**2 + 3*f - 5*f**2 - 5*f**k + 2*f**3 + 9 = 0.
-3, -1, 1
Let x = 22854 + -22854. Factor 2/9*r**5 + x*r**2 + 0*r + 0 + 0*r**3 - 2/9*r**4.
2*r**4*(r - 1)/9
Factor 0 + 6/13*c**3 + 2/13*c**4 - 6/13*c - 2/13*c**2.
2*c*(c - 1)*(c + 1)*(c + 3)/13
Let k(y) be the third derivative of 0*y + 0*y**5 + 1/8*y**4 - 1/3*y**3 - 1/120*y**6 - y**2 + 0. Suppose k(r) = 0. What is r?
-2, 1
Let x be (270/40 + -7)*-8. Let f(a) be the first derivative of -3/2*a**4 + 0*a + 0*a**2 + 4/3*a**3 - x + 2/5*a**5. Factor f(y).
2*y**2*(y - 2)*(y - 1)
Let q(x) be the first derivative of -x**3/9 - 5*x**2 - 29*x/3 - 133. Determine v so that q(v) = 0.
-29, -1
Let b(c) = 4*c**3 - 4 - 5*c**3 + 2*c**2 - 4*c + 0 - 5*c**2. Let x be b(-3). Factor x - 8 - 3*k**2.
-3*k**2
Let f be (2 + -2)*(-4)/8. Let t = 1861 + -1858. Factor -10/3*h**2 + f - h**t - h.
-h*(h + 3)*(3*h + 1)/3
Let p(x) = -3*x**3 - 12*x**2 + 12*x - 11. Let d be p(-5). Let t(g) be the first derivative of 5/7*g**3 + 3/14*g**2 + 6 + 0*g + 3/7*g**d. Factor t(z).
3*z*(z + 1)*(4*z + 1)/7
Let o(f) be the third derivative of f**7/420 - f**6/45 + f**5/15 - 5*f**3/6 + 10*f**2. Let g(v) be the first derivative of o(v). Factor g(y).
2*y*(y - 2)**2
Let n(g) be the third derivative of -4/45*g**5 + 0 - 12*g**2 + 1/36*g**6 + 0*g**3 + 0*g - 1/9*g**4. Determine l so that n(l) = 0.
-2/5, 0, 2
Find t, given that -69*t**2 - 19*t**2 - 17*t**2 + 2*t**3 - 11*t**2 - 118*t = 0.
-1, 0, 59
Let d = -9 + 13. Let h(z) = z**2 - 6*z + 10. Let c be h(d). Find t such that -14 + 4 + 12*t - 8 - 2*t**c = 0.
3
Let i = -10/291 - -1591/37830. Let p(a) be the second derivative of 1/39*a**6 + 0 + 0*a**3 + i*a**5 + 0*a**2 - 1/78*a**4 + 1/91*a**7 - 6*a. Factor p(q).
2*q**2*(q + 1)**2*(3*q - 1)/13
Let g(u) = -5*u**5 + 14*u**3 - 6*u. Let d(n) = 20*n**5 - 55*n**3 + 25*n. Let v(k) = 6*d(k) + 25*g(k). Factor v(j).
-5*j**3*(j - 2)*(j + 2)
Let q(k) be the second derivative of -16/27*k**3 + 16/9*k**2 - 1/27*k**6 + 19*k + 0 - 14/45*k**5 - 8/9*k**4. Factor q(g).
-2*(g + 2)**3*(5*g - 2)/9
Let -95/2*z**3 + 0 + 5/2*z**4 + 0*z + 85*z**2 = 0. What is z?
0, 2, 17
Let p(b) be the second derivative of 0 + 5*b + 1/24*b**4 - 1/180*b**5 - 1/9*b**3 - 2*b**2. Let z(v) be the first derivative of p(v). Let z(a) = 0. Calculate a.
1, 2
Suppose -4*p**4 + 6101*p - 6101*p - 32*p**3 = 0. Calculate p.
-8, 0
Let i be -1*4/8*-4. Suppose i*r - 1 = h - 2*r, -3*r = 4*h - 15. Factor -3/7*c**h - 24/7 - 18/7*c**2 - 36/7*c.
-3*(c + 2)**3/7
Let f be 2/(-14) + 130/364. Let u(v) be the first derivative of 2/35*v**5 + f*v**4 - 2 + 2/21*v**3 - 4/7*v - 3/7*v**2. Factor u(q).
2*(q - 1)*(q + 1)**2*(q + 2)/7
Determine w, given that -2/5*w**4 + 0 - 128/5*w**2 + 0*w - 32/5*w**3 = 0.
-8, 0
Suppose 0 = 3*x - 4*x + 14. Suppose -x*j + 9*j = -20. Factor 0*v**4 + 3*v**5 - 3*v**4 + 5*v**j.
v**4*(3*v + 2)
Suppose 32*o - 35*o = -213. Solve 3*i + 6*i**3 - 68*i**4 - i**3 + o*i**4 - 11*i**2 = 0.
-3, 0, 1/3, 1
Let r(o) be the first derivative of o**3/3 - 17*o**2/2 + 16*o - 98. Find k such that r(k) = 0.
1, 16
Let y(d) be the first derivative of 2*d**2 - 3*d - 2. Let i be y(2). Let -6*u**3 + 5*u + 2*u - 3*u - 2*u**2 + 4*u**2 - 2*u**4 + 2*u**i = 0. Calculate u.
-1, 0, 1, 2
Suppose 4*q + 8 = 0, -4*q - 2 = 2*v + 2. Let y be -4 + 46/6 - (1 + v). Factor 1/3*w**5 + 1/3 + 1/3*w**4 - 2/3*w**2 - y*w**3 + 1/3*w.
(w - 1)**2*(w + 1)**3/3
Let j be (((-27)/28)/9)/(-18). Let v(m) be the second derivative of 0*m**2 + 5*m + j*m**7 + 9/80*m**5 + 1/24*m**6 + 0 + 1/12*m**3 + 7/48*m**4. Factor v(b).
b*(b + 1)**3*(b + 2)/4
Let q(j) = -102*j + 206. Let z be q(2). Factor -11/3*a - z - 1/3*a**3 - 2*a**2.
-(a + 1)*(a + 2)*(a + 3)/3
Let k = 46 - 44. Factor 3*u**3 - u**3 - u**3 + 8*u**k - 5*u**3.
-4*u**2*(u - 2)
Let o = -486 + 492. Let t(q) be the second derivative of 0*q**3 + 0 + 1/24*q**4 + o*q - q**2. What is r in t(r) = 0?
-2, 2
Let d = 3/904 - -1127/904. Let p(r) be the first derivative of 15/2*r**2 + d*r**4 + 5*r**3 + 11 + 5*r. Factor p(b).
5*(b + 1)**3
Let u(t) be the third derivative of t**6/120 + 2*t**5/15 + 2*t**3/3 - 22*t**2. Let p be u(-8). Factor -v + 0 - v**p + 3/2*v**2 + 3/2*v**3.
-v*(v - 2)*(v + 1)*(2*v - 1)/2
Factor 4*u**3 - 47*u**2 - 178*u**2 + 87*u**2 - 46*u**2.
4*u**2*(u - 46)
Let x = -540 + 544. Let w(a) be the first derivative of 9 + 0*a + 2*a**2 - a**x + 4/3*a**3 - 4/5*a**5. Let w(j) = 0. What is j?
-1, 0, 1
Let k(n) be the first derivative of n**8/6720 - n**7/1680 - n**6/480 + n**5/120 + n**4/24 + 8*n**3/3 - 5. Let v(d) be the third derivative of k(d). Factor v(y).
(y - 2)**2*(y + 1)**2/4
Let r be (-6)/8 - 7230/(-40). Suppose 174 = -3*g + r. Factor -2/3 - 2*i**g + 2*i + 2/3*i**3.
2*(i - 1)**3/3
Let l(q) be the second derivative of 0 - 4/3*q**4 - 11/6*q**3 - 3*q**2 - 3*q. Let j(n) = -3*n**2 - 2*n - 1. Let i(y) = 11*j(y) - 2*l(y). Solve i(c) = 0.
-1, 1
Let l(d) = -14*d - 20. Suppose -2*c - 10 = -3*i, 0 = -4*c - 2*i - 2 - 2. Let g(u) = u**2 - u - 1. Let o(j) = c*g(j) + l(j). Find x, given that o(x) = 0.
-3
Let j(m) be the first derivative 