 3*r**3/2 + 14*r. Let t(z) be the second derivative of w(z). Solve t(m) = 0 for m.
0, 2/5
Suppose 0 - 2/5*u**2 - 82/5*u = 0. What is u?
-41, 0
Suppose 2*n + y + 6 = 23, n + 4*y - 5 = 0. Let g be ((-9)/(-12))/(n/24). Find m such that 3*m**3 - m**5 + 9*m**2 + 5*m**4 - 6*m**4 - 2*m - 8*m**g = 0.
-2, -1, 0, 1
Suppose 284*v - 274*v = 0. Let w(b) be the third derivative of 0*b + 0*b**3 + v + 1/30*b**5 + 1/12*b**4 + 6*b**2. Factor w(n).
2*n*(n + 1)
Let s(l) be the second derivative of -l**7/2205 - l**6/1260 + 4*l**5/315 + l**4/21 + 19*l**2 - l - 4. Let f(b) be the first derivative of s(b). Factor f(z).
-2*z*(z - 3)*(z + 2)**2/21
Let i(o) = 15*o - 9. Let p be i(-5). Let v be (2/(-8))/(-1 - 35/p). Find x such that -1/7*x**3 - v*x**2 - 3/7*x - 1/7 = 0.
-1
Let s(m) = 4*m**2 + 8*m - 4. Let z(f) = -2*f**2 - 8*f + 3. Let h(y) = -3*s(y) - 4*z(y). Suppose h(o) = 0. Calculate o.
0, 2
Let v(q) be the second derivative of q**5/4 + 65*q**4/12 + 80*q**3/3 + 50*q**2 + 159*q. Factor v(n).
5*(n + 1)*(n + 2)*(n + 10)
Suppose 0 = 2*q - 64 - 8. Factor -16*b - 17*b + 8 - q*b**2 + 5*b.
-4*(b + 1)*(9*b - 2)
Find a, given that 1/5*a**2 + 2/5*a + 1/5 = 0.
-1
Let c = 156 - 1245/8. Factor 9/8*i**2 - c*i**4 - 3/4*i + 0 + 0*i**3.
-3*i*(i - 1)**2*(i + 2)/8
Solve -42*q**3 + 24 + 288*q**2 + 168*q - 147/2*q**4 = 0.
-2, -2/7, 2
Let t(k) be the third derivative of 0 + 5/9*k**4 + 1/45*k**6 + 0*k + 0*k**3 + 13/45*k**5 - 2*k**2 - 2/315*k**7. Factor t(m).
-4*m*(m - 5)*(m + 1)*(m + 2)/3
Let v(q) be the second derivative of -4*q**5/15 - 5*q**4/3 + 7*q**3/8 - q**2/6 - q + 27. Determine m so that v(m) = 0.
-4, 1/8
Let v(y) = y - 1. Let o(d) = -d**2 + 5*d + 16. Let z(f) = -o(f) + 2*v(f). Let j be z(6). Factor -2/13*k**3 + j - 4/13*k**2 + 0*k.
-2*k**2*(k + 2)/13
Solve -3*p**3 + 3/2*p**5 - 12*p**2 + 6 + 6*p**4 + 3/2*p = 0.
-4, -1, 1
Let c(t) be the third derivative of -t**5/30 - 45*t**4/2 - 6075*t**3 + 40*t**2 + 4. Find w such that c(w) = 0.
-135
Let u(y) = -y**3 - 29*y**2 - 230*y - 190. Let g(h) = 2*h**3 + 58*h**2 + 459*h + 381. Let k(s) = 6*g(s) + 11*u(s). Find z, given that k(z) = 0.
-14, -1
Let k be 3/4 + (-30)/8. Let b be k/(-9) - (70/(-24) - -3). Factor 0 + 0*h + b*h**2 + 1/4*h**3.
h**2*(h + 1)/4
Let s be (-10 + 1)/3 + 4 + 10. Suppose x - 9*x**2 + 2*x - 3*x**3 + s*x**4 - 2*x**4 = 0. Calculate x.
-1, 0, 1/3, 1
Let c = 731 + -724. Let x(d) be the third derivative of -13/15*d**5 - 2/105*d**c - 1/5*d**6 + 0 - 2*d**4 - 8/3*d**3 + 4*d**2 + 0*d. Solve x(y) = 0 for y.
-2, -1
Let k(g) = -3*g**5 - 17*g**4 + g**3 + 12*g**2 - 18*g - 5. Let o(n) = 2*n**5 + 9*n**4 + n**3 - 6*n**2 + 9*n + 3. Let i(f) = 3*k(f) + 5*o(f). Factor i(v).
v*(v - 3)**2*(v - 1)*(v + 1)
Let x(u) be the second derivative of u**6/6 - u**5/2 + 5*u**4/12 + u - 20. Let x(a) = 0. What is a?
0, 1
Let o be ((-288)/243)/(-16)*3/28. Let k(q) be the second derivative of 5*q + 0 + 0*q**3 + 1/30*q**6 + 1/36*q**4 + 0*q**2 - 1/20*q**5 - o*q**7. Factor k(c).
-c**2*(c - 1)**3/3
Let l(c) be the third derivative of 0*c**3 - 13 - 1/420*c**6 + 1/105*c**5 + c**2 - 1/84*c**4 + 0*c. Factor l(y).
-2*y*(y - 1)**2/7
Let h be -5*(-22)/(-385) - 16/(-7). Let c(a) be the second derivative of 0 + 0*a**3 + 2*a - 2/21*a**4 - 1/70*a**5 + 0*a**h. Factor c(r).
-2*r**2*(r + 4)/7
Let d = -260661/50 - -5213. Let r = 18/25 + d. Factor r*w**3 - 5/2*w**2 - 2 + 4*w.
(w - 2)**2*(w - 1)/2
Let t(h) be the second derivative of -h**4/78 + 7*h**3/39 - 12*h**2/13 + 5*h - 2. Solve t(s) = 0 for s.
3, 4
Let p(d) = d - 60. Let v be p(19). Let f = v + 43. Factor 1/3*o**f - 2/3*o + 0.
o*(o - 2)/3
Factor 5 - 106*j**2 - 101*j**2 + 202*j**2.
-5*(j - 1)*(j + 1)
Let g(i) be the second derivative of 5*i**4/12 + 265*i**3/6 + 130*i**2 - 322*i. Determine t so that g(t) = 0.
-52, -1
Let x(i) be the third derivative of 1/18*i**4 + 1/90*i**5 + 0 - 3*i**2 - 1/3*i**3 + 0*i. Suppose x(t) = 0. What is t?
-3, 1
Let i(p) = -p + 8*p**2 + 4*p - 17*p**4 + 1 + 6*p + 8*p**2. Let h(s) = -8*s**4 + 8*s**2 + 4*s. Let d(v) = -9*h(v) + 4*i(v). What is g in d(g) = 0?
-1, 1
Let f be 24*(2/(-10) - (-494)/1995). What is h in -f*h + 4*h**2 - 16/7*h**3 - 4/7 = 0?
-1/4, 1
Solve 2*r**3 - 34/7*r**2 - 12/7 - 2/7*r**4 + 34/7*r = 0.
1, 2, 3
Let g(h) be the first derivative of -1/4*h**4 - 8 + 0*h**3 + 0*h**2 + 10*h + 3/20*h**5. Let p(x) be the first derivative of g(x). Factor p(v).
3*v**2*(v - 1)
Let x(s) be the second derivative of 3/4*s**2 + 0 + 0*s**5 - 10*s + 1/20*s**6 + 0*s**3 - 1/4*s**4. Determine r so that x(r) = 0.
-1, 1
Let y be (-1095)/(-120) + 1/(-8). Let i(d) be the first derivative of -y - 6/13*d - 4/13*d**2 - 2/39*d**3. Find b such that i(b) = 0.
-3, -1
Let g(m) be the first derivative of 8*m**5/15 + 59*m**4/6 + 118*m**3/3 - 304*m**2/3 + 128*m/3 + 173. Find y such that g(y) = 0.
-8, 1/4, 1
Let i(j) = -4*j**2 - 2*j + 3. Let o(v) = v**2 - 1. Let l(x) = i(x) + 3*o(x). Factor l(s).
-s*(s + 2)
Let w(a) be the third derivative of a**6/30 + 4*a**5/5 - 33*a**4/2 + 108*a**3 + 133*a**2. Find p, given that w(p) = 0.
-18, 3
Let v(i) = -7*i**2 + 7*i + 9. Let q be v(3). Let z = 36 + q. Factor -2/5*y**4 - 192/5*y**2 - 512/5*y - 512/5 - 32/5*y**z.
-2*(y + 4)**4/5
Let d(h) be the first derivative of 4/5*h**5 + 0*h**4 + 0*h**2 + 0*h - 1/3*h**6 + 0*h**3 + 7. Factor d(u).
-2*u**4*(u - 2)
Factor -23*w - 6217*w**3 + 5*w**5 - 7*w - 22*w**2 + 87*w**2 - 5*w**4 + 6182*w**3.
5*w*(w - 2)*(w - 1)**2*(w + 3)
Suppose -3 + 9 = -3*b. Let s = 4 + b. Find o, given that 2*o + o + 0*o - 3*o**s = 0.
0, 1
Let v(t) = 9*t**3 - 48*t**2 + 213*t - 321. Let x(q) = -2*q**3 + q**2 + q - 1. Let l(d) = v(d) + 3*x(d). Factor l(n).
3*(n - 6)**2*(n - 3)
Let 4/13 + 6*o - 40/13*o**2 = 0. What is o?
-1/20, 2
Let l = 7151 - 7149. Let -120/11*n - 48/11 - 6/11*n**4 - 108/11*n**l - 42/11*n**3 = 0. What is n?
-2, -1
Let d(p) be the second derivative of -p**8/33600 - p**7/3150 - p**6/720 - p**5/300 + 5*p**4/12 - 7*p. Let a(l) be the third derivative of d(l). Factor a(b).
-(b + 1)**2*(b + 2)/5
Let i = 89/70 - -23/70. Suppose -i - v**2 - 22/5*v = 0. What is v?
-4, -2/5
Let o(s) be the first derivative of 7/6*s**4 - 8/3*s - 9 + 13/3*s**2 - 2/15*s**5 - 10/3*s**3. Factor o(g).
-2*(g - 4)*(g - 1)**3/3
Let i = 2057/6 - 342. Let y(v) be the second derivative of i*v**4 - 7/3*v**3 + 3*v**2 + 0 + 6*v - 1/10*v**5. Factor y(d).
-2*(d - 3)*(d - 1)**2
Let r be 14/84*4 - 68/(-6). Let h(g) be the second derivative of -g**2 - r*g + 1/12*g**4 + 0 + 1/6*g**3. Factor h(v).
(v - 1)*(v + 2)
Let n(o) be the first derivative of -5*o**3 + 27*o**2/2 + 6*o - 102. Factor n(d).
-3*(d - 2)*(5*d + 1)
Suppose 4*y - 12 = 20. Factor 2 + 8*q + 6*q**2 + 2*q**4 + 11*q**2 - 5*q**2 + y*q**3.
2*(q + 1)**4
Let j(t) = 55*t**5 - 53*t**4 - 38*t**3 + 51*t**2 - 17*t + 2. Let v(w) = -w**5 - w**4 + 2*w**3 + w**2 - w. Let g(d) = 2*j(d) + 2*v(d). What is f in g(f) = 0?
-1, 1/3, 1
Let c be (-8)/10 + (-4)/(-5). Let s(q) be the third derivative of -2/9*q**3 - 1/30*q**7 + 1/6*q**4 + 0 - 11/180*q**6 + 5*q**2 + c*q + 1/12*q**5. Solve s(t) = 0.
-1, 2/7, 2/3
Factor 56/11*m**3 + 0 + 0*m - 104/11*m**2 - 2/11*m**4.
-2*m**2*(m - 26)*(m - 2)/11
Let k(x) be the first derivative of 5 + 0*x**4 + 0*x + x**2 - 1/15*x**3 + 1/150*x**5. Let m(j) be the second derivative of k(j). Solve m(o) = 0.
-1, 1
Let i be ((-2 - -2)*-1)/(-2). Suppose i = 3*t - 0*t - 6. Let 0*c - c + c - t*c**2 = 0. What is c?
0
Suppose s = 2*y - s + 10, 4*y + 24 = 2*s. Let j be (-13)/39 - y/3. Solve -1/2*d**j - 1/6*d**3 + 2/3 + 0*d = 0.
-2, 1
Let x(r) be the first derivative of -2*r**3/33 + 24*r**2/11 + 50*r/11 - 94. Factor x(m).
-2*(m - 25)*(m + 1)/11
Let f = 9 + 46. Factor f - 8*m + m**2 - 71 - 2*m**2.
-(m + 4)**2
Let y(i) = 6*i + 32. Let r be y(-5). Let t be -2*(r + 21/(-12))/(-2). Solve -t*d + 1/4*d**3 + 1/2 - 1/2*d**2 = 0.
-1, 1, 2
Let k = 1327/2 - 659. What is g in -15*g**2 + 0 + 39/4*g**4 + 6*g + 15/4*g**5 - k*g**3 = 0?
-2, 0, 2/5, 1
Let x(l) = -9*l**2 + 145*l - 14. Let q be x(16). Factor 2/5*r**q - 4/5 + 7/5*r.
(r + 4)*(2*r - 1)/5
Let o be 17 + (-30 - 3) + 20. Factor -37/5*f**3 + 16/5 + 21*f**2 - 88/5*f + 4/5*f**o.
(f - 4)**2*(f - 1)*(4*f - 1)/5
Let f(u) be the second derivative of -5*u**4/12 + 95*u**3/6 + 88*u + 2. Factor f(k).
-5*k*(k - 19)
Suppose b + 1 = a, -2*a = 4*b - 16 - 4. Suppose -152*i - 197*i = -295 - 403. Let -9/4*x - 1/4*x**4 + 0 - 7/4*x**b - 15/4