- 3/2 - p*r + 0*r**2 + 3/2*r**4 = 0.
-1, 1
Let i(n) be the second derivative of -6/25*n**5 + 1/15*n**4 - 2/75*n**6 + 4/35*n**7 - 8*n + 0*n**2 + 0 + 0*n**3. Suppose i(y) = 0. Calculate y.
-1, 0, 1/6, 1
Let i(w) be the third derivative of w**6/2520 + w**5/210 + w**4/42 + 7*w**3/6 + 19*w**2. Let s(l) be the first derivative of i(l). Let s(t) = 0. Calculate t.
-2
Suppose 20 = 5*x - 5. Determine r, given that 8*r**4 - 43*r**4 + 3*r**x - 10*r**3 + 17*r**5 = 0.
-1/4, 0, 2
Let y = 254 + -91. Let o = y - 812/5. Let -3/5*x + o*x**2 + 0 = 0. What is x?
0, 1
Let a be 214*(-1)/(-8) - (-211)/(-2532). Determine i, given that a*i + 40/3 - 20/3*i**3 - 20*i**2 + 25/6*i**4 = 0.
-2, -2/5, 2
Let q = 48 + -38. Suppose 5*b - q = -0*b. Factor 8/9*n + 1/9*n**b + 16/9.
(n + 4)**2/9
Suppose -r + 2*d = -0 - 6, 3*r + 3*d = 0. Determine u, given that -5*u**5 + 4*u**4 + 2*u - 858*u**2 + 854*u**r + 3*u**5 = 0.
-1, 0, 1
Let t(g) = 0 + 20 + 15*g - g**2 + 9*g**3 - 2 + 7*g**2. Let a(h) = h**3 + h**2 + h + 1. Let m = 47 - 35. Let q(k) = m*a(k) - t(k). Factor q(r).
3*(r - 1)*(r + 1)*(r + 2)
Suppose 0 = 3*n + 2*n + 4*v - 26, -20 = -5*v. Determine x so that 5 + 11*x - 17*x**3 - 1 + 30*x**n + 7*x + 39*x**3 + 6*x**4 = 0.
-1, -2/3
Let r(s) be the third derivative of s**6/960 - s**5/80 + s**4/16 - s**3/6 + 27*s**2 + 9*s. Factor r(m).
(m - 2)**3/8
Factor 0 - 37/8*c**2 + 5/4*c + 9/8*c**4 - 19/4*c**3.
c*(c - 5)*(c + 1)*(9*c - 2)/8
Let g(l) be the third derivative of l**6/40 + l**5/12 - l**4/8 + 5*l**3/6 - l**2. Let c(z) = -z**3 + z**2 - z - 1. Let h(s) = -5*c(s) - g(s). Factor h(v).
2*v*(v - 4)*(v - 1)
Let u(c) = 2*c**5 - 30*c**4 + 18*c**3 + 10*c**2 - 18*c. Let d(m) = -m**4 + m**2 - m. Let s(n) = 36*d(n) - 2*u(n). What is y in s(y) = 0?
0, 1, 4
Let s(b) be the first derivative of -b**6/12 + 6*b**5/5 - 7*b**4 + 64*b**3/3 - 36*b**2 + 32*b + 237. Suppose s(y) = 0. Calculate y.
2, 4
Let r(z) be the first derivative of z**4 + 12 - 4*z - 2*z**2 + 4/3*z**3. Factor r(h).
4*(h - 1)*(h + 1)**2
Suppose -4*r - 2 + 22 = 4*u, 3 = 3*r - 3*u. Solve 24*p**3 + 10*p**2 + 5*p**4 - 351 - 4*p**r + 336 - 20*p = 0.
-3, -1, 1
Determine g so that -5*g - 64 - 116*g**2 + 29*g**3 - 49*g**3 - 4*g**5 + 173*g + 36*g**4 = 0.
-2, 1, 8
Solve -2*v + v**4 - 47/6*v**3 + 22/3*v**2 + 3/2*v**5 + 0 = 0 for v.
-3, 0, 2/3, 1
Let u(v) be the third derivative of -v**7/245 - 11*v**6/420 - 2*v**5/35 - v**4/21 + 2*v**2 - 3*v. Suppose u(g) = 0. What is g?
-2, -1, -2/3, 0
Let z = -1183 - -823. Let j be ((2/1)/6)/((-300)/z). Factor -16/5*o + 32/5 + j*o**2.
2*(o - 4)**2/5
Let h(d) be the first derivative of -d**6/7 - 3*d**5/5 - 27*d**4/28 - 5*d**3/7 - 3*d**2/14 + 48. Factor h(n).
-3*n*(n + 1)**3*(2*n + 1)/7
Let r(o) be the third derivative of o**8/33600 - o**7/25200 - o**6/1800 - o**5/10 + 15*o**2. Let p(u) be the third derivative of r(u). Factor p(a).
(a - 1)*(3*a + 2)/5
Let z(m) = 7*m**4 + 32*m**3 + 31*m**2 + 6*m. Let h(w) = -w**4 - w**3. Let n(x) = 7*h(x) - z(x). Factor n(v).
-v*(v + 1)*(2*v + 3)*(7*v + 2)
Let u(i) be the second derivative of -1/30*i**6 + 0 + 3/80*i**5 + 1/12*i**3 + 0*i**2 + 3/16*i**4 - 17*i. Factor u(s).
-s*(s - 2)*(s + 1)*(4*s + 1)/4
Let x(z) be the first derivative of z**7/42 - z**5/20 - 5*z + 10. Let i(v) be the first derivative of x(v). What is d in i(d) = 0?
-1, 0, 1
Let f be (-1 - 1/(-2))*0. Let w(t) be the second derivative of 7/102*t**4 + 4/17*t**2 - 5*t + 16/51*t**3 + f. Solve w(y) = 0.
-2, -2/7
Let j(a) be the first derivative of -1/15*a**5 + 2/3*a**4 - 11 + 0*a - 1/2*a**2 - 8/3*a**3. Let p(q) be the second derivative of j(q). Solve p(c) = 0 for c.
2
Let t = -313/41 - -3235/123. Let m(o) = o**3 - 3*o**2 + o + 2. Let g be m(2). Find a such that -196/3*a**4 + t*a**3 + 16/3*a**2 - 686/3*a**5 + 0*a + g = 0.
-2/7, 0, 2/7
Let w be 3/(-21) - 170/(-14). Suppose 4*i + 4*g = w, 3*i + i - g = -3. Solve 2/15*f**5 + 0 + i*f - 2/5*f**3 + 0*f**4 - 4/15*f**2 = 0 for f.
-1, 0, 2
Let y(q) = 4*q**4 - 23*q**2 + 39*q + 5. Let x(u) = u**2 + 3*u + 1. Let t(r) = 5*x(r) - y(r). Factor t(l).
-4*l*(l - 2)*(l - 1)*(l + 3)
Let h = 1/304 + 283/6384. Let t(g) be the first derivative of 1/35*g**5 + 0*g - 1/28*g**4 + 1/14*g**2 - h*g**3 - 1. Factor t(j).
j*(j - 1)**2*(j + 1)/7
Suppose -9*y = -15*y. Let p(l) be the third derivative of 1/105*l**7 + 2*l**2 - 1/30*l**5 + y*l + 0*l**3 + 0*l**6 - 1/336*l**8 + 1/24*l**4 + 0. Factor p(a).
-a*(a - 1)**3*(a + 1)
Let v be (-12)/30*-5*2. Factor -3*u**4 - u**v + 0*u**2 - u**4 + 5*u**2.
-5*u**2*(u - 1)*(u + 1)
Let y(i) = 27*i**2 - 2 + 26*i - 23 - 37*i**2. Let m(o) = -29*o**2 + 77*o - 75. Let d(k) = 6*m(k) - 17*y(k). Suppose d(b) = 0. What is b?
5/2
Let k = -11 + 19. Factor 19*t**5 + 2*t**3 - k*t**5 - 13*t**5 - 2*t**2 + 2*t**4.
-2*t**2*(t - 1)**2*(t + 1)
Suppose 36 = 3*h - 9*h. Let c(l) = -65*l**2 + 815*l - 5070. Let r(t) = -11*t**2 + 136*t - 845. Let n(b) = h*c(b) + 35*r(b). Find y such that n(y) = 0.
13
Suppose -3*d - 8 = 4. Let b = 6 + d. Let 3*l - l + 5*l**b + 2*l - 3*l**2 - 6*l**3 = 0. Calculate l.
-2/3, 0, 1
Find a, given that 7/5*a**3 + a**4 + 0*a + 0 + 1/5*a**5 + 3/5*a**2 = 0.
-3, -1, 0
Let q(f) be the third derivative of -f**7/630 - f**6/30 - 3*f**5/10 + 7*f**4/24 - 5*f**2. Let w(n) be the second derivative of q(n). Find l such that w(l) = 0.
-3
Let n(t) = -22*t - 132. Let h be n(-6). Let w(r) be the first derivative of 1/6*r**2 + h*r + 7 + 4/9*r**3 + 1/4*r**4. Factor w(v).
v*(v + 1)*(3*v + 1)/3
Let s(w) be the first derivative of 1 - 1/8*w**2 + 0*w + 1/12*w**3. What is n in s(n) = 0?
0, 1
Let z(x) = -x**2 - 10*x + 33. Let k be z(-11). Suppose -40*i + 10 - 126*i**5 + 386*i**3 + 8*i**4 - k + 228*i**2 - 4 = 0. Calculate i.
-1, -2/9, 2/7, 2
Let i(z) = -6*z**5 - 23*z**4 + 41*z**3 + 177*z**2 + 163*z + 49. Let s(w) = -w**4 - w**3 + 3*w**2 - w + 1. Let n(c) = i(c) - s(c). What is t in n(t) = 0?
-4, -1, -2/3, 3
Let g = -1376/273 + 36/7. Let z(r) be the second derivative of 2/65*r**6 + g*r**3 + 0*r**2 + 0 + 1/10*r**5 - 6*r + 2/13*r**4 + 1/273*r**7. Factor z(q).
2*q*(q + 1)**2*(q + 2)**2/13
Find y such that 2/7*y**3 + 120/7*y - 4*y**2 - 144/7 = 0.
2, 6
Let f(n) = 123*n**2 - 321*n - 3840. Let z(l) = -15*l**2 + 40*l + 480. Let t(o) = 4*f(o) + 33*z(o). Let t(a) = 0. What is a?
-8, 20
Suppose -5*k - 1 = -6. Let s be 98/(-21)*(-6)/16. Suppose -k + s*v**2 + v - v**3 - 3/4*v**4 = 0. What is v?
-2, -1, 2/3, 1
Let f(y) = -y**3 - 6*y**2 - 10*y - 14. Let z be f(-5). Factor 20*g**3 + z*g**3 + g**4 - 32*g**3.
g**3*(g - 1)
Let y(x) = x**2 + x**3 + 5*x**3 + x**3 - 6*x**3. Let i(n) = 2*n**4 - 6*n**3 + 18*n**2 - 6*n. Let d(z) = i(z) - 4*y(z). Solve d(c) = 0.
0, 1, 3
Let h(z) be the first derivative of z**5/5 + 3*z**4/4 - 14*z**3 + 50*z**2 - 72*z - 102. Solve h(c) = 0 for c.
-9, 2
Suppose -204304 + 1366*m + 227*m + 215*m - 4*m**2 = 0. Calculate m.
226
Let p(r) be the third derivative of r**7/84 + r**6/48 - r**5/12 - 21*r**2 - 2*r. What is f in p(f) = 0?
-2, 0, 1
Let z(w) be the third derivative of -w**5/160 - w**4/32 + 3*w**3/2 - 3*w**2 + 4. Factor z(d).
-3*(d - 4)*(d + 6)/8
Suppose -371 = -154*l + 58 + 187. Suppose 0 + 1/10*h**l + 1/5*h**3 - 1/5*h - 1/10*h**2 = 0. What is h?
-2, -1, 0, 1
Let c(y) be the first derivative of y**3 + y**2/2 + 3*y - 5. Let u(a) = 4*a**2 + 2*a + 5. Let v(l) = -7*c(l) + 5*u(l). Factor v(n).
-(n - 4)*(n + 1)
Suppose -9 = -s - 5. Let 15*u**5 + 37*u**2 + 61 - 7*u**2 - 66 + 70*u**3 + 55*u**s - 5*u = 0. Calculate u.
-1, 1/3
Let d(w) be the third derivative of w**9/60480 - w**8/6720 + w**5/10 - 15*w**2. Let c(a) be the third derivative of d(a). Factor c(r).
r**2*(r - 3)
Solve -3*i - 9/2 - 3/8*i**2 = 0 for i.
-6, -2
Let m = 87 - 86. Suppose 3*d + 7 = -f, -m - 18 = -2*f + 5*d. Factor 4/7*t**f + 0 - 8/7*t.
4*t*(t - 2)/7
Suppose 7 - 1 = s + 2*v, -9 = 3*v. Suppose -2*d + 4*x = s, -d - 4*x + 24 = 3*d. Find m such that 2/15*m + 2/15*m**d - 4/15 = 0.
-2, 1
Factor 3/2*c + 18 - 1/4*c**2.
-(c - 12)*(c + 6)/4
Let n(a) be the first derivative of 3*a**4/4 + 5*a**3 - 21*a**2 - 284. Solve n(p) = 0 for p.
-7, 0, 2
Suppose -2*d - 3*d + 40 = 0. Determine o so that -5*o**2 + 5*o**2 - 2*o**3 + 0*o**3 + 8*o**2 - d*o = 0.
0, 2
Let c(t) be the third derivative of -2/75*t**5 + 0*t**3 - 43*t**2 + 1/300*t**6 + 0 + 0*t + 0*t**4. Factor c(g).
2*g**2*(g - 4)/5
Factor 22/9*j - 2/9*j**2 + 0.
-2*j*(j - 11)/9
Let g be (-18)/(-6) + 1 +