k**2 + 0*k**4 + n - k**4 - k**5 = 0. Calculate k.
-2, 1
Let r(u) be the second derivative of -3*u**5/100 + 3*u**4/5 - 11*u**3/10 + 30*u - 1. Solve r(d) = 0.
0, 1, 11
Let 141/4*h + 147/4 - 3/2*h**2 = 0. What is h?
-1, 49/2
Let v = 12782/9 - 1420. Factor 0 - 2/9*k**2 - v*k**3 + 0*k.
-2*k**2*(k + 1)/9
Let v(c) = -3*c**3 - 27*c**2 + 33*c. Let z(h) = 6*h**3 + 54*h**2 - 65*h. Let d(a) = -5*v(a) - 3*z(a). What is s in d(s) = 0?
-10, 0, 1
Suppose 3*d + 14 = 3*u + 2*d, 24 = 5*u - d. Suppose -u*v - 5 = -5*z, 5*v + 3 = 2*z + 4. Let 0 + 1/2*w**3 + 1/4*w**4 + 1/4*w**z + 0*w = 0. What is w?
-1, 0
Let n(x) = 15*x**2 + 70*x. Let z(c) = -8*c**2 - 35*c. Let t(y) = 3*n(y) + 5*z(y). Factor t(o).
5*o*(o + 7)
Let y = -9023 - -9025. Factor -1/4*t**y + 9/2*t - 81/4.
-(t - 9)**2/4
Let m(g) = -3*g**2 - 3*g + 4. Let d be (-2)/(-7) - 675/(-63). Let u(x) = 9*x**2 + 9*x - 11. Let p(f) = d*m(f) + 4*u(f). Factor p(z).
3*z*(z + 1)
Let f be (8/(32/6))/(3/4). Let -29*b**f - 7*b**4 + 2*b**4 - 2 + 15*b + 21*b**3 + 0*b**4 = 0. Calculate b.
1/5, 1, 2
Let w(d) be the third derivative of d**7/735 + d**6/105 + d**5/105 - d**4/21 - d**3/7 + 163*d**2. Factor w(s).
2*(s - 1)*(s + 1)**2*(s + 3)/7
Let j be (1 - 97/3)/(-2) + 3. Let u = 58/3 - j. Solve r**3 + u*r + 0 - 1/3*r**5 - 1/3*r**4 + 5/3*r**2 = 0 for r.
-1, 0, 2
Let o(c) be the first derivative of 5*c**3/3 - 45*c**2 - 125. Find t such that o(t) = 0.
0, 18
What is n in -184 + n**2 + 2711*n - 2161*n + 5*n**2 = 0?
-92, 1/3
Suppose -4*h = -j - 1, 3*j = -h + 5*h + 5. Let m be (h*-1)/((-5)/15). Find p such that -11*p**3 - p**4 + 7*p**m + 1 - 2*p + 6*p**3 = 0.
-1, 1
Let r = -5497/2 - -2780. Factor r*a**3 - 33/2*a**2 + 15/2*a**5 - 51/2*a**4 + 0 + 3*a.
3*a*(a - 1)**3*(5*a - 2)/2
Let g(l) be the second derivative of 5*l**4/18 - l**3/3 - 2*l**2/3 + 186*l. Find n, given that g(n) = 0.
-2/5, 1
Let m(r) be the third derivative of r**6/70 + 31*r**5/105 - 29*r**4/21 + 16*r**3/7 + 333*r**2. Solve m(q) = 0.
-12, 2/3, 1
Let s(j) be the first derivative of 2*j**3/9 - 7*j**2 + 76*j/3 - 95. Factor s(x).
2*(x - 19)*(x - 2)/3
Find h, given that -9*h**2 + 12*h + 3/2*h**3 + 0 = 0.
0, 2, 4
Let g = -8/19 + 62/57. Let w(p) be the first derivative of -1/2*p**4 + 0*p + g*p**3 - 1 + 0*p**2. Find k such that w(k) = 0.
0, 1
Let m be 346/14 + (-22)/(-77). Suppose -4*z**2 - m*z - 2 + 13*z**2 + 18*z = 0. Calculate z.
-2/9, 1
Let x(v) be the first derivative of -v**3/4 + 15*v**2/4 + 117*v/4 + 307. Determine l so that x(l) = 0.
-3, 13
Let t be ((-120)/(-36))/(4/6). Let p be (-12)/(-27)*(t/(-2) - -4). Factor 2/3*l**3 - 2/3*l**2 - p*l + 2/3.
2*(l - 1)**2*(l + 1)/3
Let n(x) be the second derivative of x**7/21 + 8*x**6/15 + 193*x. Factor n(h).
2*h**4*(h + 8)
Let i be (-55)/10 + (-3 - -10 - 1). Factor 5*a + 25/2 + i*a**2.
(a + 5)**2/2
Suppose -8 = -a + 5*m, 0*m = 2*m + 2. Let y be 1/a - (-20)/12. Factor -3*q**2 - 4*q**4 + q**5 + 0*q**3 + q**y - 2*q**3 + 7*q**3.
q**2*(q - 2)*(q - 1)**2
Let w(f) = -2*f**3 - 4*f**2 - f + 7. Let z(m) = 0*m**2 - 48*m - 4*m**2 + 48*m + 6 - 2*m**3. Let g(d) = -2*w(d) + 3*z(d). Suppose g(b) = 0. Calculate b.
-2, -1, 1
Suppose -3*t = 5*d + 14, 4*t - 2*t - 16 = 3*d. Factor -2*b**3 - 2*b**3 - 4*b**2 - b**3 + t*b + 7*b**3.
2*b*(b - 1)**2
Suppose 1/7*c**4 - 1/7 + 2/7*c - 2/7*c**3 + 0*c**2 = 0. What is c?
-1, 1
Let x(q) be the second derivative of 0*q**4 + 0*q**2 + 15*q + 0 + 2/3*q**6 + 4/21*q**7 + 2/5*q**5 + 0*q**3. Factor x(k).
4*k**3*(k + 2)*(2*k + 1)
Suppose 152*v - 327 = 43*v. Factor -5/6*c**v + 0*c**2 + 5/6*c + 0.
-5*c*(c - 1)*(c + 1)/6
Let g(d) be the first derivative of -d**4/6 + 16*d**3/3 - 64*d**2 + 5*d + 12. Let j(m) be the first derivative of g(m). Let j(y) = 0. Calculate y.
8
Let l(f) be the third derivative of f**6/240 - f**5/180 - 7*f**4/144 - f**3/18 + 62*f**2. Find a such that l(a) = 0.
-1, -1/3, 2
Let r(j) be the third derivative of j**5/60 - j**4/8 - 3*j**3 - 125*j**2. Let r(l) = 0. What is l?
-3, 6
Let t = -310 + 4349/14. Let n(w) be the second derivative of w - 3/2*w**6 + 21/20*w**5 + 0 + 0*w**3 + 0*w**2 + t*w**7 - 1/4*w**4. Factor n(i).
3*i**2*(i - 1)*(3*i - 1)**2
Let a(q) be the first derivative of 1/10*q**5 + 0*q**4 + 0*q + 0*q**2 + 0*q**3 - 39. Determine o so that a(o) = 0.
0
Let i be (6/8)/((-1755)/(-130)). Let s(c) be the first derivative of -i*c**4 + 0*c**3 + 5 + 0*c**2 + 0*c. Factor s(j).
-2*j**3/9
Let y = 1910 + -1908. Let d(g) be the first derivative of -3/4*g**3 - 3/20*g**5 + 3/8*g**y + 9/16*g**4 + 0*g - 3. Let d(u) = 0. What is u?
0, 1
Let x = -1/181 - -367/905. Let t = 5741 + -28701/5. Find w such that 2/5*w - x*w**5 + t*w**2 + 0*w**3 + 0 - 4/5*w**4 = 0.
-1, 0, 1
Determine r, given that -2/11*r**3 - 18/11*r**2 + 0*r + 216/11 = 0.
-6, 3
Let a(l) be the second derivative of l**9/3780 - l**8/560 - l**7/630 + l**6/60 - 37*l**4/12 - 3*l + 9. Let f(j) be the third derivative of a(j). Factor f(m).
4*m*(m - 3)*(m - 1)*(m + 1)
Let d be ((-5)/(-20)*10)/(654/172). Let z = d - -1/109. Find y such that -2/3*y**2 + z + 0*y = 0.
-1, 1
Let k = 122 + -120. Let g(t) be the second derivative of 7/24*t**3 - 1/4*t**k + 0 - 5/48*t**4 - 7*t. Factor g(v).
-(v - 1)*(5*v - 2)/4
Factor -130*z**3 + 4*z**2 + 138*z**3 - 4*z**4 + 0*z**4 - 8*z.
-4*z*(z - 2)*(z - 1)*(z + 1)
Let a(c) be the third derivative of c**8/1176 - 2*c**7/245 + 13*c**6/420 - 2*c**5/35 + c**4/21 - 9*c**2 - 9. Factor a(z).
2*z*(z - 2)**2*(z - 1)**2/7
Suppose -5*x = -3*r + 2*r + 8, -1 = x. Let n be 10 + -6 + -2*3/r. Find w such that -n*w**5 + 4/5*w + 6/5*w**3 + 14/5*w**4 - 14/5*w**2 + 0 = 0.
-1, 0, 2/5, 1
Suppose 3*w + 48 = 4*a, 4*w = 5*a - 47 - 13. Let s be 3 + a/24 + (-6)/4. Find d such that -4/3 - 2*d - 2/3*d**s = 0.
-2, -1
Let 4/5*c**2 - 2/5*c + 2/5*c**3 - 4/5 = 0. Calculate c.
-2, -1, 1
Let r(u) be the third derivative of 0*u + 9/40*u**4 - 4/5*u**3 + 0 - 26*u**2 - 1/100*u**5. Factor r(q).
-3*(q - 8)*(q - 1)/5
Let c = 978 - 974. Let q(t) be the first derivative of 2*t**5 - 20*t**2 + 13/2*t**c + 16*t - 4*t**3 + 3. Factor q(r).
2*(r - 1)*(r + 2)**2*(5*r - 2)
Let h(b) be the third derivative of 1/78*b**4 + 23*b**2 + 1/1365*b**7 + 0 + 0*b**3 + 0*b - 1/390*b**6 - 1/390*b**5. Determine k so that h(k) = 0.
-1, 0, 1, 2
Let l(h) be the first derivative of 2/39*h**3 + 0*h - 2/13*h**2 + 12. Determine b so that l(b) = 0.
0, 2
Determine v so that 1/2*v**5 - 3/4*v + 1/2 - 5/4*v**2 - 9/4*v**4 + 13/4*v**3 = 0.
-1/2, 1, 2
Let i be (6/24)/(3/36). Suppose -60*m + 28 - 20*m**3 - 29*m**i + 45*m**3 + 36*m**2 = 0. Calculate m.
1, 7
Let o(d) be the first derivative of -d**5/80 + d**4/12 - d**3/8 - 2*d + 33. Let r(j) be the first derivative of o(j). Factor r(q).
-q*(q - 3)*(q - 1)/4
Let q(s) be the second derivative of -2*s**6/5 - 2*s**5/5 + s**4 + 4*s**3/3 + 3*s + 2. Find r, given that q(r) = 0.
-1, -2/3, 0, 1
Let n(z) = 17*z**2 + 62*z + 37. Let x(u) = 33*u + 4*u**2 + 8*u + 7*u**2 + 26 - 1. Let s(a) = -5*n(a) + 8*x(a). Suppose s(v) = 0. Calculate v.
-5, -1
Let g be ((-1)/(-4))/((-9)/(-1656)*23). Factor 3/4*l**g + 1/4 - 3/4*l - 1/4*l**3.
-(l - 1)**3/4
Suppose 0 = 2*d - 2*q + 2, 2 = -0*q + 2*q. Let v(z) be the second derivative of 0*z**3 + 2*z + 0 + 2/15*z**6 - 1/3*z**4 + d*z**2 + 0*z**5. Factor v(s).
4*s**2*(s - 1)*(s + 1)
Factor -2*k**3 - 10/3*k - 6*k**2 + 0 + 2/3*k**4.
2*k*(k - 5)*(k + 1)**2/3
Let n be -20*(-4)/80*4. Let d(s) be the second derivative of -1/6*s**n - 1/20*s**5 + s**2 + 0 + 1/6*s**3 - 5*s. Solve d(o) = 0.
-2, -1, 1
Let d(w) = -3*w**3 + 3*w**2 + 3. Suppose -4 + 2 = 2*j. Let m(a) = -a**4 + a**3 + 1. Let k(s) = j*d(s) + 3*m(s). Determine l so that k(l) = 0.
0, 1
Let i(a) be the third derivative of -a**7/280 + a**6/32 + 3*a**5/80 - 45*a**4/32 + 27*a**3/4 + 90*a**2. Find x such that i(x) = 0.
-3, 2, 3
Let n be 64/(-24)*9/(-6). Let w(d) be the second derivative of -d**3 + 0 + 3*d - 1/10*d**5 - d**2 - 1/2*d**n. Factor w(f).
-2*(f + 1)**3
Let c be 510/72 + -3 + -4. Let w(x) be the second derivative of -1/9*x**3 - c*x**4 + 1/6*x**2 + 0 + x. Let w(m) = 0. Calculate m.
-1, 1/3
Let o(h) be the third derivative of -h**8/40320 + h**7/5040 + h**6/480 + h**5/144 - h**4/6 + 38*h**2. Let j(s) be the second derivative of o(s). Factor j(z).
-(z - 5)*(z + 1)**2/6
Let x(i) be the first derivative of -2/3*i**6 + 0*i**5 + 0*i**3 + 1 + 0*i - 2*i**2 + 2*i**4. Factor x(o).
-4*o*(o - 1)**2*(o + 1)**2
Let c be (10/1