e of -q**6/180 + q**4/12 - 2*q**3/3 - 1. Let j(t) be the third derivative of w(t). Find n such that j(n) = 0.
-1, 1
Let a be 8/48 + (-10)/(-3). Let m be (-6)/15 - (-6)/15. Let 0*q + m - 5/2*q**4 - q**2 - a*q**3 = 0. What is q?
-1, -2/5, 0
Suppose -8*x = -3*x. Let c(t) be the second derivative of -1/36*t**4 + 0 + x*t**3 - 2*t + 0*t**2. Determine f, given that c(f) = 0.
0
Let w(x) = x**2 + 20*x - 96. Let m be w(-24). Suppose -21 = -5*i + 2*i - 5*u, 3*u - 9 = 0. Let -2/5*q**i + 0 + m*q = 0. Calculate q.
0
Let w(c) be the first derivative of 2*c**6/3 + 8*c**5/5 - 6*c**4 - 16*c**3/3 + 26*c**2 - 24*c - 49. Factor w(u).
4*(u - 1)**3*(u + 2)*(u + 3)
Let z be (-1)/(-4) + (-21)/(-12). Determine n so that n**2 + 4*n**3 - 2*n**3 + 5*n**z - 2*n**2 + 2*n = 0.
-1, 0
Let h(b) = b. Let g(w) = 2*w**2 - 7*w + 2. Let z(u) = -g(u) - 3*h(u). Suppose z(c) = 0. Calculate c.
1
Let x(o) be the second derivative of -o**6/5 + 11*o**5/30 + 7*o**4/18 - 11*o**3/9 + 2*o**2/3 + 2*o. Solve x(b) = 0.
-1, 2/9, 1
Let c(b) = -245*b**2 - 215*b - 40. Let p(z) = -245*z**2 - 214*z - 41. Let o(f) = -4*c(f) + 5*p(f). Factor o(k).
-5*(7*k + 3)**2
Let o(q) be the third derivative of -q**6/180 - 6*q**2. Suppose o(c) = 0. What is c?
0
Suppose -4*z - 13 = -4*b - 5, 13 = 3*b + 4*z. Let -3*l + b*l**4 + 1 - l**3 - 5 - 9*l**2 + 5 + 1 = 0. Calculate l.
-1, 1/3, 2
Let h be (-8)/15*(-3 + 27/12). Factor 0 + 0*g + 0*g**2 - h*g**4 - 2/5*g**3.
-2*g**3*(g + 1)/5
Factor 0 + 0*j**3 + 3/2*j**2 - j - 1/2*j**4.
-j*(j - 1)**2*(j + 2)/2
Suppose j + 1 = 2*r, -4*r + 14 = 7*j - 5*j. Find h, given that 9*h - 9*h + 6*h**4 + 3*h**j - h**5 + 4*h**5 = 0.
-1, 0
Let t(q) be the first derivative of 4*q**5/5 - 2*q**4 + 4*q**2 - 4*q - 10. Determine d, given that t(d) = 0.
-1, 1
Let n(w) be the third derivative of -4*w**2 - 1/40*w**5 + 1/240*w**6 + 0*w + 0*w**3 + 0 + 0*w**4. Factor n(m).
m**2*(m - 3)/2
Let i be ((-24)/(-30))/((-4)/(-10)). Find c, given that -3 + 4 + 3*c**i - 6 - 7 = 0.
-2, 2
Suppose 3*f + 0*f + 4*s - 14 = 0, 0 = 4*f + s - 23. Determine l so that -2*l**3 - f*l**2 - 3*l**2 + 4*l - 5*l**2 + 12*l**3 = 0.
0, 2/5, 1
Let k(j) = j**3 - j**2 - 1. Let x(z) = 31*z**3 + 49*z**2 + 17*z + 7. Let q be (20/(-8))/(2/4). Let i(a) = q*k(a) - x(a). Determine r so that i(r) = 0.
-1/2, -2/9
Let m(o) = -4*o**2 + 1. Let c be m(-1). Let v = 5 + c. Find g such that -2*g**3 - 4*g**2 - g**4 - 2*g**2 + 5*g**v = 0.
-1, 0
Suppose 0 = -3*g - 2*y - 4 + 6, 5*y = 5. Suppose -w - 5*j - 6 = 0, j = -g*j - 2. Factor 2/3*u**w + 0*u**3 + 0*u**2 + 0*u + 0.
2*u**4/3
Let a = 8/31 - -7/93. Find s such that -a*s**2 - 1/3 + 2/3*s = 0.
1
Find n such that 3 - 2*n**2 + 3*n**2 - 10*n + 8*n - 2 = 0.
1
Let l(w) = 2*w - 9. Let z be 0/5 + 3*2. Let h be l(z). Solve -6*m**4 - 2*m**2 + m**h - 2*m**5 - 7*m**3 + 0*m**5 = 0 for m.
-1, 0
Let d(p) be the first derivative of -7*p**3/3 + p**2 - 2. Find z such that d(z) = 0.
0, 2/7
Let h(y) be the third derivative of y**8/840 + y**7/105 + 2*y**6/75 + 2*y**5/75 + 8*y**2. Determine w so that h(w) = 0.
-2, -1, 0
Let h(f) be the second derivative of -5/3*f**3 + 0 - 2*f + 1/3*f**4 + 2*f**2. Factor h(n).
2*(n - 2)*(2*n - 1)
Factor 0 + 0*g + 0*g**2 + 2/7*g**3.
2*g**3/7
Factor 0*h + 0*h**2 - 1/2*h**5 + 1/2*h**4 + 0 + h**3.
-h**3*(h - 2)*(h + 1)/2
Let h(w) = 8*w**5 - 16*w**4 + 12*w**3 - 4*w**2 - 2. Suppose 0 = 3*p + 5 - 2. Let b(o) = -o**5 + o**4 - o**3 + o**2 + 1. Let r(f) = p*h(f) - 2*b(f). Factor r(g).
-2*g**2*(g - 1)**2*(3*g - 1)
Suppose -2/5*t**2 + 0 + 4/5*t = 0. What is t?
0, 2
Let s be (-6)/4*(-42)/9. Let t = s - 13/2. Factor t - 1/2*v**2 + 0*v.
-(v - 1)*(v + 1)/2
Let w = 12 - 10. Find l such that 0*l + w*l + l**2 + l**2 = 0.
-1, 0
Let i = -9/2 + 5. Let d(w) be the second derivative of -2/21*w**7 + 0 + i*w**2 - w + 8/15*w**6 + 19/12*w**4 - 7/6*w**3 - 5/4*w**5. Suppose d(a) = 0. What is a?
1/2, 1
Let y = 135 + -133. Let a(o) be the second derivative of 1/4*o**y - 1/24*o**4 + 2*o - 1/12*o**3 + 1/40*o**5 + 0. Factor a(j).
(j - 1)**2*(j + 1)/2
Suppose -2*s = -4*i + 4, -i + 2*s = 4 - 8. Factor -2 - c**4 + i*c**2 - 3*c**2 + 2*c**4 + c**3 + 0 - 5*c.
(c - 2)*(c + 1)**3
Let p(s) = s + 17. Let z be p(-11). Let f be (1/z*-2)/(-1). Factor -2/3*g + 0 + 1/3*g**3 + f*g**2.
g*(g - 1)*(g + 2)/3
Let g(y) be the second derivative of y**2 + 1/6*y**4 - 2/3*y**3 + 0 + y. Determine k, given that g(k) = 0.
1
Let a = 2550/7 + -364. Factor -a*i**5 - 4/7*i**2 + 6/7*i - 2/7 - 4/7*i**3 + 6/7*i**4.
-2*(i - 1)**4*(i + 1)/7
Let d(v) be the second derivative of v**5/50 + v**4/15 + v**3/15 - 18*v. Factor d(o).
2*o*(o + 1)**2/5
Let d(z) = -10*z**4 + 30*z**2 + 10*z + 15. Let l(i) = -i**4 + i**3 + i**2 + i + 1. Let c(s) = -d(s) + 15*l(s). Suppose c(f) = 0. Calculate f.
0, 1
Let p = 417 + -2083/5. What is t in 2/5*t**2 - p*t + 0 = 0?
0, 1
Factor -27/2 + 125/2*k**5 - 95*k**3 + 81/2*k + 25/2*k**4 + 9*k**2.
(k + 1)**2*(5*k - 3)**3/2
Let p = -5 + 9. Suppose z + 5*j = -8, 7 - 1 = p*z + j. Solve 15/2*m**3 + 1/2*m + 25/2*m**4 - 9/2*m**z + 0 = 0.
-1, 0, 1/5
Suppose -3*g + 2*g + 16 = 0. Suppose 5*y - 3*c - 30 = 0, 4*c + 4 + g = 0. Factor s - 2*s**2 + 0*s + y*s**2.
s*(s + 1)
Solve 0 - 3/4*a + 3/4*a**2 = 0.
0, 1
Let s(i) be the first derivative of i**4/5 + 4*i**3/15 - 7*i**2/10 + 2*i/5 - 6. Find l, given that s(l) = 0.
-2, 1/2
Let n = 53 + -53. Suppose 0 - 6/5*h**2 + 2/5*h**4 + n*h**3 + 4/5*h = 0. Calculate h.
-2, 0, 1
Suppose y = -2*h + 6*h - 54, -2*h - 2*y = -22. Solve -h*i**3 + 8*i**3 + 3*i**3 + 2*i**5 = 0 for i.
-1, 0, 1
Let 46/9*a**3 + 4/9*a**5 - 4/9 - 22/9*a**4 + 22/9*a - 46/9*a**2 = 0. Calculate a.
1/2, 1, 2
Determine x so that -2/5*x**2 - 12/5 - 2*x = 0.
-3, -2
Let g(c) = 12*c**4 - 9*c**3 - 45*c**2 + 21. Let r(i) = -3*i**4 + 2*i**3 + 11*i**2 - 5. Let h(y) = -5*g(y) - 21*r(y). Factor h(a).
3*a**2*(a - 1)*(a + 2)
Let v(i) = i**3 + i + 1. Let b(p) = -2*p**4 + 6*p**3 - 2*p**2 + 2*p + 2. Let w(z) = b(z) - 2*v(z). Solve w(c) = 0 for c.
0, 1
Let r be 99/(-11)*4/54*-3. Let n be 0/(((-2)/2)/1). Solve n + 2/7*d**r - 2/7*d = 0 for d.
0, 1
Let g(z) be the first derivative of -2*z**6/3 - 8*z**5/5 + 2*z**4 + 16*z**3/3 - 2*z**2 - 8*z - 5. Determine w, given that g(w) = 0.
-2, -1, 1
Suppose 3*d = 6*d + 4*c + 8, -2*d + 8 = -4*c. Let w(s) be the first derivative of -1 - 5/12*s**4 + 4/9*s**3 + d*s + 2/15*s**5 - 1/6*s**2. Factor w(f).
f*(f - 1)**2*(2*f - 1)/3
Let p(i) be the second derivative of 0*i**2 + 0*i**3 + 1/18*i**4 + 3*i + 0. Suppose p(x) = 0. Calculate x.
0
Let m be (4/(-3))/(40/(-12)). Find a such that 0 - m*a**2 + 2/5*a = 0.
0, 1
Let i = 16/247 - -6182/3705. Let k = i + -8/15. Factor 4/5*o + 0 + 2/5*o**3 - k*o**2.
2*o*(o - 2)*(o - 1)/5
Let n(p) be the third derivative of p**2 + 0*p - 1/6*p**4 + 0 + 1/180*p**6 - 1/3*p**3 + 1/60*p**5. Let c(d) be the first derivative of n(d). Solve c(l) = 0.
-2, 1
Factor 0*s**2 + 2/3*s + 0 + 0*s**4 + 2/3*s**5 - 4/3*s**3.
2*s*(s - 1)**2*(s + 1)**2/3
Let n(z) be the third derivative of 0*z**3 - 1/735*z**7 + 0 + 4*z**2 + 0*z**5 + 0*z + 0*z**4 - 1/420*z**6. Determine c, given that n(c) = 0.
-1, 0
Let h = 103 - 103. Let -5/3*p**3 - 2/3*p**2 + 0*p + h + 5/3*p**5 + 2/3*p**4 = 0. Calculate p.
-1, -2/5, 0, 1
Solve -3*w**2 + 2*w**3 - 16 - 4*w**3 + 8*w + 4*w**2 + 3*w**2 = 0.
-2, 2
Let x = -27 + 29. Let r(a) be the third derivative of -4/15*a**3 - 1/150*a**5 + 0 + 0*a - a**x + 1/15*a**4. Suppose r(y) = 0. Calculate y.
2
Let r(c) be the second derivative of -2/11*c**2 + 0 + 1/66*c**4 + c + 1/33*c**3. Factor r(w).
2*(w - 1)*(w + 2)/11
Suppose -2*x + 4*x - 8 = 0. Let v(t) = 4 - x - 2*t. Let i(m) = -m**3 - 2*m. Let a(h) = 2*i(h) - 3*v(h). Solve a(q) = 0.
-1, 0, 1
Let t**2 - t**2 + 3*t**2 + t**2 = 0. Calculate t.
0
Let h(w) be the third derivative of 0*w**4 + 0 + 2*w**2 - 9/11*w**3 + 1/1155*w**7 + 0*w + 2/165*w**6 + 3/55*w**5. Factor h(o).
2*(o - 1)*(o + 3)**3/11
Factor 0*s**4 + 4/5*s**3 - 4/5*s**5 + 0*s + 0*s**2 + 0.
-4*s**3*(s - 1)*(s + 1)/5
Let n(u) be the first derivative of u**5/5 + 7*u**4/4 + 5*u**3 + 9*u**2/2 - 7. Factor n(s).
s*(s + 1)*(s + 3)**2
Let g be (7/28)/((21/6)/7). Factor g + 1/4*u**2 - 3/4*u.
(u - 2)*(u - 1)/4
Factor 1/2*o + 1/8*o**2 + 3/8.
(o + 1)*(o + 3)/8
Let i be (4/(-2))/((-36)/8 + 4). Let u = 119/12 - 37/4. Solve 1/3*l**2 + l**3 - l - u + 1/3*l**i = 0 for l.
-2, -1, 1
Let n(j) be the first derivative of -j**4/4 - j**3 + 2*j**2 + 