- -3)*(-15)/u. What is i in 0*i**3 - 1/3*i**o + 1/3*i + 0 + 2/3*i**4 - 2/3*i**2 = 0?
-1, 0, 1
Let i(m) be the first derivative of -4*m**3/21 - 8*m**2/7 + 20*m/7 + 44. Let i(o) = 0. Calculate o.
-5, 1
Let a be (-17)/6 + (-4)/24. Let q be 5*(-1 - a)/2. Find o such that 0*o**3 + 3*o**3 - o**2 + o**q - 4*o**4 + o**4 = 0.
0, 1
Solve -1/2*p**3 + 1/2*p**4 + 1/2*p + 0 - 1/2*p**2 = 0.
-1, 0, 1
Let v(y) be the first derivative of 1/24*y**6 + 1 + 0*y + 1/16*y**4 - 1/10*y**5 + 0*y**2 + 0*y**3. Let v(g) = 0. Calculate g.
0, 1
Let a(r) be the first derivative of 0*r**2 + r + 2 - 1/3*r**3. Factor a(n).
-(n - 1)*(n + 1)
Let k = -3 - -3. What is r in 2 + k + 4 + 7*r - 4 - 4*r**2 = 0?
-1/4, 2
Let z = 12 + -7. Factor 11*s**2 - 2*s**3 + 2 - s**2 + 1 - 16*s + z.
-2*(s - 2)**2*(s - 1)
Let -20 - 20*r**3 + 20*r + 35/4*r**4 + 10*r**2 - 5/4*r**5 = 0. What is r?
-1, 2
Let s be (-23)/(-7) + (-6 + -1 - -4). Suppose 2/7*a**2 - s*a**4 + 0 + 2/7*a - 2/7*a**3 = 0. What is a?
-1, 0, 1
Let l(r) be the first derivative of r**6/10 - 3*r**5/25 - 3*r**4/10 + 2*r**3/5 + 3*r**2/10 - 3*r/5 + 31. Factor l(c).
3*(c - 1)**3*(c + 1)**2/5
Let r(k) be the first derivative of -1/26*k**4 - 9 + 0*k**2 + 2/13*k**3 - 8/13*k. Factor r(c).
-2*(c - 2)**2*(c + 1)/13
Let s(v) = -v**2 - v. Let r(n) = n**3 + 45*n**2 + 861*n + 4913. Let z(t) = r(t) - 6*s(t). Solve z(x) = 0.
-17
Let c(s) = s**3 - 5*s**2 + s + 1. Suppose -3*w - 1 + 16 = 0. Let k be c(w). Solve 4*a - a**2 + 2 - k*a - 3 = 0 for a.
-1
Let s = -16 - -21. Suppose 3*k + k = -3*f - 16, s*f = -5*k - 20. Factor 0*z**2 + f - 2/11*z + 2/11*z**3.
2*z*(z - 1)*(z + 1)/11
Suppose 4*o = 3*f + 8*o + 59, 0 = -2*o + 8. Let v = -23 - f. What is z in -6/5*z + 2/5 - 2/5*z**3 + 6/5*z**v = 0?
1
Let m = -1 - -2. Let j be (6/(-4))/(m - 4). Solve -j*r**3 + 0*r**2 + 0 + 0*r = 0 for r.
0
Let x(f) be the second derivative of -f**5/90 + f**4/18 - 2*f**3/27 - 18*f. Solve x(i) = 0 for i.
0, 1, 2
Let r(f) be the second derivative of -f**4/12 - f**3/6 + f. Let d(q) = 9*q**3 - 2*q - 1. Suppose 5*k = -2*k + 7. Let s(p) = k*d(p) + 3*r(p). Factor s(y).
(y - 1)*(3*y + 1)**2
Let v(j) be the third derivative of -1/96*j**4 - 1/840*j**7 + 0*j + 0*j**3 - 2*j**2 + 1/480*j**6 + 1/240*j**5 + 0. Factor v(f).
-f*(f - 1)**2*(f + 1)/4
Let f be 8/(-12) - (-1148)/1740. Let x = 571/1305 - f. Determine r, given that 0 - 2/3*r**2 - 2/9*r - x*r**3 = 0.
-1, -1/2, 0
Let h(n) be the first derivative of 0*n - 1/12*n**3 + 6 + 1/16*n**4 + 0*n**2. Factor h(p).
p**2*(p - 1)/4
Suppose 0 = -2*y + 20*y. Let j(a) be the first derivative of a**3 + y*a + 2 + 1/4*a**4 + a**2. Factor j(h).
h*(h + 1)*(h + 2)
Let q(p) be the second derivative of p**7/84 - p**5/10 + 23*p. Find v, given that q(v) = 0.
-2, 0, 2
Let r = 0 + 8. Determine a so that 43 - 4*a**2 + r*a + 0*a**2 - 43 = 0.
0, 2
Let i(l) = -12*l**3 + 18*l**2 - 4*l - 2. Let c(w) = 25*w**3 - 37*w**2 + 8*w + 4. Let n(k) = 4*c(k) + 9*i(k). Let n(d) = 0. Calculate d.
-1/4, 1
Let i(r) be the third derivative of -1/30*r**4 - 1/75*r**6 + 0 - 1/30*r**5 - 1/525*r**7 + 0*r**3 + 0*r - 4*r**2. Solve i(j) = 0 for j.
-2, -1, 0
Let z(c) be the third derivative of -c**5/120 + 5*c**4/16 + 4*c**3/3 - 34*c**2. Determine p so that z(p) = 0.
-1, 16
Suppose -d + r = 3*d - 11, 3*d + 2*r = 0. Suppose -13 + 3*o**d - 6*o + 13 = 0. Calculate o.
0, 2
Let l(q) be the second derivative of -2/3*q**4 - 2*q**2 + 5/3*q**3 + 0 + 1/10*q**5 - 4*q. Determine x so that l(x) = 0.
1, 2
Let a = 520/771 - 2/257. Factor -2/3*z**3 - 2/3*z**2 + 0 + a*z**4 + 2/3*z.
2*z*(z - 1)**2*(z + 1)/3
Let m = 13 + -8. Let n(o) = -5*o**4 + 2*o**3 - o**2 + o - 3. Let t(b) = 9*b**4 - 4*b**3 + b**2 - b + 5. Let q(d) = m*n(d) + 3*t(d). Factor q(z).
2*z*(z - 1)**2*(z + 1)
Let k be (5/20)/(2/24). Let i**5 - 8*i + i**2 - 37*i**2 - 44*i**4 - 60*i**k - 4*i**5 - 9*i**5 = 0. Calculate i.
-1, -2/3, 0
Let d(h) = 40*h**2 - 50*h + 25. Let l(x) = -x**3 + 39*x**2 - 51*x + 25. Let t(z) = -4*d(z) + 5*l(z). Factor t(w).
-5*(w - 5)*(w - 1)**2
Suppose 0 = a - 22. Factor 4*t**3 + t**4 - 24*t**2 + a*t**2 - 3*t**4.
-2*t**2*(t - 1)**2
Let s(v) be the third derivative of 0*v**4 + 0*v**6 + 0*v**3 + 0*v - 2*v**2 + 0 - 1/1050*v**7 + 1/300*v**5. Factor s(g).
-g**2*(g - 1)*(g + 1)/5
Factor 4/5*x - 4/5*x**3 + 4/5*x**2 - 4/5.
-4*(x - 1)**2*(x + 1)/5
Let z(y) be the second derivative of -y**6/75 + y**5/25 - y**4/30 + 7*y. Factor z(n).
-2*n**2*(n - 1)**2/5
Let i(h) be the first derivative of 4*h**3/3 + 6*h**2 + 8*h - 15. Factor i(x).
4*(x + 1)*(x + 2)
Let o(f) be the first derivative of -f**9/1512 + f**8/840 + f**3/3 + 2. Let v(g) be the third derivative of o(g). Suppose v(h) = 0. Calculate h.
0, 1
Let o(b) be the first derivative of b**7/1260 - b**5/180 + 2*b**3/3 + 3. Let g(z) be the third derivative of o(z). Factor g(w).
2*w*(w - 1)*(w + 1)/3
Suppose -264*y + 260*y = 2*k + 8, -2*y = 6. Factor 0*z + 2/11*z**k - 2/11*z**3 + 0.
-2*z**2*(z - 1)/11
Solve 0 - 1/3*a - 1/3*a**2 = 0.
-1, 0
Solve 4/3*c**4 - c**5 + 0 + 2/3*c**3 + 1/3*c - 4/3*c**2 = 0.
-1, 0, 1/3, 1
Factor -8/11 - 56/11*f - 12/11*f**3 - 50/11*f**2.
-2*(f + 2)**2*(6*f + 1)/11
Let p(c) be the third derivative of c**8/336 - c**6/120 - 18*c**2 - 2*c. Factor p(d).
d**3*(d - 1)*(d + 1)
Suppose 5*g - 5*a = 20, 3*g + 2*a = -2*a - 2. Factor -9*w - 8 - 14*w**2 - 66*w**g - 54*w**3 - 39*w - 10*w**2.
-2*(3*w + 1)*(3*w + 2)**2
Let v(k) be the first derivative of k**6/60 + k**5/30 - k**4/12 - k**3/3 + k**2/2 - 1. Let q(w) be the second derivative of v(w). Factor q(s).
2*(s - 1)*(s + 1)**2
Let s(h) = -1. Let r(d) = -2 - 3 + 3*d - 3*d**2 + 1 + d**3. Let x(n) = r(n) - 3*s(n). Factor x(j).
(j - 1)**3
Let q = 407 - 399. Determine x, given that 6*x - 4/3 + 10/3*x**3 - q*x**2 = 0.
2/5, 1
Let b(z) = -z**5 + z**4 - z**3 + z + 1. Let s(a) = a**5 - 2*a**4 + 5*a**3 + 2*a**2 - 2*a - 2. Let u(g) = 2*b(g) + s(g). Factor u(t).
-t**2*(t - 2)*(t + 1)**2
Factor 0*d + 50/3*d**2 - 55/3*d**3 + 0 - 28/3*d**4 - d**5.
-d**2*(d + 5)**2*(3*d - 2)/3
Suppose 3*n = 2*r - 0*r - 13, -5*r + 4 = 2*n. Let i(d) be the third derivative of 0 + 3/40*d**5 + 1/8*d**4 + 0*d - r*d**2 + 1/12*d**3. Factor i(y).
(3*y + 1)**2/2
Let a(d) be the first derivative of -d**4 + 8*d**3/3 + 6*d**2 + 17. Solve a(r) = 0.
-1, 0, 3
Suppose 3*i + i - 7 = -g, 0 = -3*g - 15. Determine o, given that -8/5 - 2/5*o**i + 0*o + 6/5*o**2 = 0.
-1, 2
Let m = 45 - 45. Let -4/7*a**2 + 2/7*a**5 + 4/7*a**4 + 0 - 2/7*a + m*a**3 = 0. Calculate a.
-1, 0, 1
Let q(y) = y**2 + 4*y. Let m be q(6). Let c be 6/(-8) + 69/m. Let -2/5*j**2 + 2/5*j**4 - 2/5*j + 0 + c*j**3 = 0. Calculate j.
-1, 0, 1
Let k = 10 - 0. Let y = k - 7. Factor 2/3*b**4 + 2/9*b**2 + 0*b + 0 - 2/3*b**y - 2/9*b**5.
-2*b**2*(b - 1)**3/9
Let r(x) be the first derivative of x**5/2 + 9*x**4/8 + x**3/2 - x**2/4 + 2. Solve r(j) = 0 for j.
-1, 0, 1/5
Let z(w) be the second derivative of -w**7/1680 + w**6/720 + w**5/240 + w**4/6 - 2*w. Let s(f) be the third derivative of z(f). Factor s(d).
-(d - 1)*(3*d + 1)/2
Let b(k) be the third derivative of 0 + 0*k**4 + 1/35*k**7 + 1/112*k**8 + 0*k**5 + 0*k**3 + 0*k**6 + 0*k + 5*k**2. Let b(c) = 0. What is c?
-2, 0
Let m be ((-10)/(-8))/((-9)/((-126)/35)). Suppose 2*d = 6 - 2. Factor g + 1/2*g**d + m.
(g + 1)**2/2
Let v = -19487/105 - -928/5. Let i(j) be the third derivative of 0*j**5 + 0*j**3 + 0*j**4 + 0*j + j**2 + 0 + v*j**7 + 0*j**6. Factor i(r).
2*r**4
Find y such that y**3 - 3*y**2 - 49*y + 97*y - 13*y**3 + 12 = 0.
-2, -1/4, 2
Suppose 4*h - a = 2, h - 2*a - 4 = -0*h. Factor 0*i**3 + 8/9*i**5 + 0*i + h + 2/9*i**4 + 0*i**2.
2*i**4*(4*i + 1)/9
Let w(p) be the first derivative of -3 + 1/4*p**4 - p + 1/3*p**3 - 1/2*p**2. Find j, given that w(j) = 0.
-1, 1
Find y such that 1835*y + 1083*y**2 + 5488 - 999*y**2 - 659*y + 2*y**3 = 0.
-14
Suppose -8*t**2 - 4*t**3 + 0*t - 1/2*t**5 + 7/2*t**4 + 0 = 0. Calculate t.
-1, 0, 4
Let d(z) be the third derivative of 1/42*z**5 + 0*z - z**2 + 0 + 4/21*z**3 - 1/420*z**6 - 2/21*z**4. Find o such that d(o) = 0.
1, 2
Let t(w) be the first derivative of w**6/3 - w**4 + w**2 - 8. Factor t(v).
2*v*(v - 1)**2*(v + 1)**2
Suppose 6/7*o**2 + 3/7*o**5 - 9/7*o**4 + 3/7 + 6/7*o**3 - 9/7*o = 0. What is o?
-1, 1
Let f = 1 - -2. Let v(b) = 10*b**2 - 24. Let z(d) = -2*d**2 + 5. Let a(r) = f*v(r) + 14*z(r). Factor a(m).
2*(m - 1)*(m + 1)
Let j(p) be the second derivative of