e the first derivative of 4*n**5/105 + 5*n**4/42 + 8*n**3/63 + n**2/21 + 9. Suppose f(u) = 0. What is u?
-1, -1/2, 0
Let r(w) = w**3 + 7*w**2 + 6*w + 2. Let g be r(-6). Suppose -4*v = 16, 4*s - 4*v - 13 = 3. Factor -g*m**2 + s*m**4 + 2*m**4 + 0*m**4.
2*m**2*(m - 1)*(m + 1)
Let w(s) be the second derivative of -2/21*s**3 + 0*s**2 - 7*s - 1/6*s**4 + 0 - 1/14*s**5. Factor w(t).
-2*t*(t + 1)*(5*t + 2)/7
Let a = -5 - -21. Suppose 3*n - 2*j + 0*j - 4 = 0, n + 3*j = a. Solve 7*b**3 - b + n*b**2 + 3*b - 13*b**2 = 0.
0, 2/7, 1
Let b(x) = -x**3 + x**2 + x + 1. Let y = 10 + -7. Let l(p) = -72*p**3 + 87*p**2 - 30*p - 3. Let h(j) = y*b(j) + l(j). Find n such that h(n) = 0.
0, 3/5
Let k(d) = -2*d**4 - 3*d**3 + d**2 + 4. Let p(n) be the first derivative of n**5 + 7*n**4/4 - n**3 - 9*n + 2. Let t(h) = 7*k(h) + 3*p(h). Factor t(l).
(l - 1)**2*(l + 1)**2
Let h(n) be the third derivative of n**8/560 - n**7/840 - n**6/45 - n**5/30 + 7*n**3/6 - 6*n**2. Let g(i) be the first derivative of h(i). Factor g(m).
m*(m - 2)*(m + 1)*(3*m + 2)
Let f(r) be the third derivative of r**8/2520 - r**7/1260 - r**6/270 - r**3/2 - 3*r**2. Let p(g) be the first derivative of f(g). Suppose p(c) = 0. Calculate c.
-1, 0, 2
Suppose -65*u = -62*u. What is j in -2*j**2 + 8/3 + u*j + 2/3*j**3 = 0?
-1, 2
Let g = 516 + -516. Solve -2/5*p**2 + 6/5*p**4 + 4/5*p**3 + 0*p + g = 0.
-1, 0, 1/3
Let d be (4/14)/(7 - 384/56). Factor 0 - 2/9*o**d - 2/9*o.
-2*o*(o + 1)/9
Let w(f) = f**2 + 14*f - 10. Let l be w(-15). Let i be 4/(-6)*(2 - l). Let -4/3 - 1/3*r**i - 4/3*r = 0. What is r?
-2
Let c(p) = -11*p**4 + 4*p**3 - 12*p**2 - 9. Let j(q) = -q**4 + q**3 - q**2 - 1. Let v(y) = -2*c(y) + 18*j(y). Factor v(g).
2*g**2*(g + 1)*(2*g + 3)
Let v(l) be the first derivative of -l**6/6 + l**4/2 - l**2/2 - 21. Factor v(z).
-z*(z - 1)**2*(z + 1)**2
Let f(v) be the first derivative of -3/4*v**4 + 2 + 1/5*v**5 + 0*v - 1/2*v**2 + v**3. Factor f(i).
i*(i - 1)**3
Let p be ((-3)/(-4))/(2/8). Let a = 4/5 - 2/5. Let 2/5*s**p + 0*s**2 + 0*s - a*s**5 + 0*s**4 + 0 = 0. What is s?
-1, 0, 1
Let t(a) = 2*a**2 + 4*a + 5. Let g be t(-1). Let -2/9*s**2 + 0 + 2/9*s**g - 4/9*s = 0. What is s?
-1, 0, 2
Find c, given that -33/2*c - 24*c**2 - 3 - 21/2*c**3 = 0.
-1, -2/7
Determine z, given that 4/3 + 1/3*z**4 + 13/3*z**2 - 2*z**3 - 4*z = 0.
1, 2
Let n(g) be the third derivative of -g**8/840 - g**7/525 + g**6/300 + g**5/150 + 3*g**2. Factor n(x).
-2*x**2*(x - 1)*(x + 1)**2/5
Suppose 3*w + w = 8. Suppose 0 = -w*n - 3*n + 10. Determine d, given that -4/5*d - 2/5 - 2/5*d**n = 0.
-1
Factor -6/7*f - 2/7 - 6/7*f**2 - 2/7*f**3.
-2*(f + 1)**3/7
Let a(b) = -346*b**5 + 735*b**4 - 525*b**3 + 122*b**2 - 3. Let y(w) = 1037*w**5 - 2205*w**4 + 1575*w**3 - 367*w**2 + 8. Let d(i) = 8*a(i) + 3*y(i). Factor d(f).
f**2*(7*f - 5)**3
Let -8/3 - 14/3*u**4 + 20*u**3 + 16*u - 86/3*u**2 = 0. What is u?
2/7, 1, 2
Let m(s) be the second derivative of 0*s**3 - s - 1/240*s**6 + 0 + 0*s**4 + 0*s**5 + 1/2*s**2. Let l(c) be the first derivative of m(c). Solve l(i) = 0.
0
Suppose -4*r + 44 = 4*m - 0*m, -2*r = -2*m - 2. Let f(i) = i**3 + i. Let v(z) = 9*z**3 - z**2 + 8*z + 1. Let g(p) = r*v(p) - 51*f(p). Factor g(n).
3*(n - 2)*(n - 1)*(n + 1)
Let b(c) be the third derivative of 8*c**5/135 + 11*c**4/54 + 2*c**3/9 + 13*c**2. Factor b(k).
4*(k + 1)*(8*k + 3)/9
Solve 0*i**2 + 0*i + 0 + 3/2*i**3 - 1/2*i**4 = 0.
0, 3
Let k = -3070 - -6259/2. Let i = -56 + k. Suppose 2*j**3 + j + i*j**2 - 1/2 = 0. What is j?
-1, 1/4
Let s(k) be the third derivative of -k**8/168 - k**7/35 - k**6/20 - k**5/30 + 6*k**2. Suppose s(d) = 0. Calculate d.
-1, 0
Let i = 4 - -1. Let k be 12/i - 0/(-13). Factor -k*d**3 - 2/5*d - 8/5*d**4 - 8/5*d**2 - 2/5*d**5 + 0.
-2*d*(d + 1)**4/5
Let d be (200/24)/(1 + 1) + -4. Factor 1/2 - 2/3*g + d*g**2.
(g - 3)*(g - 1)/6
Suppose 6*t + 13 = 7*t. Suppose -4*g + 30 = g. Factor -3 - 5*v**4 - g*v**3 - 12*v - t*v**2 + 4*v**4 - 1.
-(v + 1)**2*(v + 2)**2
Let i(j) be the first derivative of j**6/9 - 8*j**5/15 - 11*j**4/6 - 4*j**3/3 + 12. Determine z so that i(z) = 0.
-1, 0, 6
Let b(s) be the third derivative of -s**5/390 + s**3/39 + 8*s**2. Factor b(w).
-2*(w - 1)*(w + 1)/13
Let p(h) be the third derivative of h**7/210 + h**6/60 + h**5/60 + 8*h**2. Solve p(t) = 0 for t.
-1, 0
Let k(t) be the third derivative of -t**7/735 - t**6/420 + t**5/210 + t**4/84 - 12*t**2. Determine r, given that k(r) = 0.
-1, 0, 1
Let p(m) be the third derivative of m**8/56 - 2*m**7/15 + 2*m**6/15 + 17*m**2. Factor p(r).
2*r**3*(r - 4)*(3*r - 2)
Let k be (6/7)/(2/28). Let w = 14 - k. Factor 0*x + 0*x**w + 0*x**3 + 0 - 3/4*x**4.
-3*x**4/4
Suppose 2*t - 2 = 6. Suppose -5*u - 4*z + 6*z = -34, -3*u + 12 = -t*z. Factor 54*v + 6*v - u - 4*v - 102*v**2 + 4*v**2.
-2*(7*v - 2)**2
Let r = 11 + -8. Factor 0*j**2 + 2*j + 2 - 3*j + 2*j - r*j**2.
-(j - 1)*(3*j + 2)
Let k(d) be the second derivative of 9/2*d**2 + 1/2*d**3 - d**4 - 3*d + 0. Let k(v) = 0. Calculate v.
-3/4, 1
Solve 4/7*l**2 + 0 + 0*l - 4/7*l**4 + 0*l**3 = 0 for l.
-1, 0, 1
Factor -12*j**2 - 11*j**3 - j**3 + 10*j + 24 + 4*j**4 + 18*j.
4*(j - 3)*(j - 2)*(j + 1)**2
Let m be (2/4)/(9/366). Let h = m + -20. Factor 0 + h*u**2 + 0*u - 1/3*u**3.
-u**2*(u - 1)/3
Let m(i) = 7*i - 152. Let g be m(22). Factor 2/11*f**4 + 6*f**g - 80/11*f - 20/11*f**3 + 32/11.
2*(f - 4)**2*(f - 1)**2/11
Let a(v) be the third derivative of -v**8/336 - 2*v**7/315 + v**6/180 + v**5/45 + v**4/72 + 5*v**2. Suppose a(n) = 0. What is n?
-1, -1/3, 0, 1
Let s(o) be the second derivative of o**4/48 - o**3/12 - 16*o. Determine y so that s(y) = 0.
0, 2
Let d = -89 - -625/7. Factor 0*q + 2/7 - d*q**2.
-2*(q - 1)*(q + 1)/7
Let p(b) = 2 + 4*b + b**2 + 0*b**2 + 0*b**2. Let n be p(-4). Factor -l**4 - l**3 + 2*l - l**n - l + 2*l**2.
-l*(l - 1)*(l + 1)**2
Let u = -346/3 + 116. Factor -6 - 4*y - u*y**2.
-2*(y + 3)**2/3
Let g(t) be the first derivative of -1/6*t**4 - 1/3*t**3 + 0*t + t**2 - 1/30*t**5 + 1. Let i(a) be the second derivative of g(a). What is v in i(v) = 0?
-1
Let g(p) = -p. Let c be g(-1). Let h be c - 1*(2 - 3). Factor j**3 + 0*j**3 + 2 + 5*j + j**3 + 4*j**h - j**3.
(j + 1)**2*(j + 2)
Let b(a) be the third derivative of 1/210*a**5 + 0*a**3 + 0*a**4 + 1/1176*a**8 - 1/735*a**7 + 0*a - a**2 + 0 - 1/420*a**6. Factor b(z).
2*z**2*(z - 1)**2*(z + 1)/7
Let s be -3 + 1 - -3 - 5. Let f be 2/s - (-3 - -2). Factor -1/2*r + 1 - f*r**2.
-(r - 1)*(r + 2)/2
Let k = 979 + -977. Let 4/3*l**k + 1/3*l**3 + 2/3 + 5/3*l = 0. What is l?
-2, -1
Suppose 3*h = h. Let y be 0/(0 - (2 + h)). Determine r so that -2/3*r**5 + 2/3*r**3 - 2/3*r**4 + 0*r + y + 2/3*r**2 = 0.
-1, 0, 1
Factor 754 + 5*o**3 + 0*o**3 - 309 + 735*o + 1270 + 105*o**2.
5*(o + 7)**3
Factor -2*s**2 - 5*s**3 + 5*s + 15*s**4 - 3*s**2 - 10*s**4.
5*s*(s - 1)**2*(s + 1)
Let y(f) = f**5 + 4*f**4 + 29*f**3 - 20*f**2 + 8*f. Let l be 1 + (-46 - (0 - 1)). Let o(j) = j**4 + j**3. Let r(n) = l*o(n) + 4*y(n). Solve r(d) = 0 for d.
0, 1, 2
Let z(o) = 73*o - 509. Let w be z(7). Let w + 1/8*c**2 + c = 0. What is c?
-4
Suppose -20 + 9*u**2 + 0*u**2 - 4*u**2 = 0. Calculate u.
-2, 2
Factor -8/19 + 6/19*r + 2/19*r**2.
2*(r - 1)*(r + 4)/19
Let u(j) = j + 1. Let c be u(1). Let 1 + 3*k**c + 1 - 7*k - 8 + 4*k = 0. Calculate k.
-1, 2
Suppose -4*n = -1 - 15. Let a(w) be the first derivative of 2 + 2/21*w**3 + 0*w**2 + 0*w - 1/7*w**n + 2/35*w**5. Factor a(o).
2*o**2*(o - 1)**2/7
Suppose 0*z**2 + 2/11*z**4 + 0*z + 0 + 2/11*z**3 = 0. Calculate z.
-1, 0
Let s = -621/2 - -312. Determine w so that -s*w**2 + 0 + 3/2*w = 0.
0, 1
Suppose 30*v**2 + 5 + 29*v - 33 - 34*v**2 + 3*v = 0. Calculate v.
1, 7
Let o(s) = -s**2 - 4*s - 4. Let w(r) = -r**2 - 4*r - 4. Let g(z) = -7*o(z) + 6*w(z). Find n, given that g(n) = 0.
-2
Let j(b) = b**4 - 21*b**3 - 15*b**2 - 11*b + 6. Let o(t) = -3*t**4 + 43*t**3 + 30*t**2 + 23*t - 13. Let z(s) = -13*j(s) - 6*o(s). Factor z(l).
5*l*(l + 1)**3
Let s(a) be the first derivative of -1/9*a**3 + 1/3*a**2 - 4 - 1/3*a. Let s(n) = 0. What is n?
1
Let r(a) = 2*a**2 + 3*a. Suppose -2*j + 4 = 0, 0 = 2*q + j + 33 + 9. Let s(f) = 7*f**2 + 11*f. Let t(m) = q*r(m) + 6*s(m). Determine o, given that t(o) = 0.
0
Let z be (-4)/(-1) - (11 - 11). Factor -10*j**4 + 9*j**z + 4*j**4.
3*j**4
Suppose -4 = -5*c + 16. Suppose c*a + 3 = 11. Factor 0 + 0 - u**a.
-u**2
Let q(b) be the