
Suppose 30 = 4*m + 18*o - 13*o, -m - 3*o + 18 = 0. Factor 0*z**2 + 2/5*z**3 + m + 0*z + 2/5*z**4.
2*z**3*(z + 1)/5
Let j(a) be the first derivative of 0*a + 3*a**2 - 1/10*a**5 + 1/40*a**6 + 0*a**3 + 1 + 1/8*a**4. Let x(b) be the second derivative of j(b). Factor x(u).
3*u*(u - 1)**2
Factor -29*n**3 - 37*n**2 - 4*n - 18*n**2 + 4*n - 7*n**2 + n**4.
n**2*(n - 31)*(n + 2)
Let u be (-4)/(-12) - (-1)/(-3). Let y be -4 + 5 + (-7)/7. Find w such that u + y*w + 2/5*w**3 + 0*w**2 + 2/5*w**4 = 0.
-1, 0
Suppose -133*u = -131*u. Suppose 2 = -4*x + 10. Factor 2 + u*t - 5 + 1 - 3*t - t**x.
-(t + 1)*(t + 2)
Let c(s) be the third derivative of 0 + 0*s + 14*s**2 + 1/80*s**5 + 0*s**3 - 1/480*s**6 - 1/48*s**4. Let c(b) = 0. Calculate b.
0, 1, 2
Let w(i) be the third derivative of 1/80*i**5 - 1/8*i**3 + 0*i**4 + 0*i + 0 + 29*i**2. Factor w(m).
3*(m - 1)*(m + 1)/4
Let t(i) be the first derivative of -16*i**5/5 - 5*i**4/2 + 70*i**3/3 + 20*i**2 - 24*i + 257. Solve t(h) = 0 for h.
-2, -1, 3/8, 2
Let r be 54/(-24) - 2/(24/9). Let l be 1*-3*r/45. Solve -1/5*b**2 + l*b + 0 = 0.
0, 1
Let l(s) be the second derivative of 0 - 7/18*s**3 + 3*s - 1/12*s**5 + 1/3*s**2 + 1/90*s**6 + 1/4*s**4. Determine b so that l(b) = 0.
1, 2
Let p be (0 + (-4 - -3))/(3/(-9)). Let -4*v**2 - v**3 - v**5 - 2*v**p - v**5 + 4*v + 2*v**4 + 3*v**5 = 0. What is v?
-2, 0, 1
Let f(r) be the first derivative of r**6/6 - 11*r**5/5 + 21*r**4/2 - 64*r**3/3 + 16*r**2 - 73. Let f(j) = 0. What is j?
0, 1, 2, 4
Let r(o) = 25*o**2 + 476*o + 58069. Let g(c) = 71*c**2 + 1429*c + 174209. Let k(v) = 6*g(v) - 17*r(v). Factor k(h).
(h + 241)**2
Let y(x) be the third derivative of 34*x**2 + 1/20*x**5 + 0 + 1/12*x**4 + 0*x + 0*x**3 + 0*x**6 - 1/210*x**7. Determine p, given that y(p) = 0.
-1, 0, 2
Suppose -10*v = -3*j - 12*v + 5, 0 = 3*j - 5*v - 19. Find d, given that 9/5*d**j - 6/5 + 12/5*d**2 - 3/5*d = 0.
-1, 2/3
Let f(n) be the third derivative of -n**8/448 + n**7/120 + n**6/30 - n**5/10 + 11*n**4/8 - 4*n**2. Let a(x) be the second derivative of f(x). Factor a(r).
-3*(r - 2)*(r + 1)*(5*r - 2)
Let y(s) = s**5 + s**4 - s**3 - s**2 + s + 1. Let g(n) = -12*n**4 - 40*n**3 + 52*n**2 + 140*n - 4. Let i(z) = -g(z) - 4*y(z). Find d such that i(d) = 0.
-2, 0, 3
Let n be 4/(-18) - (2 + (-53236)/17100). Let l = -1/475 + n. Factor l*o**2 + 0 + 2/9*o**3 + 8/9*o.
2*o*(o + 2)**2/9
Let p(j) be the third derivative of 0*j**5 + 0*j**3 - 16*j**2 + 0*j**4 + 0 - 1/160*j**6 + 0*j - 1/560*j**7. What is y in p(y) = 0?
-2, 0
Suppose -24*p + 24 - 24 = 0. Let w(o) be the second derivative of -3/40*o**5 + p*o**2 + 0 + o + 0*o**3 - 1/8*o**4. Find g such that w(g) = 0.
-1, 0
Let j(c) be the second derivative of -2*c**5/15 + c**4/6 + 2*c**3/3 - 5*c**2/3 + c - 92. Determine d so that j(d) = 0.
-5/4, 1
Let p(s) be the third derivative of s**8/84 + 7*s**7/45 + 11*s**6/45 - 13*s**5/5 + 55*s**4/18 + 25*s**3/9 - s**2 - 67. Let p(u) = 0. Calculate u.
-5, -1/6, 1
Factor -18*t + 5*t**3 - t**3 - 3*t**3 + 2*t**2 + 19*t**2 - 4*t**3.
-3*t*(t - 6)*(t - 1)
Solve -5/3*b**3 - 15*b**2 - 20/3 - 55/3*b + 5/3*b**4 = 0 for b.
-1, 4
Let z(w) be the third derivative of w**6/240 + w**5/15 + 13*w**4/48 + w**3/2 - 6*w**2 - 35*w. Factor z(u).
(u + 1)**2*(u + 6)/2
Let t = -3 + 6. Factor t*a**3 + 6*a**2 - a**3 - 3*a**3 - 2*a**3 - 6 + 3*a.
-3*(a - 2)*(a - 1)*(a + 1)
Let w = -1/52652 - -105309/263260. Find a, given that 4/5 - w*a - 6/5*a**2 + 2/5*a**3 + 2/5*a**4 = 0.
-2, -1, 1
Let z(p) be the first derivative of 0*p**4 + 12 + 0*p**2 + 0*p + 0*p**3 - 4/5*p**5 + 2/3*p**6. Let z(t) = 0. Calculate t.
0, 1
Let t(h) be the third derivative of -h**8/1680 + h**7/1050 + h**6/300 - h**5/150 - h**4/120 + h**3/30 + 72*h**2. Factor t(n).
-(n - 1)**3*(n + 1)**2/5
Let 113*c**2 - 52*c**2 + 24*c - 60*c**2 - 5*c - 66 = 0. What is c?
-22, 3
Suppose -2 = -2*h - 12. Let j(x) = -x**3 - 6*x**2 - 5*x + 2. Let w be j(h). Let -p**2 + 8 + p**w - 4*p**2 - 4*p = 0. Calculate p.
-2, 1
Let f(h) be the first derivative of -5*h**6/6 + 2*h**5 + 15*h**4 + 70*h**3/3 + 25*h**2/2 - 82. Factor f(w).
-5*w*(w - 5)*(w + 1)**3
Let p(y) = -81*y**3 + 2958*y**2 - 63504*y + 444528. Let x(m) = -5*m**3 + 185*m**2 - 3969*m + 27783. Let v(u) = 2*p(u) - 33*x(u). Let v(a) = 0. What is a?
21
Solve 0 - 260*f + 13*f**2 + 535*f - 260*f + 2 = 0.
-1, -2/13
Solve -14/9*w**5 - 28/9*w + 0 - 82/3*w**3 + 130/9*w**4 + 158/9*w**2 = 0.
0, 2/7, 1, 7
Let q(g) be the first derivative of -g**5/5 + 11*g**4/2 - 140*g**3/3 + 100*g**2 + 162. Let q(m) = 0. Calculate m.
0, 2, 10
Determine w so that -12/7*w + 11/7*w**4 - 9/7*w**3 - 68/7*w**2 + 0 = 0.
-2, -2/11, 0, 3
Let i = -77 - -75. Let o be i/(4 - -2)*36/(-6). Factor 3/2*j**o - 1/2*j**4 + 4*j + 2 - j**3.
-(j - 2)*(j + 1)**2*(j + 2)/2
Factor -2/3*k**2 - 26*k + 80/3.
-2*(k - 1)*(k + 40)/3
Let x = 33443/3 + -11147. Suppose -4*y + 16/3 + x*y**2 = 0. What is y?
2, 4
Let w(g) = 6*g**2 - 2*g + 5*g + 6*g. Let x(i) = -i**2 + i. Let k(o) = -w(o) - 3*x(o). Factor k(f).
-3*f*(f + 4)
Let c(r) = -r**3 + 9*r**2 - 12*r - 12. Let n be c(7). Let u = 12 + n. Solve u - 2 + 2*h**2 - 5*h**2 = 0 for h.
-2, 2
Let w(f) be the first derivative of 0*f**3 + 0*f**4 - 1 + 1/252*f**7 + 0*f**2 + f + 0*f**6 - 1/120*f**5. Let q(j) be the first derivative of w(j). Factor q(z).
z**3*(z - 1)*(z + 1)/6
Let g be (1 + (-12)/9)*-9. Let c be 15/4 + g/12. Find m such that c*m**2 + 4*m**2 - 5*m**2 = 0.
0
Let i = 2446/15 + -163. Let v(b) be the third derivative of i*b**5 + 3*b**2 + 0*b**3 + 0*b - 1/12*b**4 - 1/60*b**6 + 0. Solve v(l) = 0.
0, 1
Factor 189/2*b - 243/2 + 51/2*b**2 + 3/2*b**3.
3*(b - 1)*(b + 9)**2/2
Let n(b) be the first derivative of b**3/3 - 3*b**2 - 4*b - 6. Let d be n(7). Solve -k**3 - 4 + 3*k**4 + 6*k**2 - 2*k**2 + d*k**2 - 6*k**4 + k**5 = 0 for k.
-1, 1, 2
Let k(d) = 14 + d**2 - 2*d**3 + 10 - 22 + 2*d + d**4. Let g(z) = 9*z**4 - 16*z**3 + 8*z**2 + 16*z + 17. Let j(c) = -6*g(c) + 51*k(c). What is t in j(t) = 0?
-2, -1, 0, 1
Let m(c) = -c**3 + 9*c**2 + 12*c - 18. Let x be m(10). Let b = 0 + 4. Solve -b*d + 0*d - 4*d**2 - x*d + d**2 = 0.
-2, 0
Let b(w) be the second derivative of 11*w + 0*w**2 + 3/10*w**3 - 1/20*w**4 + 0. Suppose b(g) = 0. Calculate g.
0, 3
Let c = -28 + 24. Let z(h) = h**2 + 6*h + 10. Let q be z(c). Factor 4*u**q - u - u**3 + u**3 + u**3 - 4*u**4.
-u*(u - 1)*(u + 1)*(4*u - 1)
Suppose 0 = -u + 6*u - 40. Let l = u + -5. Find i such that -36*i - l + 9*i**2 + 40*i**3 + 9*i**4 - 10*i**3 - 9 = 0.
-2, -1/3, 1
Find o, given that 4/11*o**3 + 0*o + 8/11*o**5 + 18/11*o**4 + 0 + 0*o**2 = 0.
-2, -1/4, 0
Let k(z) be the third derivative of -z**7/210 - z**6/40 - z**5/60 + z**4/8 + z**3/3 + z**2 - 85*z. Factor k(c).
-(c - 1)*(c + 1)**2*(c + 2)
Let v(f) = -74 + 43 + 4*f - 2*f + 37. Let k be v(-2). Factor -2/5*s - 4/15 - 2/15*s**k.
-2*(s + 1)*(s + 2)/15
Let f = -18 - -21. Suppose 0 - f = -c. Let -3 + 3*a**3 + 4 - 2*a**3 - c + 2*a**2 - a = 0. What is a?
-2, -1, 1
Suppose -9*g + 0 + 5 + 5*g - 2*g**2 + 7*g = 0. Calculate g.
-1, 5/2
Let r(j) be the second derivative of 1/60*j**4 + 0*j**3 + 0*j**2 + 13*j + 0. Factor r(w).
w**2/5
Let h(l) = 2*l**3 - 66*l**2 + 660*l. Let u(m) = 2*m**3 - 67*m**2 + 658*m. Let q(r) = -5*h(r) + 6*u(r). Factor q(f).
2*f*(f - 18)**2
Find u such that -186/7 + 2/7*u**2 + 184/7*u = 0.
-93, 1
Let y = -36/61 - -424/305. Let n(f) be the first derivative of -3 + y*f**3 + 0*f - 6/5*f**2 - 3/20*f**4. Factor n(p).
-3*p*(p - 2)**2/5
Let t(v) be the third derivative of v**6/600 - v**2 + 24*v. Let t(f) = 0. What is f?
0
Let f(o) = 10*o**2 + 45*o - 45. Let z(v) be the first derivative of v**3/3 + 2*v**2 - 4*v - 3. Let t(l) = -4*f(l) + 45*z(l). Suppose t(c) = 0. What is c?
0
Let r(y) = -7*y**2 + 3*y - 5. Let c(a) = -11 - 5*a**2 + 2*a - a**2 + 7. Let q(t) = 5*c(t) - 4*r(t). Factor q(h).
-2*h*(h + 1)
Let w(z) be the second derivative of z**7/28 - 3*z**6/20 - 27*z**5/40 + 27*z**4/8 - 382*z. Factor w(d).
3*d**2*(d - 3)**2*(d + 3)/2
Let f(t) be the third derivative of t**5/90 + 43*t**4/18 + 1849*t**3/9 + 6*t**2 + 3*t. Determine k, given that f(k) = 0.
-43
Let z(i) be the first derivative of -2*i**5/5 + 2*i**4 + 8*i**3/3 - 16*i**2 + 491. Find g, given that z(g) = 0.
-2, 0, 2, 4
Let j(d) be the first derivative of 273*d**6/4 - 2019*d**5/10 + 209*d**4 - 236*d**3/3 - 4*d**2 + 8*d + 97. Suppose j(k) = 0. What is k?
-2/13, 2/7, 2/3