- 120*g**2 - 128*g + 365. Let c(u) = 0. Calculate u.
-1/4, 1, 2, 8
Let r(m) = 8*m**4 - 16*m**3 + 15*m**2 + 5*m - 16. Let o(w) = 70*w**4 - 142*w**3 + 134*w**2 + 46*w - 144. Let z(x) = 6*o(x) - 52*r(x). Solve z(l) = 0 for l.
-1, 2
Let y = 32272 - 96815/3. Find a, given that -2/3*a**2 + y*a**3 + 0 - a = 0.
-1, 0, 3
Let x = 1257 - 1253. Let d(m) be the first derivative of -2/3*m**3 + 0*m + 3/4*m**x + 1/12*m**6 + 1/4*m**2 + 3 - 2/5*m**5. Factor d(y).
y*(y - 1)**4/2
Let y be (-4)/18 + 34/153. Let b(f) be the third derivative of 0 + 5*f**2 + 0*f**3 + 0*f - 1/80*f**6 + 3/80*f**5 + 1/840*f**7 + y*f**4. Solve b(s) = 0 for s.
0, 3
Let z(k) be the first derivative of 3*k**5/20 - k**4/2 - 3*k**3/2 + 15*k + 14. Let y(a) be the first derivative of z(a). Factor y(m).
3*m*(m - 3)*(m + 1)
Let l be (-18)/10*((-63)/6 - -8). Let g(d) be the first derivative of -3*d**3 + 3/4*d**4 - 3*d + 3 + l*d**2. Factor g(m).
3*(m - 1)**3
Suppose i = -5*h - 425, -i = 2*h + 214 - 41. Let w = -335/4 - h. Factor 5/4*m - 3/4 - w*m**3 - 1/4*m**2.
-(m - 1)**2*(m + 3)/4
Factor 2044 - 2044 + 2*i**2 - 20*i.
2*i*(i - 10)
Let d(q) be the second derivative of 3*q**5/100 - 11*q**4/20 + 4*q**3/5 + 6*q**2 + 14*q - 4. Suppose d(v) = 0. Calculate v.
-1, 2, 10
Let h(o) = o**2 - 2*o - 7. Let x be h(-3). Factor -10*r**3 + 16 - r**4 - 38*r**2 + x*r + 23*r**2 + 2*r**3.
-(r - 1)*(r + 1)*(r + 4)**2
Factor 1/2*n + 0 - 2/3*n**2 + 1/6*n**3.
n*(n - 3)*(n - 1)/6
Let t(q) = -9*q**3 - 25*q**2 + 24*q + 11. Let z(m) = 5*m**3 + 13*m**2 - 12*m - 6. Let i(y) = -6*t(y) - 11*z(y). Determine b so that i(b) = 0.
0, 3, 4
Let o(t) = 19*t + 19. Let w be o(-1). Let p(f) be the second derivative of f + 0 - 1/45*f**6 - 1/30*f**5 + 1/9*f**4 + 0*f**3 + w*f**2. Factor p(n).
-2*n**2*(n - 1)*(n + 2)/3
Let t(b) be the second derivative of b**4/20 - 18*b**3/5 + 297*b**2/10 - 760*b. Let t(m) = 0. Calculate m.
3, 33
Let r(t) be the first derivative of -t**3/6 - 8*t**2 - 31*t/2 - 221. Factor r(u).
-(u + 1)*(u + 31)/2
Let t(f) be the first derivative of -f**7/672 + f**5/96 - 3*f**3 + 10. Let p(c) be the third derivative of t(c). Factor p(u).
-5*u*(u - 1)*(u + 1)/4
Let a be -6*(3 + 36/(-8)). Suppose -5*w + a = -2*w. Factor 5*l + 2*l**3 - w*l - 4*l**3.
-2*l*(l - 1)*(l + 1)
Let k(z) be the third derivative of z**9/141120 + z**8/70560 - 11*z**5/20 + 26*z**2. Let f(i) be the third derivative of k(i). Solve f(t) = 0.
-2/3, 0
Let o be -6 + (-162)/(-14) + -5. Let y = -12 - -86/7. Factor -y*z**2 + 2/7*z**4 - 4/7*z + o*z**3 + 0.
2*z*(z - 1)*(z + 1)*(z + 2)/7
Let k(a) = 13*a + 78. Let s be k(-6). Let n(c) be the third derivative of 0*c + 0*c**3 - 1/132*c**4 - 3*c**2 - 1/330*c**5 + s. Suppose n(g) = 0. Calculate g.
-1, 0
Let y(r) be the first derivative of -r**7/105 - 17*r**6/180 - 4*r**5/15 - r**4/4 - 6*r**3 + 2. Let z(t) be the third derivative of y(t). Solve z(v) = 0.
-3, -1, -1/4
Solve -420/17*c**3 - 2/17*c**5 - 250*c - 1900/17*c**2 - 3750/17 - 46/17*c**4 = 0 for c.
-5, -3
Solve -2/5*h + 0 - 12/5*h**3 - 8/5*h**2 - 2/5*h**5 - 8/5*h**4 = 0.
-1, 0
Suppose 6*o - 55 = -43. Determine c, given that 2/3*c**3 - 1/3 + 1/3*c**o - 2/3*c = 0.
-1, -1/2, 1
Let g(f) be the second derivative of -f**6/75 + f**5/25 + 11*f**4/30 - 4*f**3/5 - 36*f**2/5 - 54*f - 1. Factor g(c).
-2*(c - 3)**2*(c + 2)**2/5
Let o(i) be the third derivative of -i**5/150 + 29*i**4/20 - 86*i**3/15 - 479*i**2. What is z in o(z) = 0?
1, 86
Let q(y) = 8*y**3 - 2*y + 1. Let j be q(1). Factor 5*w - 9*w**2 + 10*w**2 - 4*w**2 + 5*w**3 - j*w**2.
5*w*(w - 1)**2
Let o = -394/3 - -132. Suppose -4/3 + 4/3*q**2 - o*q**3 + 2/3*q = 0. What is q?
-1, 1, 2
Let z(w) be the second derivative of w**7/5460 + w**6/1170 - w**5/156 - w**4/26 - w**3 + 12*w. Let p(n) be the second derivative of z(n). Factor p(d).
2*(d - 2)*(d + 1)*(d + 3)/13
Let h(p) = 2*p**2 - 2*p - 1. Let x(c) = -5*c**4 - 30*c**3 + 45*c**2 - 10*c - 20. Let d(b) = 20*h(b) - x(b). Factor d(s).
5*s*(s - 1)*(s + 1)*(s + 6)
Let n(b) = 5*b - 16. Let i be n(4). Factor -2*w**3 + 3*w**3 + i*w - 5*w**3 - 12*w**3.
-4*w*(2*w - 1)*(2*w + 1)
Let u be (10/(-25))/(4/20). Let i(f) = 79*f**2 + 34*f + 4. Let z(m) = 315*m**2 + 135*m + 16. Let y(c) = u*z(c) + 9*i(c). Factor y(t).
(9*t + 2)**2
Let f(w) = -8*w**3 + 12*w - 4. Let x(n) = n**4 - n**3 + n**2 - 1. Let g(t) = f(t) + 4*x(t). Factor g(l).
4*(l - 2)*(l - 1)**2*(l + 1)
Let x be (1 - -36)/(-1 - -2). Let u = x + -29. Factor 20*w**4 + 4*w + 24*w - u - 12*w**2 + 0 - 28*w**3.
4*(w - 1)**2*(w + 1)*(5*w - 2)
Let r be 6*((-24)/(-9))/4. Let z be 252/105 - r/2. Factor -1/5*w + 0 + z*w**2 - 1/5*w**3.
-w*(w - 1)**2/5
Let r = 2577/7 + -33487/91. Factor 4/13*t + 10/13*t**2 + 0 + 8/13*t**3 + r*t**4.
2*t*(t + 1)**2*(t + 2)/13
Let u(t) be the first derivative of -1 + 30*t**2 - 10*t**3 - 40*t + 5/4*t**4. Solve u(v) = 0 for v.
2
What is m in 2/3*m**2 - 2/3 + 1/3*m**3 - 1/3*m = 0?
-2, -1, 1
Let m be -2 + 5 + -1 + 3. Determine r so that -32*r**2 - 3*r**5 + 24*r**3 + 184 + 16*r**3 - 256 - r**m + 8*r**4 - 132*r = 0.
-2, -1, 3
Let p(j) be the second derivative of 0 - 4/9*j**2 - 4/27*j**3 + 2*j - 1/54*j**4. Factor p(b).
-2*(b + 2)**2/9
Let f(n) be the second derivative of 5*n**7/168 - 7*n**6/24 + 11*n**5/16 - 25*n**4/48 + n - 10. Factor f(p).
5*p**2*(p - 5)*(p - 1)**2/4
Let z(d) = -9*d**3 - 5*d**2 + 5*d + 9. Let x be (37 - 1)*1 - 1. Let w(u) = 80*u**3 + 45*u**2 - 45*u - 80. Let k(a) = x*z(a) + 4*w(a). Factor k(s).
5*(s - 1)*(s + 1)**2
Let k(j) be the second derivative of 0 + 2/7*j**7 + 0*j**2 + 0*j**4 - 10*j - 2/5*j**5 - 2/15*j**6 + 0*j**3. Let k(f) = 0. Calculate f.
-2/3, 0, 1
Let f(i) = -29*i**2 + 101*i + 579. Let g(x) = 5*x**2 - 17*x - 97. Let a(n) = 6*f(n) + 34*g(n). Let a(o) = 0. Calculate o.
-4, 11
Let r(j) be the first derivative of -j**6/40 - j**5/4 + j**4 - 2*j**3 - 19. Let g(o) be the third derivative of r(o). Factor g(y).
-3*(y + 4)*(3*y - 2)
Let u(o) be the first derivative of -2*o**7/147 + 2*o**6/105 - 15*o + 27. Let q(p) be the first derivative of u(p). Determine m, given that q(m) = 0.
0, 1
Let d(w) be the second derivative of 0*w**2 + 0*w**3 - 1/100*w**5 + 0 - 5*w - 1/60*w**4. Factor d(v).
-v**2*(v + 1)/5
Let d(r) be the first derivative of r**5 - 35*r**4/2 + 260*r**3/3 - 165*r**2 + 135*r + 182. Factor d(k).
5*(k - 9)*(k - 3)*(k - 1)**2
Let z(n) = -3*n - 9. Let c be z(-13). Determine j so that 1217 + 5*j - c*j + 10*j**2 - 1202 = 0.
1, 3/2
Let a = 80/249 + 1/83. Factor 0 + 0*p + 1/3*p**3 - a*p**2.
p**2*(p - 1)/3
Let f(u) = 2*u**2 - 8*u + 11. Let p(t) = 3*t**2 - 2*t + 2. Let j be p(1). Let r be f(j). Factor 0 + s**r + 6*s**3 - 2*s**2 + 0*s - 9/2*s**4.
s**2*(s - 2)**2*(2*s - 1)/2
Let s = -17 - -19. Factor 25*b**5 - 22*b**s - 13*b**4 - 7*b**4 - 65*b**4 + 105*b**3 - 33*b**2 + 10*b.
5*b*(b - 1)**3*(5*b - 2)
Let x be -7 + (-1488)/(-208) + (-58)/(-130). Determine m, given that 2/5*m**2 - 2/5 + x*m = 0.
-2, 1/2
Let m(p) be the first derivative of -p**9/1512 - p**8/210 - p**7/84 - p**6/90 - 13*p**3/3 + 5. Let u(w) be the third derivative of m(w). Solve u(s) = 0.
-2, -1, 0
Let u(q) be the first derivative of 25*q**4/8 - 35*q**3/3 - 25*q**2/4 + 35*q - 440. Solve u(s) = 0 for s.
-1, 1, 14/5
Let s = 769/570 + -3/190. Suppose 0 = -6*u + 4*u. Let -2*k**2 - 10/3*k**5 - s*k + 2*k**4 + 14/3*k**3 + u = 0. What is k?
-1, -2/5, 0, 1
Suppose 0 = -6*b + 2*b + 4. Let k = b + 1. Factor 11*m**k - 49*m**4 + 13*m**2 - 21*m**3 + 2*m - 6*m.
-m*(m + 1)*(7*m - 2)**2
Let k be (8/10)/((-8)/(-20)). Suppose -k = q - 5. Determine b so that -2*b + b**2 - 152*b**4 + q*b**3 - b + 153*b**4 - 5 + 3 = 0.
-2, -1, 1
Let x(f) be the first derivative of 2*f**3/15 + 17*f**2/5 - 413. Let x(c) = 0. What is c?
-17, 0
Let l = -5897 - -5899. Factor 74/5*d**l + 8*d**3 + 8/5*d**4 + 12*d + 18/5.
2*(d + 1)**2*(2*d + 3)**2/5
Factor 78/11*s**2 - 20/11*s - 50/11 - 32/11*s**4 + 16/11*s**3.
-2*(s + 1)**2*(4*s - 5)**2/11
Let l(u) be the first derivative of 11*u**4/4 - 10*u**3/3 + 9*u**2/2 + 14. Let k(o) = o**3 + o. Let c(t) = 18*k(t) - 2*l(t). Factor c(j).
-4*j**2*(j - 5)
Let q(i) be the first derivative of i**3/6 - 55*i**2 + 6050*i - 159. Factor q(d).
(d - 110)**2/2
Let u = -100 - -102. Let f(j) be the first derivative of -1/4*j**2 - 1/12*j**3 - u + 0*j + 3/16*j**4. Solve f(v) = 0.
-2/3, 0, 1
Let l be (-28)/20 - -1 - 44/(-10). Let 2*f**3 - l*f**3 - 3*f**2 - f**3 + 6*f = 0. C