**2*(r - 1)
Determine c so that c**4 - 2*c**3 - 5*c**2 + 7*c**4 + 5*c**2 = 0.
0, 1/4
Let w(u) be the third derivative of u**7/245 + u**6/105 - u**5/30 - u**4/21 + 4*u**3/21 + 8*u**2. Determine j so that w(j) = 0.
-2, -1, 2/3, 1
Let o(l) be the second derivative of -l**4/12 + l**3 + 19*l**2/2 - 5*l. Let r be o(8). Factor -20*k**4 + 0 + 138/7*k**r + 8/7*k + 50/7*k**5 - 8*k**2.
2*k*(k - 1)**2*(5*k - 2)**2/7
Let q(r) = -3*r**4 + 11*r**3 + 17*r**2 - 23*r + 6. Let m(d) = 2*d**4 - 7*d**3 - 11*d**2 + 15*d - 4. Let v(b) = 8*m(b) + 5*q(b). Factor v(f).
(f - 1)**3*(f + 2)
Let y(c) be the third derivative of 0*c + 0*c**5 + 1/504*c**8 + 0*c**6 + 0 - 1/315*c**7 - 4*c**2 + 0*c**3 + 0*c**4. Suppose y(n) = 0. What is n?
0, 1
Let m(p) be the first derivative of -p**6/15 + 6*p**5/25 - 3*p**4/10 + 2*p**3/15 + 6. Let m(o) = 0. What is o?
0, 1
Let l(t) be the first derivative of 1 + 0*t**2 + 1/6*t**3 - 1/10*t**5 + 0*t**4 + 0*t. Determine i, given that l(i) = 0.
-1, 0, 1
Suppose 6*u - 164 + 20 = 0. Solve 3 - 252*b**4 + u*b**2 + 45/2*b - 120*b**5 - 255/2*b**3 = 0 for b.
-1, -1/4, 2/5
Let 1/6*f**3 - 1/3*f**2 + 0 + 1/6*f = 0. Calculate f.
0, 1
Suppose 0*t + t = 8. Let d be 0 - (-1 + 2) - -25. Factor -d*q + 2 - 9 - 11 - t*q**2.
-2*(2*q + 3)**2
Let k = 23/3 + -91/12. Let u(s) be the third derivative of 1/60*s**5 + 1/6*s**3 - s**2 + 0 + k*s**4 + 0*s. Find i such that u(i) = 0.
-1
Let w(p) be the second derivative of -p**5/100 + p**4/10 - 11*p**3/30 + 3*p**2/5 - 9*p. Suppose w(g) = 0. Calculate g.
1, 2, 3
Let t(r) be the third derivative of -r**7/1050 + r**6/100 - r**5/25 + r**4/12 - r**3/10 + 17*r**2. Factor t(j).
-(j - 3)*(j - 1)**3/5
Factor -8/5*k + 4/5*k**3 + 0 + 4/5*k**2.
4*k*(k - 1)*(k + 2)/5
Let x(b) be the second derivative of 1/18*b**4 + 1/18*b**3 + 0*b**5 - 1/45*b**6 - 1/126*b**7 + 0*b**2 + 0 + b. Factor x(k).
-k*(k - 1)*(k + 1)**3/3
Solve -1/3*n**2 + 4/3*n + 0 = 0 for n.
0, 4
Let j be 17 - (-4 + -1 + 4). Suppose 5*k - j = -2*c - 0*k, -5*c - 2*k + 24 = 0. Let -3*m + 1 - 1 + 0 + c*m**2 - 1 = 0. Calculate m.
-1/4, 1
Let p(v) be the second derivative of 1/15*v**6 + 0*v**4 + 0*v**2 - 1/10*v**5 + 0*v**3 + 0 + 3*v. Factor p(x).
2*x**3*(x - 1)
Let z(j) be the first derivative of -j**5/30 - 5*j**4/18 - 8*j**3/9 - 4*j**2/3 + 3*j + 1. Let r(v) be the first derivative of z(v). Factor r(f).
-2*(f + 1)*(f + 2)**2/3
Let y(z) be the third derivative of 0 - 1/108*z**4 - 3*z**2 + 1/270*z**5 + 0*z + 0*z**3. Determine m so that y(m) = 0.
0, 1
Let p = -1 + 3. Find a such that -2 + 3 - 1 + a**p - a**3 = 0.
0, 1
Let t(u) be the third derivative of 5*u**7/42 + 13*u**6/24 - u**5/2 - 32*u**2. Factor t(d).
5*d**2*(d + 3)*(5*d - 2)
Let c(g) be the second derivative of g**7/2520 - g**6/720 + 5*g**4/12 + 3*g. Let b(n) be the third derivative of c(n). Factor b(d).
d*(d - 1)
Let c(z) = -z**2 + 2*z + 5. Let o be c(3). Factor -2/7*v**o - 2/7*v + 4/7.
-2*(v - 1)*(v + 2)/7
Let d(p) = p**4 + p**3 - p**2 + 1. Let r(f) = 4*f**4 + 29*f**3 + 26*f**2 - 1. Let a(c) = -d(c) - r(c). Factor a(v).
-5*v**2*(v + 1)*(v + 5)
Let u be -3 + 141/15 - 4. Factor 2/5*w + 9/5*w**2 + 0 + w**4 + u*w**3.
w*(w + 1)**2*(5*w + 2)/5
Let l(j) be the first derivative of -2*j**5/85 + 3*j**4/34 - 4*j**2/17 - 3. Determine q, given that l(q) = 0.
-1, 0, 2
Let z(b) be the second derivative of -b**6/180 - b**5/240 + b**4/144 - 15*b. Factor z(h).
-h**2*(h + 1)*(2*h - 1)/12
Let v = 19321 - 1159229/60. Let x = v + -4/15. Factor -1/4*t + x - 1/2*t**2.
-(t + 1)*(2*t - 1)/4
Factor 5*x**3 - 11*x**3 + 15*x**4 - 18*x**2 - x**5 + 10*x**5 - 3*x + 3.
3*(x - 1)*(x + 1)**3*(3*x - 1)
Let v(q) be the second derivative of q**8/13440 + q**7/2520 + q**6/1440 - q**4/6 - 2*q. Let y(f) be the third derivative of v(f). Factor y(d).
d*(d + 1)**2/2
Let c(a) = -a**3 + 5*a**2 - 4*a + 3. Let v be c(2). Let h(g) = -g**2 + 6*g + 8. Let m be h(v). Let m - 3 + w**4 + w**4 - 4*w + 4*w**3 = 0. What is w?
-1, 1
Let f(s) be the first derivative of -2*s + 9/2*s**2 - 2 - 4/3*s**3. Suppose f(p) = 0. What is p?
1/4, 2
Suppose d - 18 = -5*d. Let p(w) be the second derivative of 0 - 1/70*w**5 - 1/42*w**4 + 0*w**2 + 0*w**d + 4*w. Solve p(r) = 0 for r.
-1, 0
Let r(k) be the first derivative of -k**4/2 - 4*k**3/3 + 10. Find o such that r(o) = 0.
-2, 0
Suppose 0 = 4*b + 3*v - 27, 2*b - 5*v - 51 = -2*b. Suppose u - 4*u = -b. Factor 4/5*z**u + 2/5*z**2 + 2/5*z**4 + 0 + 0*z.
2*z**2*(z + 1)**2/5
Let m = 1/3 - -1. Let s(t) be the first derivative of 5/9*t**3 - m*t**2 - 4/3*t + 4. Let s(j) = 0. What is j?
-2/5, 2
Let j(m) be the first derivative of 12*m**5/5 - 2*m**4 - 16*m**3/3 + 4*m**2 + 4*m - 1. Let j(b) = 0. Calculate b.
-1, -1/3, 1
Let a(i) be the first derivative of 0*i**3 - 3/14*i**2 + 1/28*i**4 - 2/7*i - 8. Solve a(u) = 0.
-1, 2
Let t(b) = 18*b**2 - 21*b - 6. Let z(x) = x**3 + 6*x**2 - 1. Let j be z(-6). Let l(g) = -g**2. Let m(d) = j*t(d) - 6*l(d). Factor m(w).
-3*(w - 2)*(4*w + 1)
Let w(x) be the first derivative of 2*x**5/5 - 4*x**3/3 + 2*x + 8. Factor w(c).
2*(c - 1)**2*(c + 1)**2
Let m = 18 + -14. Let p(d) be the third derivative of 1/42*d**5 + 0*d - 1/140*d**6 + 0*d**3 - 3/245*d**7 + d**2 - 1/84*d**m + 0. Factor p(l).
-2*l*(l + 1)*(3*l - 1)**2/7
Let n(w) = -7*w**2 + 5*w - 4. Let o be n(2). Let k = o - -22. Suppose 0 - 1/3*i**3 + k*i**2 + 0*i = 0. Calculate i.
0
Let m(f) be the second derivative of -1/24*f**4 + 1/60*f**6 - 1/40*f**5 + 1/12*f**3 - 2*f + 0*f**2 + 0. Factor m(u).
u*(u - 1)**2*(u + 1)/2
Let k(q) be the first derivative of 2/21*q**3 + 1/21*q**6 - 2 + 0*q**2 - 1/14*q**4 - 2/35*q**5 + 0*q. Solve k(n) = 0 for n.
-1, 0, 1
Let p(a) = 18*a**3 + 48*a**2 + 30*a + 3. Let s(t) = 17*t**3 + 49*t**2 + 31*t + 3. Let o(f) = 4*p(f) - 3*s(f). Determine q, given that o(q) = 0.
-1, -1/7
Let p be (-55)/(-22)*(-16)/(-10). Let d be (3/p)/(5/20). Solve -1/2*t**4 - 2 + 3/2*t**2 - 2*t + t**d = 0.
-1, 2
Factor 0 + 2/7*o**2 - 6/7*o.
2*o*(o - 3)/7
Let k be -1*3*100/15. Let t = k + 20. Factor 1/4*o**2 + t*o + 0 + 1/4*o**4 - 1/2*o**3.
o**2*(o - 1)**2/4
Let s(n) = -n**3 + n**2 + 2*n. Let x be s(2). Let m = 0 - x. Factor m*z - 2/7 + 6/7*z**2 - 4/7*z**3.
-2*(z - 1)**2*(2*z + 1)/7
Let o(g) be the third derivative of 0*g**4 - 1/240*g**5 + 0 + 1/160*g**6 + 1/210*g**7 + 2*g**2 + 0*g**3 + 0*g. Factor o(k).
k**2*(k + 1)*(4*k - 1)/4
Factor -3/5*q**4 - 1/5*q + 0 - 7/5*q**3 - q**2.
-q*(q + 1)**2*(3*q + 1)/5
Factor -15*p - 6 + 5*p**3 + 0*p - 4.
5*(p - 2)*(p + 1)**2
Suppose -3*k + 7 = -11. Let t be (4/(-3))/((-4)/k). Factor -2*y + 2*y - t*y**2.
-2*y**2
Let g = -177/4 - -89/2. Determine q so that -1/2*q + 3/4*q**2 + 0 - g*q**3 = 0.
0, 1, 2
Factor -5*f + 5*f**5 + 16*f**3 - 23*f**4 + 10*f**2 + 13*f**4 - 16*f**3.
5*f*(f - 1)**3*(f + 1)
Let u = 11 + -9. Let z(q) be the third derivative of 0*q + 0 - 1/240*q**5 - 1/24*q**3 - 1/48*q**4 - 2*q**u. Find f such that z(f) = 0.
-1
Suppose 0 = -y + 9*y. Let p(j) be the third derivative of -j**2 - 1/96*j**4 + 0*j**5 + 0 + 1/480*j**6 + 0*j**3 + y*j. Factor p(s).
s*(s - 1)*(s + 1)/4
Suppose 0*w + 22 = -5*g + 3*w, 0 = 3*g - 4*w + 11. Let d be (22/(-33))/(g/3). Factor 2/5*j**2 + 0*j - d.
2*(j - 1)*(j + 1)/5
Let h(t) be the first derivative of 2/5*t**2 + 2 + 0*t + 2/15*t**3. Factor h(k).
2*k*(k + 2)/5
Let q(n) = -n**3 - 12*n**2 - 22*n - 20. Let z be q(-10). Let -12/7*h**2 + 3/7*h**3 + z + 12/7*h = 0. What is h?
0, 2
Determine r so that -13/2*r + 55/6*r**3 - 8/3*r**5 - 5/6 + 12*r**4 - 67/6*r**2 = 0.
-1, -1/4, 1, 5
Let r be (117/78)/(2/4). Suppose 8/7 - 14*d**r + 6*d**2 + 48/7*d = 0. What is d?
-2/7, 1
Let w be -12*((-1)/8)/((-2)/(-4)). Let l(g) be the third derivative of -1/360*g**6 + 0*g - 3*g**2 + 0 + 1/18*g**w - 1/24*g**4 + 1/60*g**5. Solve l(k) = 0 for k.
1
Let m(z) be the second derivative of -2*z**5/15 - 11*z**4/12 + z**3 - 3*z**2/2 - 2*z. Let j(b) be the first derivative of m(b). Factor j(k).
-2*(k + 3)*(4*k - 1)
Let s(m) be the second derivative of m**4/72 - m**3/18 + m**2/12 + 7*m. Find f such that s(f) = 0.
1
Let o(t) be the first derivative of t**5/240 + t**2/2 - 1. Let m(s) be the second derivative of o(s). Solve m(r) = 0.
0
Suppose x - 9 = -13. Let p be (3/x)/(72/(-64)). Determine m, given that 16/3*m + 0 + p*m**4 + 8*m**2 + 4*m**3 = 0.
-2, 0
Let x(j) be the first derivative of 5*j**4/4 + 5*j**3 - 23. What is k in x(k) = 0?
-3, 0
Determine s, given that 0*s