ative of u**4/4 - 10*u**3/3 + 33*u**2/2 - 36*u - 216. Suppose t(p) = 0. Calculate p.
3, 4
Suppose f**4 - 264*f**2 + f**4 + 132*f**2 - 3*f**3 - 3*f**3 + 124*f**2 = 0. What is f?
-1, 0, 4
Suppose 12 = 3*j, 5*j = -2*c + 21 - 1. Let k be (-4)/(-14) + (-52)/(-14). Factor 4*v**2 + 0*v**4 + 0*v**4 - v - 4*v**k + c*v + v**3.
-v*(v - 1)*(v + 1)*(4*v - 1)
Let j(n) be the second derivative of 2*n**3 + 0 + 0*n**2 - 1/6*n**4 - n. Factor j(u).
-2*u*(u - 6)
Let q(d) be the third derivative of -35*d**2 - 1/10*d**4 + 1/150*d**5 + 0*d**3 + 0*d + 0. What is u in q(u) = 0?
0, 6
Let w be 8/(-18) - (-40)/9. What is o in 372*o**4 + 15*o**4 + 304*o - 508*o**3 + 80*o**5 + 48 + 716*o**2 + 1300*o**3 + 25*o**w = 0?
-2, -1, -3/4, -2/5
Let z(r) be the first derivative of -r**6/30 - 2*r**5/25 - r**4/20 + 128. Suppose z(b) = 0. Calculate b.
-1, 0
Let u(t) = -2*t**3 - 516*t**2 - 158*t + 404. Let r(y) = -y**3 - 173*y**2 - 53*y + 134. Let j(w) = -16*r(w) + 5*u(w). Factor j(d).
2*(d + 1)*(d + 31)*(3*d - 2)
Let r be (4 - (1 - -1)) + (-507)/260. Let p(l) be the second derivative of -1/4*l**4 + 0 + r*l**5 - 1/2*l**2 - 4*l + 1/2*l**3. Solve p(i) = 0 for i.
1
Let k be (-4 - (-7)/2)*-12. Let x = 11 - k. Factor -x*r**2 - 32*r - 97 - 8*r + 17.
-5*(r + 4)**2
Let h(y) be the third derivative of 1/102*y**4 + 0 + 0*y**3 - 16*y**2 + 0*y + 1/510*y**5. Find w, given that h(w) = 0.
-2, 0
Let g(u) be the first derivative of -u**4 - 16*u**3 - 64*u**2 - 327. Find h such that g(h) = 0.
-8, -4, 0
Let d(a) be the first derivative of 5*a - 15/2*a**2 - 5/4*a**4 + 5*a**3 - 21. Solve d(i) = 0 for i.
1
Suppose -5*h = -9*h + 5*y - 7, 4*h + y = -13. Let c be 23/4 - (2 - h). Find i such that 9/2*i**3 - 3 - c*i**4 + 9*i - 39/4*i**2 = 0.
1, 2
Suppose -17*j - 19*j + 15*j = 15*j. Factor -3/2*m + j - 1/4*m**2.
-m*(m + 6)/4
Let d = -986 - -11849/12. Let s(b) be the first derivative of -11/8*b**2 + 1/8*b**4 - 1/2*b - d*b**3 + b**5 - 5 + 1/3*b**6. Suppose s(g) = 0. Calculate g.
-2, -1/2, 1
Let s = -4478 + 31354/7. Factor -2/7*b**2 - 6/7 - s*b.
-2*(b + 1)*(b + 3)/7
Let s be -12*156/(-585)*(2 - 20/16). Factor 3/5*n**3 + 0*n + s - 9/5*n**2.
3*(n - 2)**2*(n + 1)/5
Let y(g) be the second derivative of g**5/4 - 20*g**4/3 + 295*g**3/6 - 110*g**2 + 3*g + 24. Factor y(i).
5*(i - 11)*(i - 4)*(i - 1)
Let n be (27 - -237)/22*4/42. Suppose -4/7 + 10/7*p + 2/7*p**3 - n*p**2 = 0. What is p?
1, 2
Let d(v) be the first derivative of 1/18*v**3 + 0*v**2 - 4 + 0*v. Factor d(p).
p**2/6
Let r(z) be the first derivative of 0*z**3 + 1/2*z**4 + 0*z - z**2 - 13. Let r(m) = 0. Calculate m.
-1, 0, 1
Suppose -5*h = 2*s + 355, -176 = s + 2*h - h. Let g = s + 292. Let -4*o**2 + 117*o + 2 + 2*o**4 - g*o = 0. What is o?
-1, 1
Let v be (800/(-225))/(4 + 42/(-9)). Factor -2/3*z**5 - v*z**4 - 44/3*z**3 - 16*z**2 - 6*z + 0.
-2*z*(z + 1)**2*(z + 3)**2/3
Let d = 150 - 150. Let i(j) be the third derivative of 1/90*j**5 - 5*j**2 - 1/36*j**4 - 1/9*j**3 + 0 + 1/180*j**6 + d*j. Factor i(x).
2*(x - 1)*(x + 1)**2/3
Factor 14 - 1/4*w**2 - 5/2*w.
-(w - 4)*(w + 14)/4
Find s, given that 0*s**3 + 40/3*s**2 - 2/3*s**5 + 0 - 10/3*s**4 + 32/3*s = 0.
-4, -2, -1, 0, 2
Let j(g) be the first derivative of g**5/240 - g**3/6 + 8*g**2 + 37. Let t(u) be the second derivative of j(u). Find z, given that t(z) = 0.
-2, 2
Let v be (13 - -1)*(-4)/(-8). Suppose -2*u - 3 = -v. Solve -u*h + 0*h**4 - h**3 + 3*h**5 - 3*h**2 - 7*h**4 + 10*h**2 = 0 for h.
-1, 0, 1/3, 1, 2
Let m(j) = -j**2 - j - 1. Let g(c) = 5*c**3 - 31*c**2 + 9*c + 39. Let t(f) = -f + 12. Let k be t(11). Let a(n) = k*g(n) - 6*m(n). Factor a(v).
5*(v - 3)**2*(v + 1)
Let x be 20/(-4) + (-34)/(-6). Let u(p) be the third derivative of -14*p**2 + 1/6*p**5 - 1/60*p**6 + 4/3*p**3 + 0 - x*p**4 + 0*p. Factor u(y).
-2*(y - 2)**2*(y - 1)
Let r(b) be the second derivative of 3/20*b**6 + 11/8*b**4 + 7*b - b**3 - 3/4*b**5 + 0*b**2 + 0. Factor r(p).
3*p*(p - 1)**2*(3*p - 4)/2
Suppose -5*c = 2*h - 14, 4*c - 26 = h - 20. Factor 0 - 4/3*w + 0*w**h + 1/3*w**4 + w**3.
w*(w - 1)*(w + 2)**2/3
Let g = 2807/15 + -187. Let o(n) be the second derivative of 0 + g*n**6 + 1/2*n**5 + 2/3*n**4 + n + 1/3*n**3 + 0*n**2. Factor o(p).
2*p*(p + 1)**2*(2*p + 1)
Let p be (4*4/(-400))/(2/415). Let o = p - -49/5. Factor -o*z**3 + 0 - 3/2*z**2 - 1/2*z - 1/2*z**4.
-z*(z + 1)**3/2
Let s(z) be the first derivative of -12 + 1/2*z**2 + 1/6*z + 5/18*z**3. Determine n so that s(n) = 0.
-1, -1/5
Let t be 4 + ((-17)/4 - (-1)/4). Let r(z) be the first derivative of 1/27*z**6 - 14/27*z**3 + 2/9*z**2 - 2/9*z**5 + 1/2*z**4 - 3 + t*z. Factor r(v).
2*v*(v - 2)*(v - 1)**3/9
Let h(x) be the third derivative of -x**5/180 + 7*x**4/24 - 19*x**3/9 - 161*x**2. Factor h(a).
-(a - 19)*(a - 2)/3
Let d(x) be the second derivative of -x**8/16800 - x**7/2100 + 5*x**4/6 + 3*x. Let j(k) be the third derivative of d(k). Let j(h) = 0. What is h?
-3, 0
Let t be (-5)/6 + (-2)/(-2). Let m = -4990/123 - -1677/41. Determine b, given that m + t*b**3 - 1/3*b**2 - 1/6*b = 0.
-1, 1, 2
Let x(a) = -a**3 - 3*a**2 + 7*a - 1. Let s be x(-5). Suppose 0 = -y + s*y. Find r, given that 0 + 2/3*r**4 + 2/3*r**2 + y*r - 4/3*r**3 = 0.
0, 1
Let h = 57 - 54. Let s - 4*s - 7*s + 4*s - h - 3*s**2 = 0. Calculate s.
-1
Let -3*c**2 - 29*c + 3*c**2 + 4*c**2 - 240 - 14*c + 59*c = 0. Calculate c.
-10, 6
Let o(h) be the second derivative of h**5/4 - 20*h**4/3 + 125*h**3/2 - 270*h**2 + 68*h. Let o(t) = 0. Calculate t.
3, 4, 9
Let x be (20 - 4) + 4/4. Factor -14*q**4 + 15*q**4 + q**2 + q**2 + x*q**4 - 20*q**3.
2*q**2*(q - 1)*(9*q - 1)
Determine y so that 54/11*y**2 + 20/11*y + 0 + 6/11*y**4 + 40/11*y**3 = 0.
-5, -1, -2/3, 0
Let l(b) be the first derivative of -2*b**6/15 + 8*b**5/5 + 4*b**4/5 - 32*b**3/3 - 7. Determine s, given that l(s) = 0.
-2, 0, 2, 10
Let b(q) be the first derivative of 10/3*q - 14 + 2/45*q**3 + 2/3*q**2. Find v, given that b(v) = 0.
-5
Let c(g) = 14*g + 136. Let h be c(-9). Suppose 15*a - 18*a = 4*q, -a = -2*q + h. Find i such that 6/5*i**q + 0 - 4/5*i + 2/5*i**2 = 0.
-1, 0, 2/3
Let x be 8/(-16) + 26/16. Let w be 2/((-8)/20) + (-455)/(-70). Let -x - w*c - 3/8*c**2 = 0. What is c?
-3, -1
Let j(s) be the first derivative of 39 + 10/17*s**3 + 2/85*s**5 - 9/34*s**4 + 0*s + 25/17*s**2. Suppose j(n) = 0. What is n?
-1, 0, 5
Suppose -58*p + 13*p = 0. Let h(k) be the first derivative of 0*k**2 + 7 + p*k - 1/5*k**3. Determine f, given that h(f) = 0.
0
Let g(d) be the first derivative of 2*d**6/3 + 16*d**5/5 + d**4 - 8*d**3 - 190. What is q in g(q) = 0?
-3, -2, 0, 1
Let u = -74019 - -373199/5. Let g = u - 613. Factor 4*y**2 + 3/5*y**3 + g*y + 18/5.
(y + 3)**2*(3*y + 2)/5
Let g(y) be the first derivative of y**4/78 - 10*y**3/39 + 25*y**2/13 + 6*y + 11. Let v(p) be the first derivative of g(p). Determine i, given that v(i) = 0.
5
Let y(i) be the second derivative of i**3 + 0 + 1/1260*i**6 + 1/210*i**5 + 7*i + 0*i**4 + 0*i**2. Let f(p) be the second derivative of y(p). Factor f(n).
2*n*(n + 2)/7
Let u(v) be the second derivative of -v**7/70 - 4*v**6/25 - 3*v**5/4 - 19*v**4/10 - 14*v**3/5 - 12*v**2/5 - 43*v. Factor u(x).
-3*(x + 1)**2*(x + 2)**3/5
Solve -118/7*m - 62/7*m**2 - 2/7*m**3 - 58/7 = 0.
-29, -1
Let b(r) = 6*r**3 + r**2 + r - 1. Let y(d) be the third derivative of -d**6/40 - 3*d**2. Let x(w) = 3*b(w) + 7*y(w). Solve x(g) = 0.
-1, 1
Suppose 2*t - 42 = -4*k, -5*t = -3*k + 12 + 52. Factor -11 - 23 + k*y**4 - 12*y**3 - 78*y - 4*y**4 + 10 - 75*y**2.
3*(y - 4)*(y + 1)**2*(3*y + 2)
Let z(b) be the first derivative of -3/22*b**4 + 6/55*b**5 + 2/33*b**3 + 0*b + 6 + 0*b**2 - 1/33*b**6. Factor z(j).
-2*j**2*(j - 1)**3/11
Let m(x) = -2*x**4 + x**3 - 2. Let s(z) = -z**5 + 8*z**4 - 5*z**3 + 2*z**2 + z + 10. Let j(r) = 5*m(r) + s(r). Factor j(d).
-d*(d - 1)*(d + 1)**3
Let p(l) be the first derivative of -l**5/15 - 7*l**4/12 - 5*l**3/3 - 13*l**2/6 - 4*l/3 - 49. Determine d so that p(d) = 0.
-4, -1
Let q(f) = 6*f**2 - 1. Let d be q(1). Let i(o) be the second derivative of 6*o + 0 + 0*o**2 - 1/130*o**d + 1/78*o**4 + 0*o**3. Factor i(p).
-2*p**2*(p - 1)/13
Let d(w) = 4*w + 34. Let f be d(-8). Let p = 1/703 + 17564/7733. Factor 1/11*o**f + p + 10/11*o.
(o + 5)**2/11
Let l(p) be the second derivative of 5/12*p**4 - 5*p + 0 + 5/6*p**3 + 0*p**2. Let l(t) = 0. What is t?
-1, 0
Suppose -53*n + 15*n = -14*n - 19*n. Determine z, giv