c**3 = 0. Calculate c.
-2/3, 1/3, 3
Let w(u) be the second derivative of u**6/660 - u**5/110 + 4*u**3/33 + 3*u**2/2 - 21*u. Let t(f) be the first derivative of w(f). What is o in t(o) = 0?
-1, 2
Let d(r) = 6*r**2 + 18*r + 2. Let o(h) = h**3 + 6*h**2 + 18*h - 2. Let p(q) = -6*d(q) + 4*o(q). Factor p(v).
4*(v - 5)*(v + 1)**2
Let j = 543 - 538. What is g in 4/13*g**3 + 2/13 - 4/13*g**2 + 2/13*g**4 - 2/13*g**j - 2/13*g = 0?
-1, 1
Let m = 27 - 24. Let k(x) = -x**5 - x**4 - x**3 + 3*x**2 + 2*x. Let q(d) = -2*d**5 - d**4 - d**3 + 4*d**2 + 3*d. Let s(g) = m*k(g) - 2*q(g). Factor s(l).
l**2*(l - 1)**2*(l + 1)
Let s(m) be the second derivative of -m**4/12 + 238*m**3/3 - 28322*m**2 - 7*m - 4. Factor s(c).
-(c - 238)**2
Let f(w) be the first derivative of -w**4/24 + w**3/3 - w**2 + 12*w + 12. Let s(b) be the first derivative of f(b). Factor s(a).
-(a - 2)**2/2
Let g(p) = -2*p**2 - 20*p - 16. Let h be g(-9). Factor -668*s**3 + 5*s**h + 665*s**3 - 14*s**2.
-3*s**2*(s + 3)
Let u be 5/(-2)*(-2 - 0). Let m = -4018 + 4018. Factor 3*k**4 + m*k + k**3 + 4/5 - 9/5*k**u - 3*k**2.
-(k - 1)**3*(3*k + 2)**2/5
Let f(j) = j**3 - 9*j**2 - j + 11. Let k be f(9). Determine b, given that -3*b - 9*b**2 + 18*b**k + 3*b**3 - 3*b - 12*b**2 = 0.
-1, 0, 2
Find l such that -117*l**4 - 3098*l**3 - 1599*l - 1521 - 112*l**4 - 3*l**5 - 1076*l**3 + 7526*l**2 = 0.
-39, -1/3, 1
Let w be (-1)/(-4) - (-259)/(-28). Let n be (2 + 24/w)*-9. Let r(i) = -5*i**2 + 7*i + 6. Let j(y) = -4*y**2 + 6*y + 5. Let l(s) = n*j(s) - 5*r(s). Factor l(m).
m*(m + 1)
Let j(p) be the third derivative of -p**7/3780 - p**6/324 - 2*p**5/135 - p**4/27 - 14*p**3/3 - 26*p**2. Let v(i) be the first derivative of j(i). Factor v(b).
-2*(b + 1)*(b + 2)**2/9
Let a(q) be the first derivative of -q**3/5 + 66*q**2/5 - 129*q/5 + 229. Factor a(r).
-3*(r - 43)*(r - 1)/5
Let q(u) = -u**3 + 5*u**2 + 2. Let i be q(5). Suppose 0 = x + 3*v - 3, 5*v - 9*v = i*x - 4. Let x*l + 8/11 - 2/11*l**2 = 0. What is l?
-2, 2
Let s be (-13)/(-20) - 1/4. Let l = -49428/5 - -9886. Factor s*v**2 + l*v + 0.
2*v*(v + 1)/5
Suppose -357*p = -348*p - 18. Let h(u) be the first derivative of 4*u - 4/3*u**3 + 8*u**p + 10 - 4*u**4. Suppose h(g) = 0. Calculate g.
-1, -1/4, 1
Suppose 8*v - 5 = 11*v + 5*n, 5*v - n = 1. Let m(h) be the third derivative of 1/8*h**4 + 1/20*h**5 + 0 + v*h + 6*h**2 - h**3. Suppose m(w) = 0. What is w?
-2, 1
Determine h, given that 13/7*h**2 - h - 5/7*h**3 + 0 - 1/7*h**4 = 0.
-7, 0, 1
Let d(q) be the first derivative of q**6/165 - 3*q**5/110 + q**4/33 + 17*q + 10. Let g(r) be the first derivative of d(r). Determine k so that g(k) = 0.
0, 1, 2
Let h(p) be the first derivative of p**5/30 - 3*p**4/4 + 20*p**3/3 - 88*p**2/3 + 64*p - 290. Find l such that h(l) = 0.
4, 6
Suppose h + 13 = 4*p + 1, 3*p - 4 = 2*h. Let d be ((-12)/(-8))/(3/h). Factor d*w**5 + 0*w**3 - 4*w**3 + 5*w**4 + 2*w - 5*w**4.
2*w*(w - 1)**2*(w + 1)**2
Let k = 12/35 + -1/5. Let w(c) be the first derivative of -k*c**2 + 4/35*c**5 + 1/21*c**6 + 0*c**4 + 1 - 4/21*c**3 + 0*c. Factor w(y).
2*y*(y - 1)*(y + 1)**3/7
Let o(h) = -7*h**2 + 7*h - 21. Let u(p) = -11*p**2 + 10*p - 32. Suppose -25 = 156*s - 161*s. Let w(m) = s*u(m) - 8*o(m). Find y such that w(y) = 0.
2, 4
Let h(n) be the first derivative of 7*n**3 + 45/2*n**2 + 27*n + 3/4*n**4 + 4. Suppose h(j) = 0. What is j?
-3, -1
Factor 0*a**3 + 16/3*a**4 + 0 + 0*a + 0*a**2 + 1/3*a**5.
a**4*(a + 16)/3
Let n(t) be the third derivative of 0*t**4 - 1/8*t**6 + 0*t**3 + 0 + 0*t**5 + 0*t - 18*t**2 - 1/42*t**7. Factor n(v).
-5*v**3*(v + 3)
Let i(x) be the first derivative of 128/5*x - 11/10*x**4 - 2/25*x**5 - 10 - 24/5*x**3 - 16/5*x**2. Factor i(s).
-2*(s - 1)*(s + 4)**3/5
Let j(f) be the second derivative of f**5/4 + 5*f**4/12 - 25*f**3/3 + 20*f**2 + 55*f. Let j(p) = 0. Calculate p.
-4, 1, 2
Let a(y) be the second derivative of y**7/84 + 31*y**6/90 + 17*y**5/5 + 6*y**4 + 4*y**3 + 13*y. Let o(m) be the second derivative of a(m). Factor o(s).
2*(s + 6)**2*(5*s + 2)
Let z(y) be the second derivative of -1/3*y**3 - 1/30*y**6 + 0*y**5 + 8*y + 0 + 0*y**2 + 1/4*y**4. Factor z(i).
-i*(i - 1)**2*(i + 2)
Let v(d) be the first derivative of d**4/26 - 14*d**3/13 - d**2/13 + 42*d/13 + 174. Find h such that v(h) = 0.
-1, 1, 21
Let o(s) be the first derivative of -s**4/16 + 5*s**3/12 - 3*s**2/4 + 38. What is g in o(g) = 0?
0, 2, 3
Find x such that -8*x**3 + 9*x**3 - 26 - 4 + 175*x - 190*x**2 + 44*x**3 = 0.
2/9, 1, 3
Let l(k) be the first derivative of -5/2*k**2 + 15 - 1/3*k**3 + 6*k. Find a such that l(a) = 0.
-6, 1
Factor 4/3*k**3 + 0*k - 8/9*k**4 - 4/9*k**5 + 0*k**2 + 0.
-4*k**3*(k - 1)*(k + 3)/9
Let r(v) be the third derivative of -7/135*v**5 + 1/36*v**4 + 0 + 0*v + 0*v**3 - 17*v**2 + 7/540*v**6 + 4/945*v**7. What is k in r(k) = 0?
-3, 0, 1/4, 1
Let o(z) be the first derivative of 0*z**2 + 3/5*z**4 - 7/10*z**6 + 36/25*z**5 + 0*z**3 - 9 + 0*z. Suppose o(j) = 0. What is j?
-2/7, 0, 2
Let n(i) = -i**5 + i**4 + i**2 + i. Let c(s) = 3*s**3 + 2*s + 13*s**4 + 0*s**4 + 3*s**5 - 8*s**3 - 5*s**2. Let h(p) = -c(p) + 4*n(p). Find q such that h(q) = 0.
-1, -2/7, 0, 1
Let d(v) = 14*v**5 - 2*v**4 - 2*v**2 - 4*v. Let o(w) = -44*w**5 + 6*w**4 - w**3 + 8*w**2 + 12*w. Let f(q) = 19*d(q) + 6*o(q). Factor f(a).
2*a*(a - 1)**3*(a + 2)
Let f = 89 + -91. Let s(t) = t**2 - 7*t - 16. Let m be s(f). Factor 2/7 + 0*j - 2/7*j**m.
-2*(j - 1)*(j + 1)/7
Let b(i) be the second derivative of i**4/15 + 232*i**3/15 + 6728*i**2/5 + 11*i. Let b(t) = 0. Calculate t.
-58
Solve 0*d + 8*d**3 + 0 - 4/3*d**2 + 13/3*d**4 = 0.
-2, 0, 2/13
Let g = 39 + -36. Let v be 1 + (0 - 1*-2). Find a such that -4*a**2 - a**2 - 7*a**g - a**2 + 4*a**3 - v*a = 0.
-1, 0
Let s(u) be the second derivative of u**4/60 - u**3/15 - 206*u. Solve s(i) = 0 for i.
0, 2
Let x(i) = i**3 - i**2 - 3*i - 4. Let a be x(3). Let j = -3 + a. Find c such that -6 + 0*c + 3 + 3*c**j + 0*c = 0.
-1, 1
Factor -32/3*j**2 + 0 + 0*j + 44/9*j**3 + 2/9*j**4.
2*j**2*(j - 2)*(j + 24)/9
Let s(k) be the first derivative of k**4/11 + 2*k**3/33 - 5*k**2/11 + 4*k/11 + 164. Factor s(i).
2*(i - 1)*(i + 2)*(2*i - 1)/11
Let h(a) = -a**3 + 10*a**2 - 9*a + 2. Let j be h(9). Suppose 0 = -2*s - 3 + 7. Factor 10*t**j + 96*t + 128 + s*t**3 - 12*t**2 + 26*t**2.
2*(t + 4)**3
Determine v so that 4/9*v**4 - 4/3*v**2 - 8/9*v + 0*v**3 + 0 = 0.
-1, 0, 2
Let y(h) be the third derivative of h**7/70 + h**6/10 + h**5/4 + h**4/4 + 74*h**2 + 2. Let y(o) = 0. What is o?
-2, -1, 0
Factor 0 + 4*u + 3/7*u**3 - 44/7*u**2.
u*(u - 14)*(3*u - 2)/7
Let s = 2341/110 + -93/5. Let f = s - 24/11. Let -f + b + 2*b**2 - 4*b**3 = 0. Calculate b.
-1/2, 1/2
Let r(s) be the first derivative of s**6/30 + s**5/60 - s**4/4 + s**3/6 + s**2/3 + 13*s - 18. Let u(m) be the first derivative of r(m). Factor u(g).
(g - 1)**2*(g + 2)*(3*g + 1)/3
Let h(q) be the second derivative of -q**7/252 + q**6/36 - 3*q**5/40 + 7*q**4/72 - q**3/18 - q + 87. Factor h(z).
-z*(z - 2)*(z - 1)**3/6
Let s = 13 + -79. Let x be (-34)/s + (-2)/(12/2). Factor 0 + x*l - 2/11*l**2.
-2*l*(l - 1)/11
Solve 1/2*y**4 - 144 + 48*y + 83*y**2 + 25/2*y**3 = 0.
-12, -2, 1
Suppose 128/7*h + 2/7*h**2 + 2048/7 = 0. What is h?
-32
Let w(i) be the second derivative of i**5/15 - i**4/4 + i**3/3 + 5*i**2 + 2*i. Let j(p) be the first derivative of w(p). Factor j(z).
2*(z - 1)*(2*z - 1)
Suppose -4*v = 4*j + 16, -7*v = -8*v - 4*j - 13. Let s(c) = c**2 + c - 1. Let p(q) = -q**2 + 7*q + 13. Let r(d) = v*p(d) - 5*s(d). Factor r(k).
-4*(k + 1)*(k + 2)
Let t be ((-15)/2)/(-4*6/64). Let o be (t - 18) + ((-16)/3)/4. Factor -2*y**3 + o*y**4 + 2/3*y**2 - 4/3 + 2*y.
2*(y - 2)*(y - 1)**2*(y + 1)/3
Let g(m) be the second derivative of m**5/15 + 5*m**4/9 + 4*m**3/9 - 16*m**2/3 - 2*m + 260. Find y, given that g(y) = 0.
-4, -2, 1
Suppose -3*x + 16 = 5*v, 2*x = 2*v + 3*v - 6. Factor -3 - x - 4*q**2 + 8*q + 1 + 0.
-4*(q - 1)**2
Let t = -31 - -34. Factor -3*g - 4*g + 4 + g + 2*g**t.
2*(g - 1)**2*(g + 2)
Let b(z) be the second derivative of -z**6/210 + 3*z**5/70 - 2*z**4/21 - z**3/7 + 9*z**2/14 + 46*z - 4. Factor b(w).
-(w - 3)**2*(w - 1)*(w + 1)/7
Let r(v) be the third derivative of v**7/70 - 19*v**6/80 - 11*v**5/40 + 5*v**4/8 + 90*v**2 - 1. Suppose r(k) = 0. Calculate k.
-1, 0, 1/2, 10
Let p(i) = i**5 - i**4 + i**3 + 2*i - 1. Let b(o) = 13*o**5 - 53*o*