*w**3 - 2/15*w**6 + 11/525*w**7 - 1/30*w**5. Solve h(r) = 0.
-2, -1/2, -2/7, 1
Let w be (216/(-234))/((-24)/132). Suppose -60/13*k**2 + 18/13*k**5 + 18/13*k + 92/13*k**3 - w*k**4 - 2/13 = 0. What is k?
1/3, 1
Let o be 2*(3 + (-2)/4). Find g, given that 15*g**3 + 4*g**4 - g**4 + 10*g**4 - 42*g**5 + 46*g**o + 7*g**2 + g = 0.
-1, -1/4, 0
What is s in -15*s**3 + 30*s**5 - s**3 - 18*s**3 + 5*s**4 - 3*s**4 + 4*s - 2*s**2 = 0?
-1, -2/5, 0, 1/3, 1
Let x = 1 - -3. Let b be (x/(-5))/(84/(-30)). Suppose 2/7*a**2 - b*a + 0 = 0. What is a?
0, 1
Let r(h) = -8*h**2 - 56*h + 154. Let g be r(-9). Factor g*z - 2/3 - 32*z**2 - 128/3*z**3.
-2*(z + 1)*(8*z - 1)**2/3
Suppose 0*a - 8 = -4*a. Let m(y) be the second derivative of y - 1/24*y**4 - 1/4*y**a + 0 - 1/6*y**3. Determine x, given that m(x) = 0.
-1
Let o(w) be the first derivative of -2*w**3/15 - 31*w**2/5 + 125. Factor o(q).
-2*q*(q + 31)/5
Let p be -4 - 510/(-108) - (-4)/(-18). Let s(l) be the first derivative of -4 + l - p*l**2 + 1/12*l**3. Factor s(b).
(b - 2)**2/4
Let h(b) = b**2 - 222*b - 902. Let d be h(-4). Let 2/11*f + 0 + 2/11*f**d = 0. Calculate f.
-1, 0
Let v(o) be the first derivative of -o**7/1785 + o**5/255 - o**3/51 + 3*o**2/2 + 33. Let g(z) be the second derivative of v(z). Determine r so that g(r) = 0.
-1, 1
Factor 24 + 71*n**3 + 189*n**2 + 108*n - 56*n**2 - 8 + n**5 + 10*n**4 + 16 + 5*n**4.
(n + 1)**3*(n + 4)*(n + 8)
Let f = 1/267 - -175/801. Let l(s) be the first derivative of 1 - f*s + 2/27*s**3 + 0*s**2. Determine p so that l(p) = 0.
-1, 1
Let q(y) = 34*y**2 - y. Let p be q(-1). Let h be 95/p + (-6)/(-21). Factor -3*d - 3*d**h - 4*d**2 + 5 - 2*d**2 - 5.
-3*d*(d + 1)**2
Let t be (-2)/4*0/9. Let w(h) = -h**3 + 4*h**2 + 28*h + 21. Let s be w(-3). Factor s*y**2 + 0*y + 2/17*y**4 - 2/17*y**3 + t.
2*y**3*(y - 1)/17
Let x(r) = -4*r**2 - 11*r - 20. Let l be ((-30)/9 - -3)*1*-18. Let f(i) = 2*i**2 + 6*i + 10. Let g(h) = l*x(h) + 13*f(h). Factor g(z).
2*(z + 1)*(z + 5)
Suppose -2*h = 4*v + 12, -15 = -2*h - 2*v - 21. Let b(l) be the third derivative of 8/3*l**3 + 1/10*l**6 - 4*l**2 + 0*l - 4/3*l**4 + 1/15*l**5 + h. Factor b(t).
4*(t - 1)*(t + 2)*(3*t - 2)
Let w(o) = -o**2 + 137*o - 4384. Let t be w(86). Factor -4/15 - 2/15*n + 2/15*n**t.
2*(n - 2)*(n + 1)/15
Let y(b) be the third derivative of -b**5/60 - 13*b**4/6 - 338*b**3/3 + 6*b**2 + b. Factor y(k).
-(k + 26)**2
Let p be (-1507)/(-99) + -15 + (-376)/(-90). Let u(d) be the first derivative of 6*d**3 - d**6 - 8 - 15/2*d**4 + p*d**5 - 2*d**2 + 0*d. Solve u(v) = 0 for v.
0, 2/3, 1
Let n(h) be the third derivative of h**5/20 - 5*h**4/4 + 25*h**3/2 + 138*h**2. Factor n(r).
3*(r - 5)**2
Suppose 10*t - 2*t = 16. Factor -114*r + 2*r**5 + 114*r - 6*r**3 - 4*r**t.
2*r**2*(r - 2)*(r + 1)**2
Let l(p) be the second derivative of 5/12*p**4 - 7*p - 2*p**2 + 2/3*p**3 + 0 - 3/20*p**5. Factor l(t).
-(t - 2)*(t + 1)*(3*t - 2)
Let -2/3*i + 0 + i**4 - 7/3*i**2 - 2/3*i**3 = 0. What is i?
-1, -1/3, 0, 2
Let c(f) be the third derivative of -23*f**6/660 + f**5/165 + 23*f**4/132 - 2*f**3/33 + 18*f**2 + 3. Let c(k) = 0. Calculate k.
-1, 2/23, 1
Let q(o) be the third derivative of -o**6/210 + o**5/30 - o**4/12 + 2*o**3/21 + 2*o**2 + 30*o. Find y such that q(y) = 0.
1/2, 1, 2
Let m = -3498 + 3500. Determine p so that 2/5*p**3 - 8/5*p - 16/5 + 4/5*p**m = 0.
-2, 2
Let w(z) = -5*z**2 - 6*z - 1. Suppose -5 + 3 = -o. Let k(v) = 21*v**2 + 24*v + 3. Let u(f) = o*k(f) + 9*w(f). Suppose u(i) = 0. Calculate i.
-1
Let u(l) be the third derivative of l**5/30 - 2*l**4/15 - 4*l**3/15 - 3*l**2 - 26*l. Factor u(f).
2*(f - 2)*(5*f + 2)/5
Let n(w) be the first derivative of -w**5/4 - 5*w**4/4 - 5*w**3/2 - 5*w**2/2 + 11*w - 2. Let x(m) be the first derivative of n(m). Factor x(k).
-5*(k + 1)**3
Factor 3*j + 0 + 2*j**2 + 1 - 22*j + 8.
(j - 9)*(2*j - 1)
Let n(h) be the third derivative of h**5/360 + 5*h**4/48 + 7*h**3/18 - 2*h**2 - 7. Factor n(y).
(y + 1)*(y + 14)/6
Suppose f + 3*z = -3*f + 4, 3*f - 3*z = 24. Solve 3*u**4 + 51*u**2 + 2*u**3 + 0*u**f - 52*u**2 = 0 for u.
-1, 0, 1/3
Let p(d) = -14*d**3 + 54*d**2 - 70*d + 12. Let x(v) = -v**2 - 2*v. Let j(g) = -p(g) + 6*x(g). Solve j(q) = 0 for q.
2/7, 1, 3
Let c(v) be the third derivative of -v**8/8960 + v**7/672 - v**6/120 + v**5/40 - 13*v**4/12 + 10*v**2. Let n(o) be the second derivative of c(o). Factor n(k).
-3*(k - 2)**2*(k - 1)/4
Suppose 2 - 53*i**4 - 51*i**4 - 48*i**4 + 151*i**4 + 3*i - i**2 - 3*i**3 = 0. What is i?
-2, -1, 1
Let t = 13 + -10. Let a be t + (-6)/((-10)/(-5)). Find j such that -2/7*j**2 + 0*j - 2/7*j**3 + a = 0.
-1, 0
Let w(a) = -3*a - a - 6 - 186*a**2 + 89*a**2 + 89*a**2. Let s(h) = -7*h**2 - 3*h - 5. Let x = 0 - 5. Let o(d) = x*w(d) + 6*s(d). Let o(p) = 0. What is p?
0, 1
Let m(f) = 2 - 44*f**3 - 5*f + 4*f**2 + 42*f**3 - 5*f. Let x(d) = 5*d**3 - 8*d**2 + 21*d - 5. Let a(i) = -13*m(i) - 6*x(i). Factor a(t).
-4*(t - 1)*(t + 1)**2
Let y(m) be the second derivative of m**6/45 - m**5/15 - 13*m**4/18 + 14*m**3/9 + 8*m**2 + 176*m. Suppose y(z) = 0. What is z?
-3, -1, 2, 4
Suppose 5*k - 23 = 17. Find r such that 2*r**2 - 6*r**3 + 8*r**3 + k*r**2 + 6*r - 18 = 0.
-3, 1
Let q be (-2 + 52/28)/(27/(-648)). Factor -q*d - 3/7*d**2 - 48/7.
-3*(d + 4)**2/7
Let z(a) be the third derivative of 2*a**2 - 7/20*a**5 + 0*a**3 - 1/4*a**4 + 0 + 0*a - 1/8*a**6. Factor z(t).
-3*t*(t + 1)*(5*t + 2)
Let b(p) be the third derivative of -11*p**6/180 - 4*p**5/15 + p**4 - 17*p**3/3 + 34*p**2. Let d(l) be the first derivative of b(l). Let d(k) = 0. What is k?
-2, 6/11
Let o be (-36)/54 - 1/(-1). Let d = 87 + -84. Factor 0 + 1/3*c**2 - o*c + 1/3*c**d - 1/3*c**4.
-c*(c - 1)**2*(c + 1)/3
Let n(h) = 2*h + 19. Let b be n(-11). Let a be 5*b/(-15) - -2. Solve -4/9*d**2 - 2/3*d**a - 4/9 + 14/9*d = 0.
-2, 1/3, 1
Let p(u) be the third derivative of -u**5/20 - 17*u**4/8 - 130*u**2. Find x, given that p(x) = 0.
-17, 0
Suppose 0 = 3*j - 5*b + 14, 28 = 13*j - 9*j + 5*b. Determine h, given that -5*h**2 + 8*h**j + h**3 - 6*h**2 - 2*h**3 - 2*h = 0.
-2, -1, 0
Suppose 11 - 8 = 3*h. Let o be h/6*3*0. What is q in -q**2 + o*q + 0*q - q**3 - q**3 + q = 0?
-1, 0, 1/2
Suppose m - 126 = -z, 2 = -5*z + 12. Let p = m + -832/7. What is u in 48/7*u**4 + 0 + 0*u**2 - p*u**3 + 3/7*u = 0?
-1/4, 0, 1/2
Let g be 6/14 + 1881/315. Let w be (-12)/(-5) + (-2)/5. Suppose 8/5 + w*l**2 - 10*l**3 + g*l = 0. Calculate l.
-2/5, 1
Let v(f) = -5*f - 20. Let g be v(-5). Suppose -2*l = b, -l + 2*b = 4*b + 6. Factor g*z + 4*z**4 - 3*z**3 - 7*z**4 - 2*z + 3*z**l.
-3*z*(z - 1)*(z + 1)**2
Let w = 6/721 - -346789/1442. Let o = w + -240. Factor n**2 + 0 + 1/2*n**3 + o*n.
n*(n + 1)**2/2
Suppose -10*s - 2*s = -528. Suppose s = h + 10*h. Factor 1/2*k**3 - 1/4*k**5 - 1/4*k - 1/4 + 1/2*k**2 - 1/4*k**h.
-(k - 1)**2*(k + 1)**3/4
Let i(h) = -6*h - 2*h + 7*h + 8. Let a be i(8). Suppose -5/2*m**5 - 6*m**4 + 0 - m**2 + a*m - 9/2*m**3 = 0. Calculate m.
-1, -2/5, 0
Find i, given that 32*i - 2*i**3 - 11*i**2 - 52*i - 14*i**2 - 3*i**3 = 0.
-4, -1, 0
Let n(u) be the first derivative of 2*u**3/3 + 8*u**2 - 55. Suppose n(b) = 0. What is b?
-8, 0
Let v = 109 - 86. Suppose 2*u + j = 7, 4*u - 3*j - v = -2*j. Let 0 - 1/5*m**3 + 0*m**2 + 0*m + 0*m**4 + 1/5*m**u = 0. What is m?
-1, 0, 1
Let r(m) be the first derivative of -23/2*m**4 + 12 + 7*m**2 + 16/3*m**6 - 2*m - 14/3*m**3 + 16/5*m**5. Find t such that r(t) = 0.
-1, 1/4, 1
Suppose -12 = -10*o + 8. Suppose o*j + 5*p - 15 = 6*j, j = -p + 3. Find c such that 0*c - 1/4*c**4 - 1/4 + j*c**3 + 1/2*c**2 = 0.
-1, 1
Let n(q) = 91*q + 2641. Let a be n(-29). Let j(h) = h**2 + 6*h - 4. Let y be j(-7). Find m such that -4/3*m**a + 4/3 + 2/3*m - 2/3*m**y = 0.
-2, -1, 1
Factor 3/8*z**2 + 51/8*z + 0.
3*z*(z + 17)/8
Suppose 402*q**2 + 53*q**2 + 83*q**2 + 3*q**4 - 165*q**2 - 108*q**3 + 599*q**2 = 0. Calculate q.
0, 18
Let n(o) be the first derivative of 4*o**5/25 - 8*o**4/5 + 4*o**3/5 + 64*o**2/5 - 112*o/5 - 41. Determine f so that n(f) = 0.
-2, 1, 2, 7
Solve 9*x**5 + 36*x**4 + 260 - 135*x - 6*x**5 + 132*x**3 + 126*x**2 - 422 = 0 for x.
-6, -3, -1, 1
Let h(c) be the second derivative of 0*c**4 - 46*c + 0 - 6/7*c**3 + 3/140*c**5 - 24/7*c**2. Find s, given that h(s) = 0.
-2, 4
Let f be (-2)/(-4*-1*24/(-16)). Factor -16/3*x + 2*x**4 - 1/3*x**3 - f*x**5 + 0 - 8*x**2.
-x*(x - 4)**2*(x + 1)**2/3
Let o