. Suppose 30 + 6 = a*t. Factor -37*w - 5*w**3 + 30*w**2 - 41*w + 40 + t*w.
-5*(w - 2)**3
Solve 20/9*k**2 + 4/9*k**4 + 0 + 1/9*k**5 - 7/9*k - 2*k**3 = 0 for k.
-7, 0, 1
Let c(x) be the first derivative of 3 - 1/2*x + 1/12*x**3 - 1/8*x**2. Factor c(r).
(r - 2)*(r + 1)/4
Let c be 16/(-20)*((-632)/(-48) - 14). Determine p, given that c - 2*p**2 - 1/3*p = 0.
-2/3, 1/2
Let i(k) = 11*k**3 - 24*k**2 - 86*k - 60. Let a(m) = 3*m**3. Let n(v) = -3*a(v) + i(v). Determine s, given that n(s) = 0.
-2, -1, 15
Let c be (-4)/(-18) - (-68)/18. Let g be 2/(-1) + 0 + c. Factor 75*f**4 - 9*f**g - 12*f - 20*f**2 - 15*f**3 - 13*f**2 - 6*f**2.
3*f*(f - 1)*(5*f + 2)**2
Let b(f) be the first derivative of 6*f - 16 - 7*f**3 + 15/2*f**2. Factor b(j).
-3*(j - 1)*(7*j + 2)
Let o = 62 - 58. Let f(b) be the first derivative of 9/20*b**5 + 3 + 1/3*b**3 + 0*b + 0*b**2 + 3/4*b**o. Let f(d) = 0. Calculate d.
-2/3, 0
Let f(j) be the second derivative of 5*j**4/48 - 17*j**3/24 + 3*j**2/4 - 38*j - 6. Determine g so that f(g) = 0.
2/5, 3
Let u(q) be the third derivative of q**8/6720 - q**7/1890 + q**6/2160 - 7*q**4/24 - 8*q**2. Let y(c) be the second derivative of u(c). Solve y(k) = 0.
0, 1/3, 1
Let n(z) be the second derivative of z**7/1260 + z**6/180 + z**5/60 + z**4/36 - 5*z**3/2 - 6*z. Let k(d) be the second derivative of n(d). Factor k(h).
2*(h + 1)**3/3
Let b(l) be the first derivative of -l**3 - 57*l**2/2 - 102*l - 9. Let b(f) = 0. Calculate f.
-17, -2
Suppose 0 = -a - 1 - 2, -5*s + 2*a = -36. Let m be 20/(-55)*((-87)/s - -2). Factor 90/11*d**3 + 8/11*d + 48/11*d**2 + 0 + m*d**4.
2*d*(d + 1)*(5*d + 2)**2/11
Let y = -5707 - -11415/2. Determine l, given that -7/2*l - 1 - 9/2*l**2 - 5/2*l**3 - y*l**4 = 0.
-2, -1
Suppose 0 = 5*c, -4*b + 5*c + 24 = -0*b. Let v(w) = 2*w**4 + 2*w**3 - 6*w - 6. Let n(u) = u**4 + u**3 - u - 1. Let p(g) = b*n(g) - v(g). Factor p(h).
4*h**3*(h + 1)
Find u such that -10*u**3 - 74/3*u + 2/3*u**4 + 26*u**2 + 8 = 0.
1, 12
Find o, given that 4/7*o**3 + 44/7*o**2 + 0 - 104/7*o = 0.
-13, 0, 2
Let m(u) be the first derivative of u**7/20 + 9*u**6/80 + u**5/20 + 3*u**2/2 - 25. Let h(s) be the second derivative of m(s). Factor h(a).
3*a**2*(a + 1)*(7*a + 2)/2
Let c(u) be the third derivative of 0 + 0*u + 0*u**4 + 1/30*u**5 + 0*u**3 - 1/30*u**7 + 3*u**2 + 1/24*u**6. Factor c(m).
-m**2*(m - 1)*(7*m + 2)
Let t(i) be the third derivative of 0*i**6 + 0*i + 0*i**4 + 1/2*i**3 + 31*i**2 - 1/10*i**5 + 1/70*i**7 + 0. Factor t(w).
3*(w - 1)**2*(w + 1)**2
Let w(s) be the third derivative of 1/39*s**3 - 1/78*s**4 + 0*s + 1/390*s**6 - 16*s**2 - 1/1365*s**7 + 0 + 0*s**5. Solve w(f) = 0.
-1, 1
Let f(i) be the first derivative of i**6/120 - 7*i**4/48 + i**3/4 + 36*i - 26. Let o(h) be the first derivative of f(h). Find s such that o(s) = 0.
-3, 0, 1, 2
Let d be (240/50)/(6/(-380))*1. Let x be (d/(-36) - 4) + -3. Factor 1/9*l**2 + 2/9*l + 0 - l**3 - x*l**4 - 5/9*l**5.
-l*(l + 1)**3*(5*l - 2)/9
Let a(k) be the first derivative of 0*k**3 + 0*k - 1/8*k**6 - 6 - 9/20*k**5 + 0*k**4 + 0*k**2. Solve a(s) = 0 for s.
-3, 0
Let d = 11/625 - -3081/2500. Factor d*k**2 - 15/2*k + 45/4.
5*(k - 3)**2/4
Let m = -5053/13 + 389. Let y = 365/11 - 4701/143. Let -m*b**2 - 2/13*b + y + 2/13*b**3 = 0. Calculate b.
-1, 1, 2
Suppose -170*v - 11 = -16 + 5. Factor 9/8*m + v + 3/8*m**2.
3*m*(m + 3)/8
Let p(b) = -5*b**4 - 20*b**3 - 20*b**2 + 5*b + 10. Let s(q) = -7*q**4 - 30*q**3 - 31*q**2 + 8*q + 16. Let n(t) = 8*p(t) - 5*s(t). Determine d so that n(d) = 0.
-1, 0
Let -198/7*g**2 + 8/7*g**3 - 50/7*g + 0 = 0. What is g?
-1/4, 0, 25
Let z(k) be the first derivative of -k**5/18 - k**4/12 + 2*k**3/9 + 5*k**2 + 2. Let t(f) be the second derivative of z(f). Factor t(j).
-2*(j + 1)*(5*j - 2)/3
Let x be 10/30*-3 - -4. Let t(w) be the third derivative of 1/24*w**4 + 1/10*w**6 + 0*w**x + 0*w + 0 + w**2 + 7/60*w**5. Factor t(l).
l*(3*l + 1)*(4*l + 1)
Let p(q) be the third derivative of -q**6/30 - 8*q**5/15 - 3*q**4/2 + 12*q**3 + 300*q**2. Solve p(g) = 0.
-6, -3, 1
Let l be 174/(-203)*105/(-8). Let -3/4*a**3 - 27/4 - l*a - 21/4*a**2 = 0. What is a?
-3, -1
Determine k so that 8*k + 8*k - 4*k - 3*k**2 + k**3 - 4 - 6*k**3 = 0.
-2, 2/5, 1
Suppose -2*u = -4*x - 28, -x + 16 = -4*u - 5*x. Factor -4/3*w**3 + 0*w**4 + 0*w**u + 2/3*w**5 + 0 + 2/3*w.
2*w*(w - 1)**2*(w + 1)**2/3
Let d(l) be the second derivative of l**5/40 - 3*l**4/2 + 95*l**3/4 + 361*l**2/2 - 6*l + 24. Factor d(b).
(b - 19)**2*(b + 2)/2
Let m(z) be the first derivative of -5/2*z**2 + 1/54*z**4 + 0*z + 1/270*z**5 + 1/27*z**3 + 2. Let t(v) be the second derivative of m(v). Factor t(x).
2*(x + 1)**2/9
Let i(h) be the third derivative of -27*h**5/10 - 33*h**4 - 484*h**3/3 - 181*h**2. Find x, given that i(x) = 0.
-22/9
Suppose -32 = -187*o + 171*o. Let c(f) be the second derivative of 0 - 1/4*f**o - 1/24*f**4 + 10*f + 1/6*f**3. Let c(z) = 0. What is z?
1
Let t(i) be the third derivative of 3*i**5/20 + 2*i**4 - 6*i**3 + 73*i**2 + 1. Factor t(f).
3*(f + 6)*(3*f - 2)
Let 4/3*w**2 - 10/3*w + 16/9 + 2/9*w**3 = 0. What is w?
-8, 1
Let l = 24 + -35. Let h = 27 + l. Factor h - 14*g + 52*g**2 + 0*g**3 - 12*g**3 - 41*g - 9*g.
-4*(g - 2)**2*(3*g - 1)
Let d(q) be the first derivative of 5*q**9/3024 - q**8/840 - q**7/168 + q**6/180 + 11*q**3/3 + 10. Let g(w) be the third derivative of d(w). Factor g(y).
y**2*(y - 1)*(y + 1)*(5*y - 2)
Factor 638*w**2 - 638*w**2 + 2*w**3 - 2*w**4.
-2*w**3*(w - 1)
Factor -2*h**4 + 14/3*h**3 + 0*h - 4/3*h**2 + 0.
-2*h**2*(h - 2)*(3*h - 1)/3
Factor 0 - 9/7*g + 6/7*g**4 + 8/7*g**3 + 1/7*g**5 - 6/7*g**2.
g*(g - 1)*(g + 1)*(g + 3)**2/7
Let t(k) = -4*k - 73. Let n be t(8). Let z = n - -105. Let z + 6/7*c + 3/7*c**2 = 0. What is c?
-2, 0
Let s(q) = -7*q**2 + 10*q + 1. Let w be s(1). Let p(b) be the first derivative of -5*b**3 - 9/2*b**5 - 3/2*b**2 + 0*b - 111/16*b**w - 9/8*b**6 + 4. Factor p(t).
-3*t*(t + 1)**2*(3*t + 2)**2/4
Let p(v) be the second derivative of -13/48*v**4 + 14*v - 11/24*v**3 - 1/20*v**5 + 0 - 1/4*v**2. Factor p(a).
-(a + 1)*(a + 2)*(4*a + 1)/4
Let q(o) be the third derivative of -3/100*o**6 - 1/15*o**4 - 2/15*o**5 + 0 + 0*o + 7*o**2 + 0*o**3. Factor q(v).
-2*v*(v + 2)*(9*v + 2)/5
Let y(j) be the first derivative of j**6/10 - 3*j**4/5 - 62. Let y(x) = 0. Calculate x.
-2, 0, 2
Let c(i) be the first derivative of -1/110*i**5 + 0*i**3 + 1 + 0*i**2 - 5*i - 1/66*i**4. Let l(k) be the first derivative of c(k). Factor l(b).
-2*b**2*(b + 1)/11
Let x be (-2)/2*3*(-8)/12. Factor 25 - 5*d**x + 10*d + 10 - 40*d.
-5*(d - 1)*(d + 7)
Determine m so that -10*m**2 - 1271*m + 2*m**4 + 14 + 1271*m - 6 = 0.
-2, -1, 1, 2
Let v(t) = -2*t**3 - 13*t**2 - 35*t + 3. Let d(f) = 10 - f**2 - 28 + 17 + f. Let r(g) = -3*d(g) - v(g). Factor r(a).
2*a*(a + 4)**2
Let -1/3*j**4 + 0*j**2 + 0*j + 0 - 16/3*j**3 = 0. Calculate j.
-16, 0
Let b(z) be the third derivative of -z**6/540 + z**5/90 - z**4/36 + z**3/27 + 108*z**2. Factor b(x).
-2*(x - 1)**3/9
Let q(o) = -6*o**3 - 40*o**2 - 126*o - 128. Let p(m) = m**3 - m. Let n(a) = 2*p(a) + q(a). Suppose n(b) = 0. What is b?
-4, -2
Let y(z) = -2*z**3 - 15*z**2 - 44*z - 29. Let u be y(-1). Find v such that -4/5*v - 1/5*v**u + 1/5*v**3 + 4/5 = 0.
-2, 1, 2
Let a = -230 - -85. Let x = 145 + a. Factor -2/9 + 2/9*y**2 + x*y.
2*(y - 1)*(y + 1)/9
Suppose -15/4*w**3 - 3/2*w**2 + 3/2 + 15/4*w = 0. What is w?
-1, -2/5, 1
Let c(n) be the third derivative of n**8/1008 + 2*n**7/315 + n**6/120 - n**5/45 - n**4/18 - 5*n**2 - 2. Determine v, given that c(v) = 0.
-2, -1, 0, 1
Let k(x) = 5*x + 26. Let y be k(-4). Suppose -y*p - 6*p = 0. Determine d so that 0*d - 1/4*d**2 + p + 1/2*d**3 = 0.
0, 1/2
Suppose -u = 5*p - 34 + 37, p + 4*u + 12 = 0. Find z, given that 0*z + 2/9*z**2 + p = 0.
0
Let m = -290 + 1454/5. Let t(z) = -z**3 + 7*z**2 + 18*z. Let y be t(9). Factor 6/5*r**2 - m*r + y - 2/5*r**3.
-2*r*(r - 2)*(r - 1)/5
Suppose 2/11*t**2 + 60/11 - 2*t = 0. Calculate t.
5, 6
Suppose 20 = 5*q - 5*x + 10, 0 = 3*q - 4*x - 5. Factor -3*h - q*h + 2*h**2 - 6 + 4*h - 2*h.
2*(h - 3)*(h + 1)
Factor -28 - 3*o**2 + 75*o - 66*o + 22.
-3*(o - 2)*(o - 1)
Suppose -50 = k + 4*k. Let d(s) = s**2 - s**2 + s**2 - 5*s + 5 + 4*s**2. Let l(y) = 9*y**2 - 11*y + 11. Let v(r) = k*d(r) + 6*l(r). Factor v(i).
4*(i - 2)**2
Let v(r) be the third derivative of r**5/90 + 35*r**4/6 + 122