
Determine g so that -2/3 - 4/5*g - 2/15*g**2 = 0.
-5, -1
Let l(p) be the second derivative of -p**4/6 + 26*p**3/3 + 67*p. Factor l(y).
-2*y*(y - 26)
Determine q so that q**2 - 5 + 3 + 10*q + 8 + 10 = 0.
-8, -2
Let s be 2 + 6/(-4) - (-2075)/830. Factor -8/7*r**2 + 8/7*r**4 + 4/7*r + 0 - 4/7*r**5 + 0*r**s.
-4*r*(r - 1)**3*(r + 1)/7
Suppose -w = 4, -5*w = 5*v - 1 - 14. Suppose v = 2*h + 1. Factor 3*y**2 - h*y**3 + 0*y**2 + 0*y**3 + 6*y.
-3*y*(y - 2)*(y + 1)
Let x(w) be the first derivative of -1/2*w**4 + 0*w + 0*w**2 - 30 + 0*w**3 - 2/5*w**5. Solve x(z) = 0.
-1, 0
Let a(p) = 3*p**2 + 42*p - 90. Let c(s) = -3. Let l(q) = a(q) - 15*c(q). Factor l(u).
3*(u - 1)*(u + 15)
Suppose 36 = 3*z + 3*s, -6*z + 4*z = -2*s - 4. Factor -13 + 3*i**4 + 3*i**2 + z + 4*i**3 + 5*i**3 - 9*i.
3*(i - 1)*(i + 1)**2*(i + 2)
Let q be (0 - (-12)/(-10))/(12/(-20)). Let f(t) be the first derivative of 0*t - 2 - 1/3*t**q + 1/12*t**4 + 1/9*t**3. Factor f(m).
m*(m - 1)*(m + 2)/3
Let n(s) be the second derivative of s**7/252 - s**6/180 - s**5/20 + 7*s**4/36 - 11*s**3/36 + s**2/4 - 215*s. Factor n(u).
(u - 1)**4*(u + 3)/6
Let l(b) = b - 7. Let k(y) = 4*y - 20. Let m(r) = 3*k(r) - 8*l(r). Let a be m(1). Factor -2/9*d + 2/9*d**2 + a.
2*d*(d - 1)/9
Let b be 0 + (6/(-9))/(8/(-36)). Factor -b - 16*g - 2*g**4 - g**3 + 11 + 5*g**3 + 6*g**2.
-2*(g - 2)*(g - 1)**2*(g + 2)
Let l = -9/167 - -863/22211. Let y = 256/665 - l. Let 32/5 - 16/5*k + y*k**2 = 0. Calculate k.
4
Let l = 2151 - 2149. Factor 16/3*j - 4/3*j**3 - 16/3 + 4/3*j**l.
-4*(j - 2)*(j - 1)*(j + 2)/3
Let t(k) be the first derivative of -36*k**3 + 126*k**2 - 147*k + 26. Factor t(o).
-3*(6*o - 7)**2
Determine k so that -56*k**3 - 6178*k**2 + 56*k + 392 - 2*k**4 + 11787*k**2 - 5999*k**2 = 0.
-14, -1, 1
Let i(y) be the first derivative of -7/15*y**6 + 44/5*y**2 + 17/10*y**4 - 124/15*y**3 + 32/25*y**5 - 16/5*y + 11. Suppose i(j) = 0. What is j?
-2, 2/7, 1, 2
Suppose 0 = -8*i + 112 + 48. Factor -4*k**2 - 14 - i*k + 29 - 15.
-4*k*(k + 5)
Let o be ((-264)/(-660))/(2/16*2). Factor -2/5*s**4 + 0 + o*s**2 + 2/5*s**3 - 8/5*s.
-2*s*(s - 2)*(s - 1)*(s + 2)/5
Factor -7*t**2 - 26/9*t + 0 + 5/9*t**3.
t*(t - 13)*(5*t + 2)/9
Find f such that -42*f**2 + 76*f**2 - 2*f - 5*f**4 - 54*f**2 + 23*f**3 - 10*f = 0.
-2/5, 0, 2, 3
Let b(q) be the second derivative of -q**7/14 + 3*q**6/5 - 39*q**5/20 + 3*q**4 - 2*q**3 - 25*q. Factor b(u).
-3*u*(u - 2)**2*(u - 1)**2
Find f, given that -3/8*f**3 - 513/8*f**2 - 555579/8 - 29241/8*f = 0.
-57
Let u(p) be the third derivative of p**7/630 - p**6/360 - p**5/30 + p**4/18 + 4*p**3/9 + 84*p**2. Factor u(l).
(l - 2)**2*(l + 1)*(l + 2)/3
Suppose 4*j = j + 18. Suppose 3*y = m + j + 5, 5*y = -3*m + 9. Suppose -15*a**2 + 3*a**y - 22*a + 70*a - 18*a**2 + 9*a**2 = 0. Calculate a.
0, 4
Let k(v) = -15*v**3 + 15*v**2 + 775*v - 25. Let l(u) = -2*u**3 + 2*u**2 + 97*u - 3. Let a(o) = 3*k(o) - 25*l(o). Let a(w) = 0. Calculate w.
-4, 0, 5
Let l(w) = 2*w**2 - 41*w + 132. Let d be l(4). Factor -2/11*r**2 - 10/11*r + d.
-2*r*(r + 5)/11
Let w be ((-38)/(-10) - 4)*-20. Find k, given that -5*k**w + k**4 + 7*k**3 + k**3 - k**4 + k**5 - 4*k**2 = 0.
0, 1, 2
Let d be 1*(3 - -1) + -3. Suppose -8 = -3*h + d. Solve -i**3 + 1 + 6*i - i**h + 3 = 0.
-1, 2
Let w(d) be the first derivative of d**4/4 - 5*d**3/3 + d**2 - 6*d + 5. Let b be w(5). Suppose -23*h**4 + 4*h**5 + 0*h**5 + 27*h**b = 0. What is h?
-1, 0
Let u(h) = h**2 - h + 1. Let p(i) = 2*i**2 - 12*i + 17. Let j(r) = p(r) - 3*u(r). Let g be j(-10). Factor x**2 + x**5 + 0*x**5 + x**2 - x + 0*x**2 - 2*x**g.
x*(x - 1)**3*(x + 1)
Let t = -227 + 227. Let w(p) be the first derivative of t*p + 1/5*p**5 - 1/2*p**2 + 1/4*p**4 + 6 - 1/3*p**3. Suppose w(g) = 0. What is g?
-1, 0, 1
Let o(u) = -u**3 - 3*u + 1. Let l(c) = 2*c**3 - 30*c**2 + 46*c - 27. Let k(t) = l(t) - 3*o(t). Find d such that k(d) = 0.
1, 2, 3
Let n be ((-20)/15)/((-2)/3). Let s(y) = -y**4 + y**2 + y + 1. Let o(x) = -2*x**4 + x**2 + 3*x + 4. Let g(h) = n*o(h) - 6*s(h). Let g(v) = 0. Calculate v.
-1, 1
Suppose 3*l + 4*i - 1 - 81 = 0, -4*i - 68 = -2*l. Let j = l - 27. Factor -2*z**2 + 5*z**2 + j*z**2 - 3*z - 5*z**2.
z*(z - 3)
Let k = -2698/5 + 540. Let c = 5 - 5. Factor -8/5*l**2 + 8/5*l + c + k*l**3.
2*l*(l - 2)**2/5
Suppose 4*n + 107 - 99 = 0, -5*n - 18 = -4*h. Factor 10/3*q**h - 4/3*q + 0.
2*q*(5*q - 2)/3
Let y(r) be the third derivative of -r**7/1820 - r**6/2340 - 5*r**3/6 + 11*r**2. Let z(m) be the first derivative of y(m). Solve z(j) = 0.
-1/3, 0
Let m(x) be the second derivative of 1/8*x**3 - 3/80*x**5 - 22*x + 0 - 1/4*x**4 + 3/2*x**2. Find c such that m(c) = 0.
-4, -1, 1
What is b in 1/2*b**2 + 1/2*b - 28 = 0?
-8, 7
Let q(s) be the third derivative of -s**5/140 + 3*s**4/56 + 2*s**3/7 - 46*s**2. Factor q(r).
-3*(r - 4)*(r + 1)/7
Suppose 8*i - 3*i - 576 = 2*w, 4*i = w + 459. Suppose i - 42 = 4*x. Factor -x*p**2 - 2 + 10*p + 11*p - 9*p.
-2*(3*p - 1)**2
Let s = 74 - 44. Determine h so that -3*h**2 - s + 0*h + 3*h + 30 = 0.
0, 1
Let z(r) = -r + 1. Let w(x) = -5*x**2 - 20*x - 35. Suppose -u - 4*m = -2 + 5, -3*u = 2*m - 11. Let v(l) = u*z(l) + w(l). Determine d so that v(d) = 0.
-3, -2
Suppose -9*s**3 - 7/2*s**4 - 4*s - 10*s**2 + 0 - 1/2*s**5 = 0. Calculate s.
-2, -1, 0
Factor 6265 - 3*o**3 + 38*o**2 - 6345 + 33*o**2 - 216*o.
-(o - 20)*(o - 4)*(3*o + 1)
Let m(j) be the third derivative of j**7/525 + 3*j**6/100 + j**5/6 + 9*j**4/20 + 2*j**3/3 - 2*j**2 - 3*j. Solve m(h) = 0 for h.
-5, -2, -1
Let p = 40 - 38. Factor 8*u**2 + 18 - 48*u - p + 2*u**2 + 4*u**4 + 42*u**2 - 24*u**3.
4*(u - 2)**2*(u - 1)**2
Let q(d) be the third derivative of d**7/1260 - 7*d**6/720 + d**5/60 + d**2. Factor q(o).
o**2*(o - 6)*(o - 1)/6
Let c(v) = v**3 - 8*v**2 + 15*v + 4. Let q be c(4). Let z(f) be the first derivative of -1/3*f**3 + 1 + 5/4*f**4 - 6/5*f**5 + q*f**2 + 0*f. Factor z(a).
-a**2*(2*a - 1)*(3*a - 1)
Suppose -4*n - 3*w = -37, -5*w - 12 = -n - 3*w. Let f(z) = -z**3 - 5*z**2 - 6*z - 6. Let t be f(-4). Let -122*g + 138*g + n + 4*g**2 + t = 0. Calculate g.
-3, -1
Let l(u) be the third derivative of u**6/180 - 3*u**5/20 + 2*u**4/3 - 6*u**3 - 34*u**2. Let x(q) be the first derivative of l(q). Solve x(s) = 0 for s.
1, 8
Let m(h) be the second derivative of h**6/150 - h**5/25 + h**4/12 - h**3/15 + 205*h. Factor m(u).
u*(u - 2)*(u - 1)**2/5
Let i(h) be the first derivative of -2*h**3/51 - 10*h**2/17 - 18*h/17 - 81. Determine x so that i(x) = 0.
-9, -1
Let y(q) be the third derivative of q**6/1260 - q**4/84 + 4*q**3/3 + 25*q**2. Let l(k) be the first derivative of y(k). Factor l(i).
2*(i - 1)*(i + 1)/7
Factor 51/5*b - 38/5*b**2 - 18/5 + b**3.
(b - 6)*(b - 1)*(5*b - 3)/5
Let k(r) = 5*r**2 + 30*r + 6. Let g(i) = -1. Let p(v) = -6*g(v) - k(v). Let p(c) = 0. What is c?
-6, 0
Let q(j) be the second derivative of -j**7/2520 + j**6/1080 + 5*j**3/6 - 17*j. Let x(a) be the second derivative of q(a). Factor x(g).
-g**2*(g - 1)/3
Suppose 2*n + 6 = 5*n. Factor 10 - 2*w**2 + w + 10*w + 7*w**n + 4*w.
5*(w + 1)*(w + 2)
Let q(u) = -u**2 + u + 2. Let x be q(0). Determine h so that -512*h + 2*h**3 + 512*h + 10*h**x = 0.
-5, 0
Find i such that 1910/7*i**3 + 2/7*i**5 - 8640/7*i + 1206/7*i**2 + 5400/7 + 122/7*i**4 = 0.
-30, -3, 1
Solve 45 + 3/2*m**3 - 177/2*m + 42*m**2 = 0 for m.
-30, 1
Let n(y) be the second derivative of -y**5/20 + 7*y**4/12 - 7*y**3/6 - 15*y**2/2 + 20*y - 1. Factor n(x).
-(x - 5)*(x - 3)*(x + 1)
Factor -24/7*t**3 - 12/7 + 3*t + 3/7*t**5 + 6/7*t**4 + 6/7*t**2.
3*(t - 1)**3*(t + 1)*(t + 4)/7
Let z(o) be the first derivative of 0*o + 1/6*o**3 - 30 + o**5 - 13/16*o**4 - 3/8*o**6 + 0*o**2. Factor z(m).
-m**2*(m - 1)**2*(9*m - 2)/4
Factor 0*s + 96/7 - 3/7*s**3 - 18/7*s**2.
-3*(s - 2)*(s + 4)**2/7
Suppose -4*w - 2*t - 3*t + 12 = 0, w + 2*t = 3. Find s, given that -20*s + s**3 + 22*s - 3*s**w = 0.
-1, 0, 1
Let g be ((-40)/102)/((-16)/24)*29/145. Let 12/17*f + 16/17*f**3 - 24/17*f**2 - g = 0. What is f?
1/2
Let c(r) be the second derivative of r**6/15 - r**5/5 - r**4/6 + 2*r**3/3 - 3*r - 28. Find u such that c(u) = 0.
-1, 0, 1, 2
Suppose -6 = 26*q - 29*q. Determine i, given that -i**2 + 2 - i - 7*i**2 + 7*i**q = 0.
-2, 1
Let 39/5*i**3 + 18/5*i**2 + 3/5*i + 36/5*i**4 + 12/5*i**5 + 0 = 0. Calculate i.
-1, -1/2, 0
Let s be (-12)/2*(-42)/28 - 6. Let b(c) be the first derivative 