2
Suppose 67*k = 71*k + r - 19, 5*k - 17 = r. Solve 4/9*g**3 + 0*g + 2/9*g**2 + 0 + 2/9*g**k = 0.
-1, 0
Let p(n) be the first derivative of n**6/6 + n**5/5 - 17*n**4/4 + 5*n**3 - 77. What is t in p(t) = 0?
-5, 0, 1, 3
Let n be (-18)/(-5) - 8/(-20). Suppose -2*f - n*m - 3 = 11, 5*f = 3*m + 30. Factor -d**2 - 3*d**3 + 2*d**5 + 2*d**4 + 5*d**f - 4*d**5 - d**2.
-2*d**2*(d - 1)**2*(d + 1)
Suppose -36*b**3 + 16*b + 30*b - b**4 + 91*b**2 + 33*b**3 + 47*b**3 = 0. Calculate b.
-1, 0, 46
Let x(n) be the third derivative of -n**9/5040 - n**8/2240 + n**7/840 + n**6/240 - n**4/24 - 6*n**2. Let i(p) be the second derivative of x(p). Factor i(s).
-3*s*(s - 1)*(s + 1)**2
Let n = 900 + -129601/144. Let y = 109/144 + n. Determine j so that y*j**3 - 1/4*j + j**2 - 1/2 = 0.
-1, 2/3
Let s = 0 - 1. Let m(f) = -2*f**4 + 11*f**3 + f**2 + 5*f - 5. Let y(t) = -3*t - 1 + t**2 + 3*t**3 + 7*t - 2*t**3 - 3*t. Let b(d) = s*m(d) + 5*y(d). Factor b(r).
2*r**2*(r - 2)*(r - 1)
Suppose -1066*n = -1080*n + 70. Let o(c) be the first derivative of 12 - 5*c**2 + 5/4*c**4 - 3*c**n + 0*c + 5/6*c**6 + 5*c**3. Let o(s) = 0. Calculate s.
-1, 0, 1, 2
Suppose 0 = 2*o - 4*u + 76, 2*u + 68 = -2*o + 4*u. Let n be 83/8 - o/(-80). Find t such that -6*t**2 - 4 - n*t - 2*t**3 + 9*t - 8*t + t**3 = 0.
-4, -1
Let j(y) be the first derivative of 1/10*y**6 + 0*y**5 - 17 + 6/5*y - 3/5*y**4 - 2/5*y**3 + 9/10*y**2. Let j(h) = 0. What is h?
-1, 1, 2
Let p(u) be the second derivative of -u**4/15 - 16*u**3/15 + 8*u**2 - 235*u. What is m in p(m) = 0?
-10, 2
Find s such that -3/8*s**2 - 13/8*s**3 - 1/8*s**5 + 7/8*s**4 + 0 + 9/4*s = 0.
-1, 0, 2, 3
Let r be 7*(-6)/(-15)*(-5)/(-2). Let z be (21/105)/(r/(-10) + 1). Solve -z*j**2 - 1/9 + 4/9*j + 4/9*j**3 - 1/9*j**4 = 0 for j.
1
Let v(s) be the first derivative of s**5/390 + 5*s**4/156 + 2*s**3/13 + 5*s**2 - 24. Let x(m) be the second derivative of v(m). Factor x(g).
2*(g + 2)*(g + 3)/13
Let f(q) be the third derivative of -q**6/24 + 2*q**5/3 - 52*q**2. Find s, given that f(s) = 0.
0, 8
Let p be 2/6 + 6/((-72)/(-44)). Factor v**5 - 8*v**3 + 4*v**3 + 4*v**2 + 12*v**p - 13*v**4.
v**2*(v - 2)*(v - 1)*(v + 2)
Let c(y) be the first derivative of -179*y**3/12 + 45*y**2 - y - 617. Let c(u) = 0. Calculate u.
2/179, 2
Let p(x) be the second derivative of x**4/60 - 29*x**3/15 + 841*x**2/10 - x - 14. Solve p(v) = 0 for v.
29
Let j(l) be the first derivative of -l**5/18 + 7*l**4/144 + l**3/12 + 9*l**2 - 18. Let f(i) be the second derivative of j(i). Find s, given that f(s) = 0.
-1/4, 3/5
Let u(v) be the first derivative of 0*v**5 - 3 - 1/200*v**6 + 0*v + 1/40*v**4 + 0*v**3 + v**2. Let a(k) be the second derivative of u(k). Solve a(o) = 0 for o.
-1, 0, 1
Let k(a) be the first derivative of -1/11*a + 3/22*a**2 - 1/11*a**3 + 1/44*a**4 + 6. Factor k(u).
(u - 1)**3/11
Let n(r) be the second derivative of -r**4/6 - r**3 - 6*r + 8. What is j in n(j) = 0?
-3, 0
Suppose -2*x = 3*k + k + 50, -2*x - 6 = 0. Let i(a) = 4*a**2 + 45*a + 14. Let b be i(k). Determine q so that 0 - q**2 - 1/3*q**b - 2/3*q = 0.
-2, -1, 0
Let 2654*n + 16*n**3 + 876*n**2 - 1027*n + 10685*n + 8748 = 0. What is n?
-27, -3/4
Let s(o) be the first derivative of -o**5/10 + 5*o**4/6 - 8*o**3/3 + 4*o**2 + 10*o - 3. Let t(d) be the first derivative of s(d). Factor t(q).
-2*(q - 2)**2*(q - 1)
Suppose 5*l = j - 45, 2*l - 6*l + j = 36. Let x be 15 - (-12)/l*3. Let -14*c**4 - x*c**4 + 29*c**4 + 4*c**3 = 0. Calculate c.
-1, 0
Let k(p) = p**5 - p**4 - p**2 - p. Let l(w) = 10*w**5 + 55*w**4 + 225*w**3 + 105*w**2 - 965*w - 1440. Let q(x) = -5*k(x) + l(x). Let q(f) = 0. Calculate f.
-4, -3, 2
Suppose -95*g = -50*g - 27*g. Solve -2/5*m**3 + 2/5*m**4 + 0 + 0*m**2 + g*m = 0.
0, 1
Let w be (-9 + 5)*((-70)/8)/(-1). Let j be 51/84 + (4 - (-135)/w). Factor -1/4*a**2 - 1/2 + j*a.
-(a - 2)*(a - 1)/4
Suppose -19 = -5*z - 0*d - d, 0 = 3*z + 4*d - 25. Factor -24*f**3 - 6*f**z + 48 + 157*f**2 + 3*f**4 - 58*f**2 - 120*f.
3*(f - 4)**2*(f - 1)**2
Let s be (-9)/24 - (-67)/8. Factor -12*m**4 - 5*m**5 + 146*m**2 - 25*m**3 - 156*m**2 - s*m**4.
-5*m**2*(m + 1)**2*(m + 2)
Let j(b) = 4*b + 2. Let t be j(-1). Let u be 0*2/(-4)*t/(-3). Solve 0 + 3/5*m**2 - 1/5*m**4 + u*m - 2/5*m**3 = 0 for m.
-3, 0, 1
Let s be 30/(-45) - (-121)/21 - 5. Let t(n) be the third derivative of 1/105*n**5 - 1/21*n**4 + 9*n**2 + s*n**3 + 0 + 0*n. Solve t(l) = 0.
1
Let d(f) = -81*f - 727. Let j be d(-9). Let v(b) be the second derivative of 13*b + 1/20*b**4 - 1/50*b**6 - 1/30*b**3 + 0 + 0*b**j + 1/100*b**5. Factor v(c).
-c*(c - 1)*(c + 1)*(3*c - 1)/5
Let m(k) = -105*k**4 + 545*k**3 + 1205*k**2 + 715*k. Let v(x) = -8*x**4 + 42*x**3 + 93*x**2 + 55*x. Let h(p) = -3*m(p) + 40*v(p). Let h(d) = 0. Calculate d.
-1, 0, 11
Factor -2/5*o**4 + 0*o - 32/15*o**3 - 2/3*o**2 + 0.
-2*o**2*(o + 5)*(3*o + 1)/15
Let l(x) be the first derivative of -5/12*x**4 + 5*x**2 + 4*x + 9 - 5/6*x**3. Let k(b) be the first derivative of l(b). Factor k(y).
-5*(y - 1)*(y + 2)
Let s be -1 + 3 + (10 - 6). Let p(z) = -25*z**2 - 66*z - 26. Let w(j) = j + 1. Let g(h) = s*w(h) + p(h). Factor g(m).
-5*(m + 2)*(5*m + 2)
Let z = -379/165 - -26/11. Let m(o) be the first derivative of -2 - 9/5*o - z*o**3 - 3/5*o**2. Let m(t) = 0. What is t?
-3
Let m = -9 - -9. Let i be (m - 3) + 5 + 0. What is n in 11*n**2 + 48*n**5 - 57*n**i - 23*n**2 - 27*n - 21*n**3 + 2 + 72*n**4 - 5 = 0?
-1, -1/4, 1
Let u(w) be the second derivative of w**7/168 - w**6/24 + w**5/20 + w**4/3 - 4*w**3/3 + 2*w**2 - w + 140. Factor u(h).
(h - 2)**3*(h - 1)*(h + 2)/4
Let l(s) be the third derivative of s**5/60 + 11*s**4/12 - 23*s**3/6 + 58*s**2 - 2*s. Factor l(m).
(m - 1)*(m + 23)
Suppose 0 = -6*y + 3*y. Suppose -4*w + 28 = -y*w + 5*j, -2*w - 2*j + 12 = 0. Factor 2 - 9*i - 4*i**4 - 4*i**3 + 13*i + w*i**4.
-2*(i - 1)*(i + 1)**3
Solve 24/5*o - 3/5*o**2 - 9 = 0.
3, 5
Let l(y) be the second derivative of 0*y**4 + 7*y + 0*y**2 + 1/70*y**5 - 4/21*y**3 + 0. Determine v so that l(v) = 0.
-2, 0, 2
Let a(s) = 6*s**4 - 5*s**3 - 6*s**2 - 5. Let k(z) = z**4 - z**2 - z - 1. Let y(q) = 3*a(q) - 15*k(q). What is t in y(t) = 0?
-1, 0, 1, 5
Let q(m) be the third derivative of m**5/60 - 3*m**4/8 - 5*m**3/2 - 8*m**2. Let f be q(11). Suppose 3*k**2 + k**3 - 13*k**3 - f*k**2 = 0. Calculate k.
-1/3, 0
Let n(p) be the first derivative of -p**5/240 - 3*p**4/32 + 5*p**3/12 + 8*p**2 + 19. Let t(w) be the second derivative of n(w). What is s in t(s) = 0?
-10, 1
Let n(l) = 7*l**3 + 20*l**2 + 25*l. Let p(z) = z**3 + z. Let d(u) = n(u) - 6*p(u). Let d(m) = 0. What is m?
-19, -1, 0
Let l = -256 + 259. Factor 0*g**2 - 2/17*g + 6/17*g**l + 0 + 4/17*g**4.
2*g*(g + 1)**2*(2*g - 1)/17
Let c = 984 - 980. Let j(k) be the first derivative of 0*k**2 - 1/20*k**5 + 12 + 0*k**3 + 0*k + 1/16*k**c. Suppose j(u) = 0. Calculate u.
0, 1
Let a(n) be the first derivative of -4*n**5/5 - 3*n**4 + 28*n**3/3 + 30*n**2 - 72*n - 749. Factor a(c).
-4*(c - 2)*(c - 1)*(c + 3)**2
Factor 9/2*k**4 + 0*k**2 + 0 + k**3 + 0*k - 5/2*k**5.
-k**3*(k - 2)*(5*k + 1)/2
Let g(z) be the second derivative of 6*z**2 + 4/5*z**5 - 8/3*z**3 + 0 - 5*z - z**4. Let g(y) = 0. What is y?
-1, 3/4, 1
Let u = 878 - 17553/20. Let l(b) be the second derivative of -1/6*b**4 + 0 - 1/10*b**6 + u*b**5 - b + 0*b**2 + 0*b**3. Factor l(h).
-h**2*(h - 2)*(3*h - 1)
Let 19*w**3 + 4356/7*w + 0 - 1/7*w**4 - 4488/7*w**2 = 0. Calculate w.
0, 1, 66
Suppose -639 = 37*h - 252*h + 2*h. Factor 0*w + 0*w**2 - 3/2*w**3 + 0 - h*w**4 - 3/2*w**5.
-3*w**3*(w + 1)**2/2
Suppose -3*r = 9*r - 541 + 541. Factor r*k - 2/3*k**2 + 0 - 4/3*k**3 - 2/3*k**4.
-2*k**2*(k + 1)**2/3
Let l = -39 - -42. Factor -2*g**3 + 3*g**3 + 5*g**2 + 10*g + 4*g**l + 10*g**2.
5*g*(g + 1)*(g + 2)
Suppose s - 2*s + 10 = 0. Suppose -3*z**2 + 6*z**2 - s*z**3 + 4*z**2 - 2*z**2 + 10*z - 5 = 0. What is z?
-1, 1/2, 1
Let c(q) be the first derivative of 4*q**3/3 - 10*q**2 + 16*q + 190. Factor c(l).
4*(l - 4)*(l - 1)
Let p be (-398 - -400) + (-2)/1*1. Factor p*f + 0 + 3/4*f**4 + 0*f**3 + 0*f**2.
3*f**4/4
Let x be -14*((-3)/30 + (-222)/(-1020))/(-2). Factor x*w + 12/17 + 2/17*w**2.
2*(w + 1)*(w + 6)/17
Let r(u) be the third derivative of -u**7/6720 + u**6/320 + 3*u**4/8 + 4*u**2. Let b(h) be the second derivative of r(h). Factor b(q).
-3*q*(q - 6)/8
Let d(k) be the second derivative of k**6/540 - 2*k**5/45 +