+ 2)**2/5
Suppose -n = n - 10. Let 4 - 5*t**3 - 4 - n*t**5 - 3*t**4 - 7*t**4 = 0. What is t?
-1, 0
Let k = 19 - 5. Suppose -2*n - 2*t - k = -3*n, -t = -n + 10. Factor 2*c**3 - n*c**2 - 8*c + 3*c**3 + 16*c**2 + 13*c.
5*c*(c + 1)**2
Suppose 0 = -7*m - 7*m - 336. Let q be (m/32)/((-108)/32). Factor 0 + q*s - 2/9*s**2.
-2*s*(s - 1)/9
Let b(f) be the third derivative of 0*f**3 + 1/24*f**4 + 0*f - 1/120*f**6 + 39*f**2 + 0 + 7/120*f**5 - 1/60*f**7. Factor b(w).
-w*(w - 1)*(w + 1)*(7*w + 2)/2
Let s(w) = 3*w**2 + 12*w + 6. Let j(c) = -c**3 + 2*c**2 + 11*c + 2. Let b(f) = 3*j(f) - 2*s(f). Determine z so that b(z) = 0.
-2, 1
Suppose 8 = 2*j - 6. Factor -4*s**5 - s - j*s - 16*s**4 - 9*s**2 - 24*s**3 + 4*s - 7*s**2.
-4*s*(s + 1)**4
Factor 3/8*c + 1/4 + 0*c**2 - 1/8*c**3.
-(c - 2)*(c + 1)**2/8
Let y be 4/(12/(-9)) - (-80)/12. Let h = 23/6 - y. Suppose 1/2*f - h*f**2 + 0 = 0. What is f?
0, 3
Let h(o) be the third derivative of -o**9/4032 - o**8/1120 - 11*o**3/6 + 9*o**2. Let i(x) be the first derivative of h(x). Find z, given that i(z) = 0.
-2, 0
Let r(f) be the third derivative of -14*f**2 + 0 + 1/28*f**4 - 1/140*f**5 + 0*f - 1/14*f**3. Find y, given that r(y) = 0.
1
Let y(q) be the third derivative of q**7/1155 + q**6/330 + q**5/330 + q**2 + 3*q. Solve y(m) = 0 for m.
-1, 0
Let w = 862/9 + -850/9. Let g be (-2)/4 - (-19)/6. Let w + 10/3*c - 8/3*c**4 - 2/3*c**5 - g*c**3 + 4/3*c**2 = 0. What is c?
-2, -1, 1
Let -66*t - 2*t**3 + 10 + 34*t**2 + 22 + 2*t**2 = 0. Calculate t.
1, 16
Let n = -26 - -26. Let z be n/3*(1 - 3/6). Factor 2/3*k - 4/3*k**2 + z.
-2*k*(2*k - 1)/3
Let m(g) = 3*g**5 - 2*g**4 - g**3 - 2*g. Let p(k) = 13*k**5 - 9*k**4 - 3*k**3 + k**2 - 9*k. Let u be (-4 - -6)/(2/9). Let q(r) = u*m(r) - 2*p(r). Factor q(v).
v**2*(v - 2)*(v + 1)**2
Let d(o) be the first derivative of -o**5 + 17*o**4/4 - o**3/3 - 17*o**2/2 + 6*o + 115. Solve d(i) = 0.
-1, 2/5, 1, 3
Suppose -j - 2*f = 2*j - 10, 2*j = 3*f - 2. Suppose 2*y = -5*n + 44, -3*y - 4*n = -7*n - 108. Factor -y*q + 32*q + q**3 + 2*q**j.
q**2*(q + 2)
Let y be (-1)/8*(-4)/3. Let a(p) be the third derivative of y*p**3 + 5*p**2 + 1/30*p**5 - 1/240*p**6 + 0 + 0*p - 5/48*p**4. Factor a(c).
-(c - 2)*(c - 1)**2/2
Suppose -n + 0 = -3. Let x be 2*n - (-7)/35*-15. Factor -x - 2*p - 1/3*p**2.
-(p + 3)**2/3
Let z = 107/5 + -316/15. Factor -4/3*h + 1 + z*h**2.
(h - 3)*(h - 1)/3
Let g be (-33)/(-9)*(52 - 51). Factor 0 - b**4 - 4*b**2 + 4/3*b + g*b**3.
-b*(b - 2)*(b - 1)*(3*b - 2)/3
Factor 6/17*y**2 + 4/17 - 2/17*y**4 + 10/17*y - 2/17*y**3.
-2*(y - 2)*(y + 1)**3/17
Let s(p) be the second derivative of 5*p**7/42 - 5*p**6/6 + 2*p**5 - 5*p**4/3 + p + 40. Factor s(k).
5*k**2*(k - 2)**2*(k - 1)
Suppose 43 = 5*h - 52. Suppose 4*q = 7 + 9. Let q*b + 2*b**2 + h - 1 - 8*b - 8*b = 0. Calculate b.
3
Let n = 44797/4 + -11199. Factor n*c**3 + 0 + 0*c - 1/2*c**2.
c**2*(c - 2)/4
Let z = 25 - 17. Factor 7 - 5*a**3 - 9 + 5*a - z + 15*a**2 - 5*a**4.
-5*(a - 1)**2*(a + 1)*(a + 2)
Let s be 456/405 - (-44)/594. Factor 8/5*b**3 - 28/5*b + s + 14/5*b**2.
2*(b - 1)*(b + 3)*(4*b - 1)/5
Let g(w) = -15*w + 80. Let q be g(5). Let 0*i + 2/5*i**2 - 6/5*i**4 + 0*i**3 + 0 + 4/5*i**q = 0. Calculate i.
-1/2, 0, 1
Let 31 - 3*c**3 + 4*c**2 + 57*c - 13 + 8*c**2 + 20 + 4 = 0. Calculate c.
-2, -1, 7
Suppose -5*n = -0*n - 5*s - 100, 0 = -2*n + 3*s + 45. Suppose 0 = 8*o - 3*o - n. Find q such that -2*q**3 - 3*q**2 - 5*q**2 + q**o + 2*q + 7*q**3 = 0.
0, 1/3, 1
Suppose -11/2*x**2 + 121/4*x + 1/4*x**3 + 0 = 0. Calculate x.
0, 11
Let h be ((-15)/4)/((-66)/88). Let n(c) be the first derivative of 0*c**2 - 2/3*c**3 + 2*c + h. Factor n(d).
-2*(d - 1)*(d + 1)
Let g(z) be the third derivative of 0*z**3 + 0*z + 0*z**4 + 1/60*z**5 + 1/672*z**8 + 1/48*z**6 + 1/105*z**7 + 0 + 8*z**2. Factor g(l).
l**2*(l + 1)**2*(l + 2)/2
Let n(l) = -22*l**4 + 93*l**3 - 57*l**2 - 40*l. Let c = -9 + 12. Let s(w) = -45*w**4 + 185*w**3 - 115*w**2 - 80*w. Let g(i) = c*s(i) - 5*n(i). Factor g(k).
-5*k*(k - 2)**2*(5*k + 2)
Let p = 94 + -90. Factor 2*n**3 + 3*n**2 - 3*n**3 - p*n**2.
-n**2*(n + 1)
Suppose -7*x + 12 = -2*g - 3*x, 0 = 5*g + 5*x. Let b be (7 + g)*(-4)/(-10). Factor -m**2 + 6*m**3 + 4*m**2 + 3*m**4 + 0*m**b.
3*m**2*(m + 1)**2
Let m(s) be the first derivative of 2*s**4/17 - 22*s**3/17 + 56*s**2/17 - 24*s/17 + 6. Factor m(b).
2*(b - 6)*(b - 2)*(4*b - 1)/17
Let s(v) be the second derivative of -3*v**5/100 - v**4/10 + v**3/10 + 3*v**2/5 + 6*v + 1. Determine r so that s(r) = 0.
-2, -1, 1
Let g(l) be the third derivative of -l**5/15 - 59*l**4/3 - 6962*l**3/3 - 32*l**2 + 3*l. Factor g(j).
-4*(j + 59)**2
Let s be (-87)/(-24) + (-18)/(-48). Factor -1363 + 6*r**2 - 2*r**4 + 1355 - 5*r**3 + 3*r**s + 4*r.
(r - 2)**3*(r + 1)
Let p(w) be the third derivative of w**6/24 + w**5/6 + 5*w**4/24 - 43*w**2. Factor p(q).
5*q*(q + 1)**2
Suppose -9*g = 9*g - 72. Let z(k) = -6*k + 2. Let w = -15 + 9. Let d(b) = -b**2 - 6*b + 1. Let i(p) = g*d(p) + w*z(p). Factor i(a).
-4*(a - 2)*(a - 1)
Let j(w) be the third derivative of -w**6/6 - 17*w**5/12 - 10*w**4/3 - 5*w**3/2 + 133*w**2. Suppose j(u) = 0. What is u?
-3, -1, -1/4
Let o be (-154)/(-77) - (-21)/(-12). Factor 0*r + o*r**2 - 1/4.
(r - 1)*(r + 1)/4
Factor 12*k**2 - 8*k**2 + k**3 - 2*k**3 - 5*k**2.
-k**2*(k + 1)
Let j(y) be the second derivative of -y**4/6 - 16*y**3 - 576*y**2 - 25*y + 2. Suppose j(r) = 0. Calculate r.
-24
Let n be 1/((-16)/(-54))*12. Let f = n - 121/3. Factor -1/2*x**2 + 0 + f*x.
-x*(3*x - 1)/6
Let v(r) = 8*r**3 + 148*r**2 - 304*r + 158. Let t(m) = 2*m**3 + 2*m + 1. Let f(k) = -2*t(k) + v(k). Factor f(z).
4*(z - 1)**2*(z + 39)
Let j(d) be the first derivative of -1/3*d**6 + 0*d + 26/3*d**3 - 15/2*d**4 + 26 + 14/5*d**5 - 4*d**2. Solve j(w) = 0 for w.
0, 1, 4
Let r(h) be the second derivative of h**5/15 + 5*h**4/3 + 112*h**3/9 + 40*h**2 + 203*h + 2. Factor r(w).
4*(w + 2)*(w + 3)*(w + 10)/3
Suppose -3*f = -22 + 16. Factor 0*b**2 + 3*b**f - 3*b + 3*b**2.
3*b*(2*b - 1)
Suppose -3*o = 3*r - 0*r + 9, -3*r - 19 = -2*o. Let f be (-12 + 10)/((1 + 0)*-8). Factor f*b**o - 1/2 + 1/4*b.
(b - 1)*(b + 2)/4
Let t(j) be the first derivative of j**6/40 - j**4/8 - 7*j**2/2 + 9. Let y(d) be the second derivative of t(d). Solve y(m) = 0 for m.
-1, 0, 1
Let -160/3 + 1675/3*s**3 + 15*s**5 - 2000/3*s**2 + 980/3*s - 180*s**4 = 0. What is s?
1/3, 2/3, 1, 2, 8
Factor -4 - 26*g**4 - 4*g**5 + 109*g**3 + 4 - 6*g**4 - 157*g**3.
-4*g**3*(g + 2)*(g + 6)
Factor 1350*s**2 - 16000*s + 1050*s**2 - 188*s**4 - 120*s**3 + 190*s**4.
2*s*(s - 20)**3
Determine o, given that 1/8*o**2 - 1/2*o - 5/8 = 0.
-1, 5
Let t(z) be the first derivative of -z**6/15 + 14*z**5/25 - z**4 - 4*z**3/15 + 11*z**2/5 - 2*z - 46. Let t(f) = 0. What is f?
-1, 1, 5
Let o(u) be the second derivative of 6*u**5 + 27*u + 720*u**3 - 90*u**4 - 1/6*u**6 + 0 - 3240*u**2. Factor o(z).
-5*(z - 6)**4
Suppose -16*a = 17*a - 99. Factor 0 + 0*u + 2/7*u**2 - u**a.
-u**2*(7*u - 2)/7
Let o(j) be the first derivative of -4*j**5/5 - 2*j**4 + 44*j**3/3 + 24*j**2 - 144*j - 253. What is k in o(k) = 0?
-3, 2
Let o(v) = -7*v + 31. Let j be o(4). Factor 10*z**2 + 7*z**j - 4*z**3 - 8*z**3.
-5*z**2*(z - 2)
Factor -19*h**2 - 30*h + 6 + 67*h**2 - 4 + 2 + 32*h**3.
2*(h + 2)*(4*h - 1)**2
Let l(n) = -5*n**3 + 23*n**2 + 89*n + 61. Let m(o) = 2*o**3 - 8*o**2 - 30*o - 20. Let z(j) = -2*l(j) - 7*m(j). Determine u, given that z(u) = 0.
-1, 9/2
Let j = -2742 - -2746. Let y(v) be the first derivative of 1/28*v**j - 2/21*v**3 + 1/14*v**2 + 0*v - 4. Factor y(c).
c*(c - 1)**2/7
Factor 30*c**3 + 4*c**2 + 4*c**4 + 30*c**3 + 34*c**3 + 25*c**3 - 127*c**3.
4*c**2*(c - 1)**2
Suppose -10640*q + 40 = -10620*q. Factor -3/8*p - 3/8*p**q + 0.
-3*p*(p + 1)/8
Let z(x) = -20*x**2 - 48*x + 183. Let q(d) = 45*d**2 + 95*d - 365. Let j(h) = -3*q(h) - 5*z(h). Determine u, given that j(u) = 0.
-3, 12/7
Let 8 - 1/2*g**2 + 0*g = 0. What is g?
-4, 4
Let n(g) be the third derivative of -g**8/1680 - g**7/840 + g**6/180 + g**3 - 6*g**2. Let v(x) be the first derivative of n(x). Determine h so that v(h) = 0.
-2, 0, 1
Find s, given that 338/5*s**2 - 816/5*s + 68*s**3 + 288/5 + 10*s**4 = 0.
-4, 3/5
Suppose 5*p + t = 12, 3*p - 9 = t + 3. Let j = 527 + -525. Factor -o - j*o - p*o + 3*o + 3*o**3.
3*o*(o - 1)*(o + 1)
Let n(k) be the third derivative of k**7/6720 - k**6/960 + k**5/3