k - 21 = -5*q + 7. Suppose 0 = q*i + 4*w - 3, 4*i - 18*w + 13*w - 27 = 0. Factor 16/3*h - 10/3*h**2 + 2/3*h**i - 8/3.
2*(h - 2)**2*(h - 1)/3
Suppose 0 = -4*y + 23 - 15. Determine q so that -356*q**3 + 7*q**y - q - 12 + 358*q**3 - q**4 - 7*q = 0.
-2, -1, 2, 3
Let b(i) be the second derivative of i**7/210 - i**6/25 + 2*i**5/25 + i**4/10 - 3*i**3/10 + 1221*i. Let b(w) = 0. What is w?
-1, 0, 1, 3
Suppose -28 = -8*w + 6*w. Factor 15*q**2 + 10*q - q - 3*q + w*q.
5*q*(3*q + 4)
Let j be 138/(-42) - -3 - (-840)/196. Let y(d) be the third derivative of -8/57*d**3 + 0*d + 5/114*d**5 - 5/114*d**j + 0 - 8*d**2. Let y(c) = 0. What is c?
-2/5, 4/5
Suppose -3*l + 2*p = 2 + 2, 4*p = 3*l + 14. Factor 100*w**3 - 206*w**3 - w**4 - 4*w - 7*w**2 + 104*w**3 + l*w**4.
w*(w - 4)*(w + 1)**2
Let a = -155/21 + 23/3. Let t be 6/21 + (-10)/(-60)*0. Factor 4/7*s**2 - a*s - 4/7 + t*s**3.
2*(s - 1)*(s + 1)*(s + 2)/7
Let 496/9 + 4/9*o**2 - 256/9*o = 0. What is o?
2, 62
Let i(w) be the first derivative of w**6/9 - 4*w**5/15 - w**4 + 40*w**3/9 - 19*w**2/3 + 4*w + 529. Factor i(g).
2*(g - 2)*(g - 1)**3*(g + 3)/3
Let b be (-44)/57*(-9843)/36091. Let l be (-8)/(0/2 - 19). Solve 8/19*w**3 + b*w**2 - 10/19*w + 2/19*w**5 - l*w**4 + 4/19 = 0 for w.
-1, 1, 2
Suppose -5*t + 5 = -10. Suppose f + t - 6 = 0. Factor -10*j + 7*j - 5*j - 7*j**2 + f*j**2.
-4*j*(j + 2)
Let v = -1505620 - -1505625. Solve -1/5*o**v - 2/5*o + 1/5*o**4 + 0 - 1/5*o**2 + 3/5*o**3 = 0.
-1, 0, 1, 2
Let t(o) be the third derivative of 4*o**5/255 - 47*o**4/204 - 21*o**3/17 + 16*o**2 + 15. Solve t(k) = 0 for k.
-9/8, 7
Let b(g) be the second derivative of -g**4/48 - 1015*g**3/24 + 1017*g**2/4 + 6310*g. Let b(f) = 0. What is f?
-1017, 2
Let h be (6/(-15))/((-328)/(-110) - 3). Suppose o + 3 = 2*j, -h*o = -23*o - 4*j + 15. Find p such that p + 1/4*p**4 - p**o + 1/2*p**2 - 3/4 = 0.
-1, 1, 3
Let t(k) be the third derivative of 0*k - 3/5*k**5 + 1/15*k**7 + 1/6*k**6 + 8*k**2 - 9/4*k**4 + 2 + 9*k**3 + 1/168*k**8. Factor t(y).
2*(y - 1)**2*(y + 3)**3
Let n(i) be the second derivative of -2*i**6/75 - 4216*i**5/25 - 2221832*i**4/5 - 9367243712*i**3/15 - 2468268718112*i**2/5 + 3710*i + 2. Factor n(o).
-4*(o + 1054)**4/5
Let n(o) = -43*o**2 - 23932*o - 4752094. Let l(u) = 7*u**2 + 3988*u + 792016. Let p(h) = 13*l(h) + 2*n(h). Let p(w) = 0. What is w?
-398
Let 4*g**3 - 374*g - 345*g - 64*g**2 + 975*g = 0. Calculate g.
0, 8
What is s in -10368/5 + 8/5*s**5 - 55*s**4 + 6696*s + 654*s**3 - 3348*s**2 = 0?
3/8, 6, 16
Let d = 20 + 106. Suppose 0 = -10*q + d + 74. Let 4*p**3 + q*p**2 - 16*p - 20*p**2 + 12*p**2 = 0. What is p?
-4, 0, 1
Suppose 0 = -4*c - 3*c + 2996. Let i = c - 424. Solve -8/15*o + 4/15*o**3 + 2/5*o**2 - 8/15 - 2/15*o**i = 0.
-1, 2
Let i = -12 + 12. Suppose 5*o - c - 20 = 2*o, i = -4*c - 20. Factor -5*d**o - 12*d**3 + 26*d**3 - d**2 - 13*d**3 + 9*d**4 - 4*d**3.
-d**2*(d - 1)**2*(5*d + 1)
Suppose 76 = 128*s - 122*s - 20. Let a(x) be the third derivative of -16/3*x**3 + 1/15*x**5 + 0*x - s*x**2 - 1/3*x**4 + 0. Factor a(z).
4*(z - 4)*(z + 2)
Let s(q) be the third derivative of -q**8/1848 - 4*q**7/385 - 3*q**6/55 - 16*q**5/165 - q**2 - 4266*q. Factor s(l).
-2*l**2*(l + 2)**2*(l + 8)/11
Let x be 7/((-154)/(-4)) - 291/(-33). Suppose 19 = x*o + 1. Suppose 40*t**o - 3033*t + 0*t**5 - 96*t**3 + 3133*t - 4*t**5 - 40*t**4 = 0. What is t?
-5, -1, 0, 1
Let h(n) be the third derivative of 17/42*n**4 - 1/210*n**5 + 0*n + 5/3*n**3 + 221*n**2 + 0. Factor h(s).
-2*(s - 35)*(s + 1)/7
Factor 20/3 + 8/3*q**2 + 2/9*q**3 + 82/9*q.
2*(q + 1)*(q + 5)*(q + 6)/9
Let 48/19*y**2 - 2/19*y**3 - 748/19 + 702/19*y = 0. Calculate y.
-11, 1, 34
Suppose 3*h + 5*i - 110 = 0, 0 = -5*h + 4*i + 101 + 70. Factor -25*b + 44*b**3 - 9*b**2 - 21*b**2 - 5 + 15*b**5 + h*b**4 - 34*b**3.
5*(b - 1)*(b + 1)**3*(3*b + 1)
Let w(c) be the third derivative of -5/36*c**3 + 0 + 0*c - 1/360*c**5 + 42*c**2 + 1/24*c**4. Solve w(q) = 0.
1, 5
Let d(x) = -2*x**3 + 7*x**2 + 24*x + 90. Let m be d(-6). Let b = m + -628. Solve -1/8*s**b - 1/2 - 1/2*s = 0.
-2
Factor 148/19 - 226/19*u + 80/19*u**2 - 2/19*u**3.
-2*(u - 37)*(u - 2)*(u - 1)/19
Factor -729 - 29/2*i**2 - 945/4*i - 1/4*i**3.
-(i + 4)*(i + 27)**2/4
Let v(r) = -20*r**4 + 525*r**3 - 520*r**2 + 10. Let f(d) = -29*d**4 + 788*d**3 - 780*d**2 + 14. Let m(p) = 5*f(p) - 7*v(p). Factor m(i).
-5*i**2*(i - 52)*(i - 1)
Let b = -306 - -2759. Suppose b*m**2 - 52*m + 2435*m**2 + 4*m**3 - 4936*m**2 = 0. Calculate m.
-1, 0, 13
Let i = -7296122/13 - -561805. Let t = -563 + i. Suppose 22/13*j - 4/13 - 2/13*j**3 + 8/13*j**4 - t*j**2 = 0. Calculate j.
-2, 1/4, 1
Let g(j) = -32*j**2 + 22148*j - 5504. Let v(y) = 7*y**2 - 4429*y + 1101. Let r(n) = 3*g(n) + 16*v(n). What is h in r(h) = 0?
1/4, 276
Let m(w) be the second derivative of -40*w - 2*w**4 - 3/5*w**6 - 1/14*w**7 + 0*w**3 + 0 + 0*w**2 - 9/5*w**5. Find t such that m(t) = 0.
-2, 0
Let h(k) be the third derivative of -k**8/168 + 4*k**7/35 - 3*k**6/5 + 16*k**5/15 + 2*k**2 + 581. Factor h(y).
-2*y**2*(y - 8)*(y - 2)**2
Let s(a) = -30*a**2 - 40470*a + 17015271. Let d(b) = -11*b**2 - 15176*b + 6380726. Let j(h) = 27*d(h) - 10*s(h). Suppose j(c) = 0. What is c?
842
Suppose -6*r = -9*r + t + 82, -3*r = -4*t - 67. Suppose 3*d + 2 = 5*a - 14, -3*d - 4*a + r = 0. Factor -10/7*i**2 + 18/7 + 2/7*i**d + 6/7*i.
2*(i - 3)**2*(i + 1)/7
Let y(z) be the third derivative of 31*z**2 + 13/420*z**6 + 1/1176*z**8 - 1/6*z**4 + 1/105*z**7 - 8/21*z**3 + 0 + 1/210*z**5 + 0*z. Solve y(h) = 0 for h.
-4, -2, -1, 1
Let s = 52311/20 + -13074/5. Factor -27/2 + s*x**2 - 21/4*x.
3*(x - 9)*(x + 2)/4
Let t(v) be the third derivative of v**6/780 + 164*v**5/65 + 26896*v**4/13 + 35287552*v**3/39 - 1547*v**2. Solve t(i) = 0 for i.
-328
Let 3/7*i**4 - 12*i - 93/7*i**2 + 0 - 6/7*i**3 = 0. What is i?
-4, -1, 0, 7
Let p = 441 + -402. Suppose p*h - 3*h - 180 = 0. Solve 27/2*z**2 + 0 - 1/4*z**h + 5/2*z**4 - 27/4*z - 9*z**3 = 0 for z.
0, 1, 3
Let 3/4*t**2 + 327/8 - 657/8*t + 327/4*t**3 - 333/8*t**4 + 3/8*t**5 = 0. Calculate t.
-1, 1, 109
Let r = 50 - 40. Suppose u - r = -4*g, 3*g + 0*g + 3*u = 12. Factor -4*v**g - v**2 + 668*v**3 - 673*v**3.
-5*v**2*(v + 1)
Let q = 361831/30 - 12061. Let a(r) be the third derivative of 12*r**2 + 0*r - 5/24*r**4 + q*r**5 + 0 + 1/3*r**3. Factor a(s).
(s - 2)*(2*s - 1)
Let l(t) be the third derivative of -t**6/60 + 64*t**5/15 + 131*t**4/12 - 86*t**3 + 2*t**2 - 2606*t - 1. Factor l(j).
-2*(j - 129)*(j - 1)*(j + 2)
Let a(w) = 3 + 83*w**4 - 26*w**2 + 15*w + 36*w**3 - 89*w**4 - 10*w**2. Let b(u) = -u**4 - u**3 - u - 1. Let t(m) = a(m) + 3*b(m). Suppose t(p) = 0. Calculate p.
0, 2/3, 1, 2
Let f(i) = 6*i**2 - 709*i + 1059. Let l(c) = 5*c**2 - 710*c + 1065. Let j(h) = 5*f(h) - 4*l(h). Factor j(p).
5*(p - 69)*(2*p - 3)
Let v(h) be the second derivative of h**4/72 - h**3/18 - 2*h**2/3 + 681*h. Factor v(c).
(c - 4)*(c + 2)/6
Let h(q) be the third derivative of -77*q**5/540 - 34*q**4/27 + 14*q**3/9 - 2769*q**2. Factor h(a).
-(7*a - 2)*(11*a + 42)/9
Let f(l) be the first derivative of -l**3/27 + 11*l**2/9 - 85*l/9 - 2485. Let f(x) = 0. Calculate x.
5, 17
Let f(q) = 24*q**4 + 36*q**3 - 120*q**2 - 9*q. Let v(k) = k**5 - 23*k**4 - 37*k**3 + 123*k**2 - 18*k. Let c(a) = 2*f(a) + 3*v(a). Factor c(s).
3*s*(s - 8)*(s - 1)**2*(s + 3)
Let q(h) be the second derivative of -h**5/50 - 41*h**4/30 - 116*h**3/15 - 76*h**2/5 + 1138*h. What is y in q(y) = 0?
-38, -2, -1
Let h(t) be the third derivative of -1/100*t**5 - 1/600*t**6 + 0 + 0*t**4 + 14/3*t**3 + 0*t + 37*t**2. Let a(o) be the first derivative of h(o). Factor a(z).
-3*z*(z + 2)/5
Find u such that 2/3 - 13/6*u - 1/6*u**2 + 13/6*u**3 - 1/2*u**4 = 0.
-1, 1/3, 1, 4
Let y be -1 + -2 + (-87)/(-27) + (-50 - (-37632)/756). Determine g so that 0*g - 3/4*g**4 + 0*g**2 + y - 3/2*g**3 = 0.
-2, 0
Let q be 30*(-31)/(-744)*(-40)/(-25). Factor 15/2*k - 3/4*k**q - 18.
-3*(k - 6)*(k - 4)/4
Suppose 17*q - 4*b + 1 = 12*q, b = 4. Let 0*m + 3/2*m**2 + 0 + 3/4*m**q = 0. Calculate m.
-2, 0
Let a(n) be the first derivative of -n**5/30 - 19*n**4/4 - 1624*n**3/9 + 19*n**2/2 + 1083*n/2 + 2026. Determine x so that a(x) = 0.
-57, -1, 1
Let l(q) be the first derivative of -4*q**4 + 79 - 4*q**2 + 28/3*q**3 - 4*q. Let l(b) = 0. What is b?
-1/4, 1
Factor -58/9*v**2 - 1568/9 - 896/9*v - 1/9*v**3.
-(v + 2)*(v + 28)**2/9
