. Let y(c) = -20*c - 5. Let a be y(x). Suppose -6 - a*u**3 + 15*u + 30*u**4 - 16*u**5 + 5*u**3 + 7*u**5 = 0. Calculate u.
-2/3, 1
Let x = 13 + -10. Factor -3*k**x + 8*k**2 - 3*k + k**3 + 0*k**2 - 3*k.
-2*k*(k - 3)*(k - 1)
Suppose -6*k**3 - 344/3*k + 52*k**2 - 2/3*k**4 + 80 = 0. Calculate k.
-15, 2
Let i = -2878 + 2882. What is s in 0 - 4/3*s**2 + 2/3*s**5 + 2*s + 4/3*s**i - 8/3*s**3 = 0?
-3, -1, 0, 1
Suppose 4*a**3 + a**5 - 4*a - 6*a + 2*a**2 + 5*a + 2 - a**4 - 3*a**4 = 0. Calculate a.
-1, 1, 2
Factor -120*w**2 + 110*w**3 - 13*w**5 - 40*w**4 - 28*w**5 + 46*w**5 + 45*w.
5*w*(w - 3)**2*(w - 1)**2
Let g be 2*-1 + (1760/108 - 14). Let z(r) be the first derivative of 4/9*r**2 - 7/18*r**4 + 0*r + 2 - g*r**3 - 4/45*r**5. Solve z(j) = 0 for j.
-2, 0, 1/2
Let x(n) = -n**3 - n**2 - 2*n. Let a be x(-2). Suppose 0 = -0*f - 4*f + a. Factor -3*y**4 + 2*y**5 - f + 2 + y**4.
2*y**4*(y - 1)
Suppose -5/8*b**4 + 13/8*b**2 - 9/8*b**3 - 1 + 3/8*b**5 + 3/4*b = 0. Calculate b.
-4/3, -1, 1, 2
Let p = 4 - 1. Suppose -7*y + 24 = -p*y. Factor 0*b**4 + y*b**2 - 4*b**2 + 2*b**4 - 4*b**3.
2*b**2*(b - 1)**2
Let x be 2 - ((-2)/(-7) - 60/(-35)). Let l(r) be the first derivative of -2*r**2 - 7/4*r**4 + 2 - 16/3*r**3 + x*r. Factor l(t).
-t*(t + 2)*(7*t + 2)
Let v(j) be the first derivative of -j**5/35 + 3*j**4/28 + 23*j**3/21 + 33*j**2/14 + 2*j + 356. Factor v(c).
-(c - 7)*(c + 1)**2*(c + 2)/7
Let t = 7 - 2. Suppose -7 = t*p - 17. Factor 8 + 67*k + 189*k**p - 4*k**2 + 153*k**2 - 171*k.
2*(13*k - 2)**2
Let j be ((-234)/(-5) - 4)*-5. Let n = -640/3 - j. Factor -n*z**2 + 1/3*z + 0 + 1/3*z**3.
z*(z - 1)**2/3
Let n(b) be the second derivative of -1/42*b**4 - 1/42*b**3 + 0 - 37*b + 5/7*b**2. Solve n(l) = 0.
-5/2, 2
Suppose 99/5*g - 6*g**3 - 6/5*g**4 + 54/5 + 24/5*g**2 + 3/5*g**5 = 0. Calculate g.
-2, -1, 3
Let v(y) be the third derivative of y**5/20 + 5*y**4/8 + 3*y**3 - 4*y**2 - 26*y. What is a in v(a) = 0?
-3, -2
Suppose 0 = s + 5*s - 18. Suppose -2*d + s*d + 0*d = 0. Factor d - 2/9*f + 2/9*f**3 + 0*f**2.
2*f*(f - 1)*(f + 1)/9
Let s(x) = 9*x**3 + 133*x**2 + 38*x - 8. Let p(f) = 46*f**3 + 664*f**2 + 190*f - 44. Let a(o) = 6*p(o) - 33*s(o). Factor a(l).
-3*l*(l + 19)*(7*l + 2)
Let w(d) be the third derivative of 0*d + 0 - 9*d**2 - 1/450*d**5 + 1/180*d**4 + 0*d**3. Factor w(l).
-2*l*(l - 1)/15
Let a(d) be the third derivative of d**8/784 - d**7/98 - d**6/35 + 3*d**5/35 - 2*d**2 - 33. Suppose a(p) = 0. Calculate p.
-2, 0, 1, 6
Let p(v) be the first derivative of v**6/120 + 3*v**5/20 - 7*v**4/8 - 22*v**3/3 - 15. Let m(a) be the third derivative of p(a). What is g in m(g) = 0?
-7, 1
Let s = -28 + 16. Let a = s - -26. Let 6 - a*g**2 - 12*g**2 - 2*g**2 + g**2 + 15*g + 21*g**4 - 15*g**3 = 0. What is g?
-1, -2/7, 1
Suppose 0 = -4*c - 0*c + 5*t + 24, 2*t - 24 = -4*c. Suppose -9*o = -0*o - c*o. Factor 2*y**2 + 0*y + o - 2/3*y**3.
-2*y**2*(y - 3)/3
Let j(c) be the first derivative of -3*c**4/4 - 6*c**3 - 15*c**2/2 - 675. Factor j(k).
-3*k*(k + 1)*(k + 5)
Let n(m) = m**3 - 83*m**2 + 161*m + 83. Let x be n(81). Factor 3*r**4 - 3*r**x - 5/2*r + 0 + 2*r**3 + 1/2*r**5.
r*(r - 1)*(r + 1)**2*(r + 5)/2
Suppose 33*j - 40*j = -12*j + 15. What is k in 4/9*k**4 + 0 + 8/9*k**2 + 0*k - 4/3*k**j = 0?
0, 1, 2
Let y be (3/(-2))/(36/(-96)). Factor y*u**4 - u**5 - u**5 - 2*u**2 + 4*u**2 + 2*u**3 - 6*u**4.
-2*u**2*(u - 1)*(u + 1)**2
Let a(w) be the third derivative of -w**5/210 - 16*w**4/21 - 1024*w**3/21 + 118*w**2. Let a(m) = 0. What is m?
-32
Let f be (-194)/(-22) + 26/143. Factor -h + 3*h + 8 - 6*h**2 - h - f*h.
-2*(h + 2)*(3*h - 2)
Let l(s) = -40*s - 38. Let j be l(-1). Let a(i) be the first derivative of 5/6*i**4 + 0*i + 8/15*i**5 + 0*i**j + 4/9*i**3 + 1/9*i**6 + 3. Factor a(y).
2*y**2*(y + 1)**2*(y + 2)/3
Let k = -6/577 - -1292/13271. Factor -2/23*c**5 + 0 + 0*c**2 + 0*c**4 + 4/23*c**3 - k*c.
-2*c*(c - 1)**2*(c + 1)**2/23
Let l = -4/141 + 149/282. Let y(f) be the first derivative of l*f**4 + 0*f + 14/45*f**5 + 4 + 0*f**2 + 4/27*f**3. Determine v so that y(v) = 0.
-1, -2/7, 0
Let r(c) = -3*c**3 - 192*c - 10*c**3 + 204*c + c**2. Let h(g) = 3*g**3 - 3*g. Let z(d) = 9*h(d) + 2*r(d). Let z(l) = 0. Calculate l.
-3, 0, 1
Let c(k) = -k**2 - 8*k + 10. Let i(b) = 6*b + 15. Let m be i(-4). Let v be c(m). Find g, given that -v + 3/2*g - 1/2*g**2 = 0.
1, 2
Suppose 4*u = -20, 2*u + 14 = n - 0*n. Let o be 1 - (-6)/(-15)*10/n. Factor 2/3*d**2 - 1/3*d**4 + 0*d + o - 1/3*d**3.
-d**2*(d - 1)*(d + 2)/3
Let m be (-112)/(-168) - (-3 + 26/12). Factor -m - k + 1/2*k**2.
(k - 3)*(k + 1)/2
Let o(b) be the first derivative of 34*b**3/15 - 11*b**2/5 - 12*b/5 + 141. Factor o(p).
2*(p - 1)*(17*p + 6)/5
Let j(w) be the second derivative of 32/15*w**6 + 4/5*w**5 + 2*w + 2/3*w**7 + 0 - 14/3*w**4 - 22/3*w**3 - 4*w**2. Solve j(n) = 0 for n.
-1, -2/7, 1
Find s such that 3/5*s**4 - 6/5*s**2 + 11/5*s**3 + 0 - 8/5*s = 0.
-4, -2/3, 0, 1
Let o be (-636)/30 - 1/(5/4). Let t = -20 - o. Find p such that -8/7*p + 8/7 + 2/7*p**t = 0.
2
Let j(s) be the first derivative of 2*s**5/45 - 7*s**4/18 - 2*s**3/9 + 55*s**2/9 + 100*s/9 + 957. Factor j(w).
2*(w - 5)**2*(w + 1)*(w + 2)/9
Let i(a) = -2*a**4 - 264*a**3 + 8448*a**2 + 17692*a + 8978. Let c(b) = 3*b**4 + 264*b**3 - 8449*b**2 - 17693*b - 8978. Let r(q) = -4*c(q) - 5*i(q). Factor r(z).
-2*(z - 67)**2*(z + 1)**2
Suppose 5*o - 8 = o. Let l(m) = -2*m**3 + 2*m**2 - m - 3. Let g be l(-1). What is k in 3*k + 4*k**g - o*k - 5*k = 0?
0, 1
Suppose 13*z + 6*z = 9*z. Let m(j) be the second derivative of 1/12*j**3 + 1/48*j**4 + z + 3*j + 0*j**2. Factor m(a).
a*(a + 2)/4
Suppose -4*v = 3*x - 28, 16*x + 2*v = 12*x + 24. Suppose -2/3*j**2 + 4/9 - 2/9*j**3 + 2/9*j + 2/9*j**x = 0. Calculate j.
-1, 1, 2
Let f(j) be the first derivative of -j**7/280 + j**5/10 + 8*j**3/3 - 3*j + 16. Let u(q) be the third derivative of f(q). What is d in u(d) = 0?
-2, 0, 2
Let y(q) be the first derivative of -q**5/15 + q**4 - 16*q**3/3 + 7*q**2/2 - 28. Let c(f) be the second derivative of y(f). Find v, given that c(v) = 0.
2, 4
Factor -1/6*j**5 - 61/6*j**3 + 0 - 6*j + 14*j**2 + 7/3*j**4.
-j*(j - 6)**2*(j - 1)**2/6
Let w(y) be the first derivative of 5 + 1/27*y**3 + 1/108*y**4 + 0*y - 1/540*y**6 - 2*y**2 - 1/270*y**5. Let t(h) be the second derivative of w(h). Factor t(i).
-2*(i - 1)*(i + 1)**2/9
Let b(z) be the third derivative of z**8/33600 + z**7/3150 - 11*z**4/6 + 3*z**2. Let r(p) be the second derivative of b(p). Factor r(o).
o**2*(o + 4)/5
Let b(w) be the third derivative of 0*w**3 + 1/10*w**5 + 0*w + 31*w**2 - 1/40*w**6 + 0*w**4 + 0. Factor b(j).
-3*j**2*(j - 2)
Let x(g) = 3*g**4 + 12*g**3 + 3*g**2 - 32*g - 18. Let j(p) = 14*p**4 + 49*p**3 + 12*p**2 - 130*p - 71. Let i(q) = 2*j(q) - 9*x(q). Let i(h) = 0. What is h?
-1, 2, 10
Let o(x) be the first derivative of 2*x**5/5 - 19*x**4 + 214*x**3 + 760*x**2 + 800*x + 39. Factor o(v).
2*(v - 20)**2*(v + 1)**2
Factor -2/3*l**3 + 50*l**2 + 0*l + 0.
-2*l**2*(l - 75)/3
Let z = -19 + 15. Let m(v) = v**4 - 4*v**3 + 3*v**2 + 4*v + 4. Let s(c) = -2*c**4 + 4*c**3 - 4*c**2 - 5*c - 5. Let d(a) = z*s(a) - 5*m(a). Factor d(o).
o**2*(o + 1)*(3*o + 1)
Let m = -32 + 34. Factor -14*a**2 - 2*a**3 + 34*a**m - 4*a**3 + a**3 + 25*a.
-5*a*(a - 5)*(a + 1)
Let b(k) = 8*k**2 + 41*k + 15. Let t(m) = 23*m**2 + 122*m + 45. Let f(u) = 17*b(u) - 6*t(u). Let d be f(-17). Let 8/11 - 8/11*y + 2/11*y**d = 0. What is y?
2
Suppose -3*b - 8 = -5*b. Suppose -t = 2*j + 3*j + 19, -4*j - 20 = -b*t. Factor 4*d + d**2 + 0*d**2 + t - 2*d.
(d + 1)**2
Determine j so that -624*j - 90 + 25*j**2 - j**2 - 84*j**4 + 40 + 844*j**3 - 142 + 32 = 0.
-2/3, -2/7, 1, 10
Let y(o) be the first derivative of 3/7*o**4 + 2/35*o**5 + 10/7*o**2 + 17 + 6/7*o + 8/7*o**3. Let y(j) = 0. Calculate j.
-3, -1
Let g(r) be the second derivative of 17*r - 3/8*r**5 + 5/4*r**3 + 65/72*r**4 - 11/36*r**6 - 5/6*r**2 + 0. Suppose g(a) = 0. Calculate a.
-1, 2/11, 1
Let u(k) be the second derivative of k**5/4 - 235*k**4/12 - 5*k**3/6 + 235*k**2/2 - 182*k - 1. Factor u(q).
5*(q - 47)*(q - 1)*(q + 1)
Suppose c = 5*p - 15, -25 = 6*p - 11*p - c. Let t(x) be the third derivative of 0*x - 1/120*x**5 - 6*x**2 + 0 + 0*x**p + 1/3*x**3. Solve t(n) = 0.
-2, 2
Let z = -18 + 20. Suppose 3 = s - u - 1, -z*s + u = -13. Suppose -5*n**4 - 3*n**4 + 29*n**3 - 13*n**3 + 8*n**2 - 4*n - 3*n**