- s(j). Determine r, given that t(r) = 0.
-1, 0, 2
Let q(g) be the third derivative of -g**7/770 - g**6/165 - g**5/110 + g**3/66 + 13*g**2. Factor q(l).
-(l + 1)**3*(3*l - 1)/11
Let m(n) be the first derivative of n**4/7 - 4*n**3/21 + 29. Determine u so that m(u) = 0.
0, 1
Let y(m) = 6*m**2 + 6*m - 12. Let c(f) = -3*f**2 - 3*f + 6. Let h(k) = -9*c(k) - 5*y(k). Find x such that h(x) = 0.
-2, 1
Suppose -9 - 7 = 2*y. Let r(p) = -9 + 22*p**2 + 1 - 4*p - 8*p. Let m(u) = 7*u**2 - 4*u - 3. Let v(x) = y*m(x) + 3*r(x). Factor v(j).
2*j*(5*j - 2)
Let o be ((-60)/35)/((-25)/7). Let u = 14/75 + o. Find h, given that -4/3 + u*h**2 - 2/3*h = 0.
-1, 2
Let c be ((-31)/7)/(-1) + -1. Let p = -9 + 9. Factor 0 + 10/7*r**5 + p*r + 4/7*r**2 + 18/7*r**3 + c*r**4.
2*r**2*(r + 1)**2*(5*r + 2)/7
Let w(j) be the third derivative of -j**8/60480 - j**7/7560 - j**6/2160 + j**5/30 + 2*j**2. Let i(l) be the third derivative of w(l). Factor i(u).
-(u + 1)**2/3
Let v(u) be the second derivative of 9*u**5/20 + u**4/2 - u**3/2 + 10*u. Suppose v(f) = 0. Calculate f.
-1, 0, 1/3
Let a(u) be the third derivative of u**8/3360 - u**7/315 + u**6/90 + u**4/6 - u**2. Let m(f) be the second derivative of a(f). Factor m(i).
2*i*(i - 2)**2
Suppose v + 3*v = 4*p - 48, -3*v + 5*p - 44 = 0. Let l(g) = -g - 7. Let i be l(v). Find n such that i - 3*n**2 + 6*n**2 - 4*n**2 = 0.
-1, 1
Factor -24*j + 12*j + j**2 + 14*j.
j*(j + 2)
Let y(q) be the first derivative of -3*q**4/4 + q**3/3 - 2*q**2 + 2. Let p(o) = o**3 + o**2 + o. Let z(s) = -4*p(s) - 2*y(s). Find w such that z(w) = 0.
0, 1, 2
Let a be (45/54 - 1) + 199/42. Factor -2/7*x**2 + 16/7*x - a.
-2*(x - 4)**2/7
Let b = -1/6 + 17/6. Suppose -10*n**2 + 8/3*n + b = 0. What is n?
-2/5, 2/3
Let w(c) be the second derivative of -c**4/60 - c**3/15 + 7*c. Factor w(y).
-y*(y + 2)/5
Suppose -c - 2 + 8 = 0. Suppose 3*f**3 - 2*f - c*f**2 + 0*f + 2*f = 0. What is f?
0, 2
Suppose 2*p + 9 = 2*u + 5, 0 = -4*u - 5*p + 8. Factor 0*l**3 - 4/5*l + 0 + 2/5*l**4 - 6/5*l**u.
2*l*(l - 2)*(l + 1)**2/5
Let f(y) be the second derivative of -y**6/1080 + y**5/360 + y**3/3 - y. Let t(z) be the second derivative of f(z). Suppose t(s) = 0. Calculate s.
0, 1
Suppose -p + 12 = 3*v + v, 2*p = 5*v - 15. Find r such that p*r + r**2 - 3 + 3 - 2*r = 0.
0, 2
Suppose s - 2*c = -2*s + 4, 2*c - 12 = -5*s. Let m be 1*((-2)/s + 1). Factor m*b - 1/4*b**2 + 1/4*b**3 + 0.
b**2*(b - 1)/4
Let u = -17 - -25. Let c(o) be the third derivative of -1/1008*o**u - 1/45*o**5 + 0 + 0*o - 1/72*o**4 + 2*o**2 + 0*o**3 - 2/315*o**7 - 1/60*o**6. Factor c(j).
-j*(j + 1)**4/3
Let q(x) be the second derivative of x**6/120 - x**5/80 - x**4/48 + x**3/24 + 4*x. Suppose q(h) = 0. Calculate h.
-1, 0, 1
Let w be (-16)/(-10)*5/2. Let 0 + 5/3*a**w - 4*a**2 - a**3 - 4/3*a = 0. Calculate a.
-1, -2/5, 0, 2
Let 4*m**2 + 7*m**2 - 2*m**2 - 3*m**4 - 6 - 3*m**3 + 3*m = 0. Calculate m.
-2, -1, 1
Let u = -991/35 - -201/7. Find l such that u*l**2 + 0 - 2/5*l = 0.
0, 1
Let t = -261/2 - -133. Let m = t - 2. Factor -1/2*i**2 + 1/2 - 1/2*i + m*i**3.
(i - 1)**2*(i + 1)/2
Let l(f) be the first derivative of -1/6*f**3 - f**2 - 2 + 0*f**4 + 1/60*f**5 + 0*f. Let u(a) be the second derivative of l(a). Solve u(j) = 0.
-1, 1
Factor 1/3*k**2 + 3 - 2*k.
(k - 3)**2/3
Find c, given that -16/23*c + 0 + 10/23*c**4 - 8/23*c**2 + 2/23*c**5 + 12/23*c**3 = 0.
-2, 0, 1
Let l(s) be the first derivative of s**8/1008 - s**7/630 - s**6/360 + s**5/180 + s**2 + 2. Let y(u) be the second derivative of l(u). Factor y(d).
d**2*(d - 1)**2*(d + 1)/3
Let l(k) = -3*k**2 + 22*k - 7. Let n be l(7). Let x(m) be the first derivative of n*m + 2/9*m**3 + 1/3*m**2 - 3. Factor x(i).
2*i*(i + 1)/3
Let f(v) be the second derivative of -15*v**7/28 + 11*v**6/8 - v**5/8 - 145*v**4/48 + 25*v**3/6 - 5*v**2/2 + 3*v. Determine i so that f(i) = 0.
-1, 1/2, 2/3, 1
Let a = 1 - -6. Let s be ((-2)/(-8))/(a/21). Factor -s*u + 3/2*u**2 - 3/4.
3*(u - 1)*(2*u + 1)/4
Let m(t) = t**3 - 7*t**2 + 8*t - 9. Let u be m(6). Suppose d - u*a = -7 + 1, 4*d - 3*a + 6 = 0. What is p in -2/5*p**3 + d*p**2 + 0*p + 0 = 0?
0
Let k be (38/57)/(4/30). Let i(f) be the second derivative of 0 + 1/20*f**k + 0*f**3 - 3*f + 1/12*f**4 + 0*f**2. Factor i(n).
n**2*(n + 1)
Let t = -15 + 35. Let h be 0 - (32/t + -2). What is v in 0 + 4/5*v**2 - h*v**3 + 0*v = 0?
0, 2
Determine d so that 3*d**3 + 4*d**2 + 15*d - 7*d**2 - 6 - 2*d**2 - 7*d**2 = 0.
1, 2
Let h(s) = s + 6. Let g be h(-6). Suppose -3 + 29 = 2*z. Let -16 - 2*k**3 + g*k**3 - 14*k + 3*k - 12*k**2 - z*k = 0. What is k?
-2
Let s = 39 + -155/4. Factor 1/2 - 5/4*r - s*r**3 + r**2.
-(r - 2)*(r - 1)**2/4
Determine s so that 1/2*s - 3/4*s**2 + 0 + 1/4*s**3 = 0.
0, 1, 2
Solve -3/5*o**3 + 0*o + 1/5*o**2 + 3/5*o**4 - 1/5*o**5 + 0 = 0 for o.
0, 1
Find t, given that -10/17*t**3 + 2/17*t**4 + 0 + 10/17*t - 2/17*t**2 = 0.
-1, 0, 1, 5
Let o = 4/158883 + -21769259/90881076. Let w = -3/52 - o. Factor w + 6/11*z + 2/11*z**3 + 6/11*z**2.
2*(z + 1)**3/11
Let s(t) be the first derivative of -t + 1 - 5/2*t**2 - 49/20*t**5 + 35/8*t**4 + 1/4*t**3. Factor s(k).
-(k - 1)**2*(7*k + 2)**2/4
Let l(k) = -2*k - 12. Let p be l(-6). Suppose p = -11*u + 13*u - 8. Suppose -21/2*y + 3/2*y**5 - 3*y**3 + 3*y**u - 12*y**2 - 3 = 0. Calculate y.
-1, 2
Let o(w) be the third derivative of -1/12*w**4 + 0*w**3 + 2/15*w**5 + 3*w**2 - 1/48*w**6 - 1/60*w**7 + 0*w + 0. Factor o(p).
-p*(p - 1)*(p + 2)*(7*p - 2)/2
Let q(r) = r**2 - 8*r - 7. Let t be q(9). Let w(n) be the third derivative of 0 - 1/180*n**6 - n**t + 0*n**4 + 0*n**3 + 0*n**5 + 0*n. Find s such that w(s) = 0.
0
Solve -147*g + 2 + g**2 + 73*g + 77*g = 0 for g.
-2, -1
Factor 1/3*v + 0 - v**3 - 2/3*v**2.
-v*(v + 1)*(3*v - 1)/3
Suppose -4*g = -2*g - 5*m + 33, 0 = -m + 5. Let l be g/(-12)*(1 + -1). Factor l + 1/5*k - 1/5*k**2.
-k*(k - 1)/5
Let o(p) be the third derivative of -7*p**2 - 1/52*p**4 + 0*p**5 + 0*p + 0 + 2/39*p**3 + 1/780*p**6. Determine u, given that o(u) = 0.
-2, 1
Let y(k) be the second derivative of -k**4/30 - 2*k**3/5 + 8*k. Solve y(f) = 0.
-6, 0
Let m(q) be the second derivative of 1/40*q**5 - 8*q - 1/60*q**6 + 1/24*q**4 - 1/12*q**3 + 0 + 0*q**2. Determine h, given that m(h) = 0.
-1, 0, 1
Let r = 23 + -23. Let x(y) be the second derivative of 4/15*y**6 + 0*y**2 + r - 3/5*y**5 - 1/3*y**3 - 1/21*y**7 + 2/3*y**4 - y. Factor x(v).
-2*v*(v - 1)**4
Suppose -4 = -5*d + 6. Let g(a) = -6*a**3 - a**2 + 6*a + 3. Let n(f) = -f**3 + f + 1. Let r(b) = d*n(b) - g(b). Solve r(y) = 0 for y.
-1, -1/4, 1
Let a(q) be the first derivative of q**4/2 - 4*q**3/3 - 3*q**2 - 12. Find d, given that a(d) = 0.
-1, 0, 3
Factor -3/7 + 0*f**2 - 6/7*f**3 + 6/7*f + 3/7*f**4.
3*(f - 1)**3*(f + 1)/7
Suppose -2 = i - 4*u + 12, 0 = -4*u + 16. Factor -4/3*j**3 + 2*j**4 - 2/3*j**5 - 4/3*j**i - 2/3 + 2*j.
-2*(j - 1)**4*(j + 1)/3
Let b(y) be the second derivative of -y**7/840 - y**6/480 + y**5/240 + y**4/96 + y**2/2 - 4*y. Let g(s) be the first derivative of b(s). What is x in g(x) = 0?
-1, 0, 1
Let n(r) be the first derivative of r**7/210 + r**6/120 - r**2 + 1. Let l(s) be the second derivative of n(s). Suppose l(k) = 0. What is k?
-1, 0
Let t(h) be the first derivative of 4*h**3/21 + 4*h**2/7 + 4*h/7 + 20. What is p in t(p) = 0?
-1
Let w(f) be the second derivative of -f**6/12 + 5*f**4/8 + 5*f**3/6 - 25*f. Suppose w(t) = 0. What is t?
-1, 0, 2
Let j be 6/(-35)*(-10)/4. Let i(g) be the first derivative of j*g**2 + 0*g**3 - 1/14*g**4 - 2 - 4/7*g. Factor i(k).
-2*(k - 1)**2*(k + 2)/7
Let y(z) be the second derivative of -9*z**4/16 + 7*z**3/8 + 3*z**2/4 - 2*z. Suppose y(v) = 0. Calculate v.
-2/9, 1
Let x be 12/5*(-4920)/(-252). Let b = x + -46. Find m such that -4*m**5 + 0 + 32/7*m**3 + b*m**4 - 6/7*m**2 - 4/7*m = 0.
-1, -2/7, 0, 1/2, 1
Let v = 4/3 - 5/6. Let b(n) be the first derivative of 0*n - 2/3*n**3 + 0*n**2 - v*n**4 + 1. Factor b(i).
-2*i**2*(i + 1)
Suppose m - 5*z = -15, -2*m + 5*z - 3*z = -2. Let x(n) be the second derivative of 0*n**2 - 1/18*n**3 + n - 1/36*n**4 + 1/90*n**6 + 1/60*n**m + 0. Factor x(k).
k*(k - 1)*(k + 1)**2/3
Let r(b) = -3*b**4 - 13*b**3 + 15*b**2 + 13*b - 8. Let k(g) = 3*g**4 + 12*g**3 - 15*g**2 - 12*g + 9. Let f(w) = -4*k(w) - 3*r(w). Factor f(n).
-3*(n - 1)**2*(n + 1)*(n + 4)
Suppose -2*i - 2*g = -3*i + 213, -5*g + 639 = 3*i. Find f such that i*f**