
-2*w**2*(w - 1)**3/3
Let r be 1/(-4)*-2*2. Let z be ((-6)/(-4))/(r/2). Solve z - 2*a**3 + a**4 - 3 + a**2 = 0 for a.
0, 1
Let c = 59/30 - 11/6. Let k(j) be the first derivative of -1/5*j + c*j**3 - 2 + 1/10*j**2. Factor k(t).
(t + 1)*(2*t - 1)/5
Let x be -6*(-3 - 72/(-27)). What is b in 2/7*b**3 - 2/7 + 2/7*b**x - 2/7*b = 0?
-1, 1
Let g(t) = 4*t - 38. Let m be g(10). Solve 0*b + 1/4*b**3 + 0 + 0*b**m + 1/4*b**5 + 1/2*b**4 = 0.
-1, 0
Let k be (0*(-4)/24)/(-5). Solve 0*m**2 + 0*m**3 + 1/3*m**4 + 1/3*m**5 + 0*m + k = 0.
-1, 0
Let a be (1 + -1)*(3/2 + -1). Let y(v) be the first derivative of -3 - 1/8*v**4 - 1/4*v**2 + a*v - 1/3*v**3. Factor y(c).
-c*(c + 1)**2/2
Let n = -665/4 - -167. Factor 0*u - n*u**3 - 1/4*u**5 + 0 - 1/4*u**2 - 3/4*u**4.
-u**2*(u + 1)**3/4
Let f(r) = -r**2 + 6*r - 1. Let z be f(5). Let v(h) = 6*h**2 - 5*h - 1. Let t(p) = -5*p**2 + 4*p + 1. Let o(g) = z*v(g) + 5*t(g). Find n, given that o(n) = 0.
-1, 1
Let l(v) be the first derivative of -2*v**3/3 + v**2/7 - 27. Factor l(r).
-2*r*(7*r - 1)/7
Let h(m) be the first derivative of 3*m**5/10 + 3*m**4/4 + 4. Factor h(u).
3*u**3*(u + 2)/2
Let m(o) be the first derivative of -o**6/180 - o**5/60 + o**4/6 - 2*o**3/3 + 2. Let a(r) be the third derivative of m(r). Factor a(d).
-2*(d - 1)*(d + 2)
Factor -9/4*f - 3/2 - 3/4*f**2.
-3*(f + 1)*(f + 2)/4
Let i(j) = -835*j**3 + 2245*j**2 - 890*j + 155. Let g(d) = -76*d**3 + 204*d**2 - 81*d + 14. Let a(b) = -45*g(b) + 4*i(b). Suppose a(w) = 0. Calculate w.
1/4, 2
Suppose 104 = -4*p - 0*p. Let x = p + 29. Solve 0 - 2/5*t**5 + 0*t + 0*t**2 - 2/5*t**4 + 0*t**x = 0 for t.
-1, 0
Let g(z) be the third derivative of z**7/315 - z**6/45 - z**5/45 + z**4/3 + z**3 - 6*z**2. What is l in g(l) = 0?
-1, 3
Suppose 2*c + j - 15 = 0, -3*j = -4*j + 1. Suppose -6*h + c*h - 4 = 0. Factor 4/3*o**3 + 4/3 - 4/3*o - 1/3*o**h - o**2.
-(o - 2)**2*(o - 1)*(o + 1)/3
Let h(k) be the first derivative of 0*k - 4/3*k**3 + 6*k**2 - 3*k**4 + 2 + 4/5*k**5. Suppose h(i) = 0. Calculate i.
-1, 0, 1, 3
Let w(s) be the first derivative of 2*s**2 + 0*s - 2/3*s**6 + 0*s**4 + 4 - 8/5*s**5 + 8/3*s**3. Factor w(i).
-4*i*(i - 1)*(i + 1)**3
Let g(w) = 5*w. Let r(q) = -q**2 + 4*q. Let l be (2/4)/((-4)/(-40)). Suppose h + l*b = 9, -3*b + 1 = -h + 2*b. Let o(s) = h*r(s) - 3*g(s). Factor o(v).
-v*(4*v - 1)
Let t(v) be the third derivative of v**9/90720 - v**8/15120 + v**7/7560 - v**5/60 + v**2. Let p(h) be the third derivative of t(h). Find u, given that p(u) = 0.
0, 1
Let i(r) be the second derivative of 5*r**7/42 + 2*r**6/3 + r**5 - 5*r**4/6 - 25*r**3/6 - 5*r**2 + 2*r. Factor i(p).
5*(p - 1)*(p + 1)**3*(p + 2)
Let r(a) be the third derivative of -a**8/504 + a**7/63 - a**6/60 - a**5/10 + a**2. Factor r(h).
-2*h**2*(h - 3)**2*(h + 1)/3
Factor -26/5*w - 169/5 - 1/5*w**2.
-(w + 13)**2/5
Let h be (3/(-2) + -1)*2. Let s(n) = n**2 + 3*n - 5. Let g be s(h). What is a in -a**g - 4*a - a + 4*a + 2*a**3 = 0?
-1, 0, 1
Let y(l) be the first derivative of -2/3*l**3 + 4 + 0*l + 1/2*l**2 - 1/4*l**4 + 2/5*l**5. What is g in y(g) = 0?
-1, 0, 1/2, 1
Let g(u) be the first derivative of -2*u**2 + 5*u**2 + 0*u**2 - 3*u + 2 - u**3. What is m in g(m) = 0?
1
Let t(k) be the third derivative of 9*k**3 + 0*k + 11/5*k**5 - 10*k**2 + 0 - 75/8*k**4 - 7/40*k**6. Solve t(s) = 0.
2/7, 3
Solve 2/7*o**3 + 2/7*o**2 - 2/7 - 2/7*o = 0.
-1, 1
Factor -6/7*o**2 - 2/7*o**3 + 2/7*o + 6/7.
-2*(o - 1)*(o + 1)*(o + 3)/7
Let d = 15 - 12. Let y be d*((-10)/4 - -3). Determine o, given that o + y*o**2 + o**3 + 1/4 + 1/4*o**4 = 0.
-1
Let p(h) be the third derivative of h**6/2160 + h**5/240 + h**4/72 + h**3/2 + h**2. Let o(x) be the first derivative of p(x). Suppose o(u) = 0. What is u?
-2, -1
Suppose -4*m + 4 = -12. Let r(n) be the second derivative of 1/15*n**5 + 1/18*n**m + 1/45*n**6 + 0 - 2*n + 0*n**3 + 0*n**2. Factor r(o).
2*o**2*(o + 1)**2/3
Let s(w) be the second derivative of 0 + 10*w + 0*w**2 + 1/84*w**4 + 1/42*w**3. Factor s(i).
i*(i + 1)/7
Let l(w) be the first derivative of -w**5/50 + w**4/20 - w**2/10 + 4*w - 4. Let p(x) be the first derivative of l(x). Suppose p(t) = 0. What is t?
-1/2, 1
Let l(i) be the first derivative of i**5/10 + 3*i**4/8 - i**3/3 - 3*i**2 - 4*i + 24. Factor l(k).
(k - 2)*(k + 1)*(k + 2)**2/2
Let t(r) be the third derivative of r**7/630 + r**6/60 - 11*r**5/180 - 5*r**4/6 + 50*r**3/9 - 10*r**2. Factor t(c).
(c - 2)**2*(c + 5)**2/3
Let u(l) = -2*l - 8. Let d be u(-7). Let t be (-3)/d - 6/(-4). Let t + 3 - 24*m**2 + 16*m**3 + 9*m - 5 = 0. What is m?
1/4, 1
Let z = 4713/80 + 23/80. Let u = z + -59. Factor -2/5 + u*o**2 - 1/5*o.
(o - 2)*(o + 1)/5
Let o(p) be the first derivative of -1/6*p**4 + 0*p + 4/9*p**3 + 1/9*p**6 - 4/15*p**5 + 0*p**2 + 2. Let o(z) = 0. What is z?
-1, 0, 1, 2
Let p(j) = -6*j**3 - 9*j**2 - 6*j + 21. Let w(z) = -z**3 - 2*z**2 - z + 4. Let h(k) = 4*p(k) - 21*w(k). Suppose h(v) = 0. What is v?
0, 1
Let t be -1*(-3 + 2) - -15. Factor 7*c**5 + 7*c**5 + t*c**4 - 7*c**5 + 4*c**3.
c**3*(c + 2)*(7*c + 2)
Let l(h) be the third derivative of -h**5/36 - 5*h**4/72 - 7*h**2. Factor l(u).
-5*u*(u + 1)/3
Let i(l) = -5*l**5 - l**4 - 4*l**3 + 4*l**2 - 4*l - 4. Let h(j) = j**5 + j**3 - j**2 + j + 1. Let f = 2 + -1. Let y(g) = f*i(g) + 4*h(g). Factor y(t).
-t**4*(t + 1)
Let m = 14 - 11. Factor 0*f - 1/4*f**4 - 1/4*f**2 + 0 - 1/2*f**m.
-f**2*(f + 1)**2/4
Let i be 132/180 - (-6)/10. Factor 2/9*s**2 - i*s + 2.
2*(s - 3)**2/9
Let t(f) be the third derivative of -f**6/1620 + f**3/2 + 5*f**2. Let z(u) be the first derivative of t(u). Factor z(n).
-2*n**2/9
Let w(l) be the first derivative of -l**6/39 + 14*l**5/65 - 11*l**4/26 + 10*l**3/39 - 36. Let w(g) = 0. What is g?
0, 1, 5
Let u = -352/3 - -118. Factor u*h**2 + 0 + 0*h.
2*h**2/3
Let c(z) = z**2 - 13*z - 26. Let s be c(18). Let p = -190/3 + s. Factor -2/3*r + p*r**3 + 0 - 2/3*r**4 + 2/3*r**2.
-2*r*(r - 1)**2*(r + 1)/3
Suppose 0 = -t, 3*n = 8*n - 5*t - 15. Let s be ((-2)/n)/((-7)/14). Solve -u**5 - 2/3*u**4 + 2*u**3 - u - 2/3 + s*u**2 = 0.
-1, -2/3, 1
What is a in -a**4 - 3*a**5 - 2*a**2 - 2*a**4 + 3*a**3 + 5*a**2 = 0?
-1, 0, 1
Let m be 6*(-1 + 4/3). Let r be 3/(((-48)/(-20))/4). Factor 8*y**2 + r*y**4 - 10*y**3 + 1 + y**5 - m*y**5 - 5*y + 2*y**2.
-(y - 1)**5
Let r(i) be the first derivative of i**7/420 - i**6/90 + i**5/60 + 5*i**3/3 + 3. Let m(w) be the third derivative of r(w). Let m(k) = 0. What is k?
0, 1
Let x(t) = -32*t**3 - 37*t**2 + 2*t + 3. Let y(z) = -63*z**3 - 75*z**2 + 3*z + 6. Let j(r) = 9*x(r) - 4*y(r). Factor j(c).
-3*(c + 1)*(3*c - 1)*(4*c + 1)
Let f(o) be the second derivative of o**5/4 - 5*o**4/6 + 5*o**3/6 - 24*o. What is g in f(g) = 0?
0, 1
Let k be 2/9*(-84)/(-4). Solve -k*x**3 + 14/3*x + 4/3*x**2 - 4/3 = 0.
-1, 2/7, 1
Solve -3/7*v**2 + 0 - 3/7*v**3 + 0*v = 0.
-1, 0
Suppose -8*d = -155 + 139. Factor 8/13 + 8/13*x + 2/13*x**d.
2*(x + 2)**2/13
Factor 1/5*d**3 + 1/5*d**2 - 1/5*d**5 - 1/5*d**4 + 0*d + 0.
-d**2*(d - 1)*(d + 1)**2/5
Let n(v) be the first derivative of 0*v - 2 + 0*v**2 - 4/15*v**3 + 1/10*v**4. Factor n(k).
2*k**2*(k - 2)/5
Let u be 1/(-3) + (-14)/(-6). Let b = u + 2. Determine i, given that -b*i**2 + 2*i**2 + i**2 = 0.
0
Let o(p) = -p**2 - p. Let j(f) = -12*f**2 - 18*f - 8. Let m(h) = 2*j(h) - 20*o(h). Factor m(u).
-4*(u + 2)**2
Let y(a) be the second derivative of 0 + 4*a + 1/9*a**4 + 1/30*a**5 + 0*a**2 + 0*a**3. Find x, given that y(x) = 0.
-2, 0
Let l(n) be the second derivative of 0 - 3*n**2 + 2/3*n**3 + 1/6*n**4 - 6*n. Factor l(y).
2*(y - 1)*(y + 3)
Let x(q) = 2*q**2 + 7*q - 8. Let m be x(6). Factor 2*w**2 + 52*w**2 + w**4 - m*w - 2*w - 15*w**3 + 3*w**3 + 81.
(w - 3)**4
Let c(z) be the first derivative of z**5 + 5*z**4/2 - 5*z**3/3 - 5*z**2 - 11. Let c(b) = 0. What is b?
-2, -1, 0, 1
Let g(w) = -26*w**2 + 156*w. Let c be g(6). Factor 3/4 - 3/2*o - 3/4*o**4 + 3/2*o**3 + c*o**2.
-3*(o - 1)**3*(o + 1)/4
Let z(q) = -7*q**2 - 3*q + 4. Let a(d) = -d**2 + 1. Let m(x) = -4*a(x) + z(x). Factor m(w).
-3*w*(w + 1)
Let z(j) be the first derivative of j**7/3360 + j**6/1440 - j**3/3 + 2. Let w(n) be the third derivative of z(n). Let w(s) = 0. Calculate s.
-1, 0
Let n(l) be the second derivative of 5*l**4/12 - 5*l**3/6 - 13*l. Solve n(w) = 0.
0, 1
Let q(j) be the second derivative of 8*j**6/285 - 17*j**5/95 + 13*j**4/38 - 4*j**3/57 - 4*j**2/19 