 1
Let f(g) be the first derivative of 0*g - 1/2*g**4 + 2 + 4/3*g**3 - g**2. Factor f(d).
-2*d*(d - 1)**2
Let w(o) be the third derivative of o**6/1080 + o**5/108 + 11*o**2. Find a, given that w(a) = 0.
-5, 0
Let h(i) be the first derivative of i**4/12 + 8*i**3/27 + 2*i**2/9 + 15. Find u, given that h(u) = 0.
-2, -2/3, 0
Let s(v) = -v**3 - 8*v**2 - 7*v. Let t be s(-7). Let g = 14 - 14. Find m such that -1/3*m**4 - 1/3*m**5 + 0*m**3 + t + 0*m + g*m**2 = 0.
-1, 0
Let n(v) = 4*v**3 + v**2 - v - 1. Let p(b) = -b**3. Suppose 2*o + 11 = -1. Let h(w) = o*p(w) - 2*n(w). Solve h(k) = 0 for k.
-1, 1
Let j(n) = 6*n**3 - 36*n**2 + 21*n + 21. Let l(o) = -o**3 + 7*o**2 - 4*o - 4. Let f(d) = 4*j(d) + 21*l(d). What is b in f(b) = 0?
-1, 0
Let r(l) be the first derivative of 3/2*l**4 - 14/3*l**3 + 2 + 2*l**2 + 0*l. What is b in r(b) = 0?
0, 1/3, 2
Let p(b) be the first derivative of b**8/420 + b**7/70 - 2*b**5/15 - 2*b**3 + 7. Let f(d) be the third derivative of p(d). Solve f(x) = 0.
-2, 0, 1
Let y(x) be the first derivative of 2*x + 3 + 3/4*x**4 - 4/3*x**3 - 5/2*x**2. Factor y(v).
(v - 2)*(v + 1)*(3*v - 1)
What is y in -2/9*y**5 - 14/3*y + 2/3*y**4 - 20/9*y**2 - 2 + 4/3*y**3 = 0?
-1, 3
Let k = -4 - -4. Find r such that k + 2*r**3 + 18/7*r**2 + 4/7*r = 0.
-1, -2/7, 0
Let g(s) be the second derivative of s**6/30 + 3*s**5/20 + s**4/4 + s**3/6 - 14*s. Solve g(i) = 0 for i.
-1, 0
Let k(b) be the third derivative of 0*b + 0*b**3 + 1/40*b**6 + 3*b**2 - 1/20*b**5 + 0 - 1/4*b**4. What is t in k(t) = 0?
-1, 0, 2
Factor 0 - 6/5*r**4 + 2/5*r**5 - 2/5*r**2 + 6/5*r**3 + 0*r.
2*r**2*(r - 1)**3/5
Let r be (-1 - 18/(-6)) + (2 - 0). Find h, given that 0*h**3 + 1/7 - 2/7*h**2 + 0*h + 1/7*h**r = 0.
-1, 1
Let g be ((-14)/35)/((-2)/10). Determine n, given that 20*n**3 + 9*n**4 - n**2 + 3*n**2 + g*n**5 - 3*n**4 - 14*n**3 = 0.
-1, 0
Let a(k) = -k**4 + k**3 - k**2. Let s(l) = -7*l**4 - 5*l**3 - 13*l**2 - 3*l. Let j = 12 - 11. Let f(o) = j*s(o) - 4*a(o). Solve f(y) = 0 for y.
-1, 0
Let y(n) be the first derivative of n**5/20 + 5*n**4/12 + 4*n**3/3 + 2*n**2 + n - 3. Let g(r) be the first derivative of y(r). Determine c, given that g(c) = 0.
-2, -1
Factor 4/7 - 24/7*u + 20/7*u**2.
4*(u - 1)*(5*u - 1)/7
Let y be (-10)/(-4)*8/10. Suppose -2/9*j**y + 4/9*j + 0 = 0. What is j?
0, 2
Let k(o) be the second derivative of 1/2*o**3 + 3*o - 5/12*o**4 + o**2 + 0. Let k(c) = 0. Calculate c.
-2/5, 1
Let p(f) = 5*f**5 - f**4 - 6*f**3 + 11*f**2 - 11. Let m(b) = -3*b**5 + 3*b**3 - 6*b**2 + 6. Let v(w) = -11*m(w) - 6*p(w). Let v(l) = 0. What is l?
-1, 0
Let a(k) = -k**2 + 13*k - 27. Let y be a(10). Factor -1/2*t - 1/4 + 1/2*t**2 + 7/4*t**4 + 1/2*t**5 + 2*t**y.
(t + 1)**4*(2*t - 1)/4
Let f(d) = 6*d - 78. Let u be f(13). Let z(k) be the second derivative of -1/21*k**7 + 0 + 0*k**6 + 1/10*k**5 + 0*k**4 + u*k**3 + 0*k**2 + 3*k. Factor z(j).
-2*j**3*(j - 1)*(j + 1)
Let r(w) be the second derivative of 0 + 1/27*w**3 - 2/9*w**2 + 6*w + 1/54*w**4. Factor r(a).
2*(a - 1)*(a + 2)/9
Suppose -2 = -2*c + h, 4*h = c + 7 - 1. Factor -y**c + 10 - 2*y - 5 - 6.
-(y + 1)**2
Let v(f) = f**4 + f**3 + f**2 - f - 1. Let g(s) = 13*s**2 - 5 + 5*s**2 - 10*s - 18*s**3 + 4 + 7 - 4*s**4. Let o(k) = g(k) + 6*v(k). Factor o(h).
2*h*(h - 2)**3
Let v = -413 + 416. Let n = 2/13 - -35/26. Let -v - n*a**3 + 3/2*a + 3*a**2 = 0. Calculate a.
-1, 1, 2
Let o(b) be the third derivative of 0*b**3 + 0 - 4*b**2 + 0*b**4 + 0*b - 1/20*b**5. Find a, given that o(a) = 0.
0
Suppose 5 + 3 = 2*u. Let y(h) be the third derivative of 0*h**u + h**2 + 0 + 0*h**6 + 1/60*h**5 + 0*h**3 + 0*h - 1/210*h**7. Factor y(t).
-t**2*(t - 1)*(t + 1)
Let v(y) be the first derivative of -y**6/12 + y**4/4 - y**2/4 - 6. Find r, given that v(r) = 0.
-1, 0, 1
Let v be 5*(0 - -1 - 0). Factor -3 + 0*l**2 + v*l**2 + 12*l - 36*l**3 + l**2 - 27*l**4 + 0*l**2.
-3*(l + 1)**2*(3*l - 1)**2
Let t(w) = -676*w**5 + 1565*w**4 - 1113*w**3 + 245*w**2 - 16*w + 5. Let x(j) = j**4 - j**3 + j**2 + 1. Let n(i) = -t(i) + 5*x(i). Suppose n(v) = 0. What is v?
0, 2/13, 1
Let w(v) be the first derivative of 3/20*v**4 + 3/2*v**2 + 4 - 6/5*v - 4/5*v**3. Factor w(s).
3*(s - 2)*(s - 1)**2/5
Suppose -9 = -3*k - 0*k. Factor -k - 4*s + 1 + 9 - 5 + 2*s**2.
2*(s - 1)**2
Let d(u) = 3*u**4 + 4*u**3 + 2*u. Let m be (2/4)/(2/(-4)). Let s(r) = r**4 + r**3 + r. Let p(a) = m*d(a) + 2*s(a). Factor p(x).
-x**3*(x + 2)
Let t(a) be the first derivative of a**6/180 - a**5/60 - 2*a**3/3 - 2. Let d(h) be the third derivative of t(h). Solve d(p) = 0 for p.
0, 1
Suppose 2*k + 6 + 2/3*k**3 - 10/3*k**2 = 0. What is k?
-1, 3
Let k(o) be the third derivative of 1/108*o**4 + 1/540*o**6 - 1/135*o**5 + 4*o**2 + 0*o + 0 + 0*o**3. Factor k(v).
2*v*(v - 1)**2/9
Let d be (-1)/(-3)*3 - -4. Let h = -9/2 + d. Factor 1 - 1/2*g - h*g**2.
-(g - 1)*(g + 2)/2
Let j(h) = -8*h**4 + 27*h**3 - 20*h**2 + 5*h - 2. Let b(q) = 15*q**4 - 55*q**3 + 40*q**2 - 10*q + 5. Let i(g) = -2*b(g) - 5*j(g). Factor i(a).
5*a*(a - 1)**2*(2*a - 1)
Let h = -22 + 24. Let x(s) be the first derivative of 2/7*s**h - 1 - 2/7*s - 2/21*s**3. Factor x(i).
-2*(i - 1)**2/7
Let t(u) be the second derivative of -u**5/130 - u**4/39 - u**3/39 + 6*u. Find s, given that t(s) = 0.
-1, 0
Suppose 34*c - 42*c = -16. Factor 1/3*q**c - 1/3 + 0*q.
(q - 1)*(q + 1)/3
Let -47 - 4*y - 22*y**2 + 47 = 0. What is y?
-2/11, 0
Suppose 3*f - 68 = -5. Let a be ((-1)/f)/(2/(-12)). Solve -6/7*m + a*m**2 + 4/7 = 0.
1, 2
Let m(i) be the first derivative of i**5/5 + i**4 - 2*i**3 - 2*i**2 + 5*i + 9. Determine w so that m(w) = 0.
-5, -1, 1
Let i be 3 - 2 - 133/105. Let k = 23/30 + i. Factor 0*q - 1/2 + k*q**2.
(q - 1)*(q + 1)/2
Let i = -361 - -723/2. Let k be (-4)/(-10) - (-3)/(-20). Suppose 3/4*r**4 - k*r**5 + 3/4*r - 1/2*r**2 - 1/4 - i*r**3 = 0. What is r?
-1, 1
Let x(m) = -m + 5. Let g be x(3). Let -3*y + y - g*y**2 + 0*y**2 = 0. Calculate y.
-1, 0
Let s = -25 - -28. Let 2/9 - 2/9*r**2 + 2/9*r - 2/9*r**s = 0. Calculate r.
-1, 1
Let o(m) = -4*m**2 + 44*m + 11. Let y(d) = d**2 - 15*d - 4. Let g(q) = 6*o(q) + 17*y(q). What is k in g(k) = 0?
2/7, 1
Let u be (1 + -1)/((-2)/(-1 + 2)). Factor -2/13*m**3 + 4/13*m**2 + u*m + 0.
-2*m**2*(m - 2)/13
Let b = 4 + -2. Factor 0 + 4*a**3 + 0*a**2 - a**b + 1 - 4*a.
(a - 1)*(a + 1)*(4*a - 1)
Let q(f) be the second derivative of 0*f**3 - 1/105*f**6 - 3*f - 1/147*f**7 + 1/70*f**5 + 0 + 0*f**2 + 1/42*f**4. Factor q(w).
-2*w**2*(w - 1)*(w + 1)**2/7
Let j(d) be the second derivative of d**5/14 - 26*d**4/21 + 145*d**3/21 - 50*d**2/7 - 52*d. Factor j(q).
2*(q - 5)**2*(5*q - 2)/7
Let j(u) be the second derivative of -5*u + 0 + 0*u**2 - 1/5*u**5 - 2/3*u**4 + 2*u**3. Let j(v) = 0. What is v?
-3, 0, 1
Let r be -4*(-3)/(-6) + 96/44. Suppose -w + 18 = -4*p, -4*w + 4*p + 11 + 13 = 0. Factor -r*l**w - 8/11 + 8/11*l.
-2*(l - 2)**2/11
Let s = -13 - -18. Suppose 0 = 2*h + f - 2 + 3, 4*h - 3*f - 23 = 0. Determine v, given that -4*v**3 - 2*v**h - 5*v + s*v = 0.
-1/2, 0
Let w(k) be the first derivative of -k**4/22 - 4*k**3/33 - k**2/11 - 1. Determine u, given that w(u) = 0.
-1, 0
Find g, given that 4*g - g**2 + 3*g + g**3 - 2*g**2 - 5*g = 0.
0, 1, 2
Let b(p) be the first derivative of -3 - 1/2*p**4 - 2/3*p**3 + 0*p**2 + 0*p. Factor b(m).
-2*m**2*(m + 1)
Suppose -2/5*h**4 + 6/5*h**3 + 16/5 - 24/5*h + 4/5*h**2 = 0. What is h?
-2, 1, 2
Let v(l) = -l**2 + 5*l + 6. Let d be v(5). Let w = d - 6. Factor -1/3*r**4 + 1/3 + 2/3*r + w*r**2 - 2/3*r**3.
-(r - 1)*(r + 1)**3/3
Find b such that -92*b**3 + 36*b**5 + 16*b - 11*b**4 + 50*b**2 - 34*b**2 + 35*b**4 = 0.
-2, -1/3, 0, 2/3, 1
Let q(s) be the second derivative of 3*s**5/20 - s**4 + 2*s**3 - s. Solve q(d) = 0.
0, 2
Let w = -10655/9 + 1185. Let w*f**2 - 16/9*f - 8/9 = 0. What is f?
-2/5, 2
Let b be 1 - ((-364)/180 + 3) - 0. Let t(n) be the second derivative of 1/6*n**5 - n + 7/9*n**3 + 2/3*n**2 + 1/2*n**4 + b*n**6 + 0. Factor t(j).
2*(j + 1)**3*(j + 2)/3
Let q(g) be the third derivative of -2*g**2 + 1/12*g**4 + 0 - 1/15*g**5 + 1/3*g**3 + 0*g. Suppose q(f) = 0. What is f?
-1/2, 1
Suppose 2*d - 13 = -3*n, -4*d = -0*n - n - 5. Suppose 0 = -0*s - s - 3*q, 3*q = -n*s. Factor -1/3*v + s + 1/3*v**2.
v*(v - 1)/3
Let n(d) = -85*d**3 - 135*d**2 + 595*d - 340. Let v(f) = -5*f**3 - 8*f**2 + 35*f - 20. Let r(a) = -2*n(a) + 35*v(a). Suppose r(k) = 0. Calculate k.