2*u**3*(u - 1)*(3*u - 1)/9
Let v(w) = 12*w**4 + 8*w**3 - 4*w**2 + 8*w. Let k(l) = -l**4 - l**3 - l. Let i(u) = -8*k(u) - v(u). Factor i(z).
-4*z**2*(z - 1)*(z + 1)
Let r be -1 + 2 + 2 + -1. Factor 8/7*g**2 - 4/7 - r*g.
2*(g - 2)*(4*g + 1)/7
Let u(j) be the third derivative of -j**9/15120 + j**8/2240 - j**7/1260 + j**4/12 + 7*j**2. Let p(l) be the second derivative of u(l). Factor p(a).
-a**2*(a - 2)*(a - 1)
Let i be 1 + -14*4/(-8). Find w, given that 6*w**5 - w**3 - 11*w**3 - 3*w**5 + w**5 - i*w**2 = 0.
-1, 0, 2
Solve 270*h**3 + h**2 - 268*h**3 - 2 + 3*h**2 - h**2 - 3*h = 0.
-2, -1/2, 1
Suppose 0*t - 8 = -4*t. Suppose 4*h - 10 - t = 0. Factor -s**2 + s + 1 - 2*s**3 - s**3 + 2*s**h.
-(s - 1)*(s + 1)**2
Suppose 2*y = o + 6*y - 21, 4*o - 42 = 5*y. Let u = o + -3. Factor 2*k**2 - 6*k - 6 + u + 0*k**2.
2*(k - 2)*(k - 1)
Let s(y) be the third derivative of y**11/207900 + y**10/75600 + y**9/151200 - y**5/30 - 3*y**2. Let j(o) be the third derivative of s(o). Factor j(u).
2*u**3*(u + 1)*(4*u + 1)/5
What is t in 32/11*t - 8/11*t**4 - 26/11*t**3 + 8/11 - 6/11*t**2 = 0?
-2, -1/4, 1
Let g(d) be the first derivative of -2*d**5/165 - 7*d**4/132 + 2*d**3/33 + 5*d**2/2 - 7. Let v(z) be the second derivative of g(z). Factor v(m).
-2*(m + 2)*(4*m - 1)/11
Let y(j) = -2 - 2 - 2 + j + 2. Let d be y(6). Find m, given that -1/2*m**d + 1/4*m**5 + 0 - 1/4*m + 0*m**3 + 1/2*m**4 = 0.
-1, 0, 1
Factor 16 - 31*z**3 - 6*z**2 + 27*z + 3*z**3 - 10 + z**3.
-3*(z - 1)*(z + 1)*(9*z + 2)
Let j = -140 + 143. Let y(i) be the second derivative of 49/6*i**4 - 28/3*i**j + 4*i**2 + 0 + 4*i. Determine u so that y(u) = 0.
2/7
Factor -25/2*m**2 - 10 - 45/2*m.
-5*(m + 1)*(5*m + 4)/2
Let o be 4/10 - (-46)/10. Suppose 0 = -o*y + 3*y + 8. Factor -2/3*x**3 + 0*x - 1/3*x**2 + 0 - 1/3*x**y.
-x**2*(x + 1)**2/3
Let c(k) be the second derivative of -5*k**7/42 + k**6/6 + 3*k**5/4 - 5*k**4/12 - 5*k**3/3 - 17*k. Suppose c(j) = 0. Calculate j.
-1, 0, 1, 2
Let k(v) be the second derivative of -4*v**7/231 - v**6/3 - 113*v**5/55 - 70*v**4/33 + 50*v**3/3 - 125*v**2/11 + 14*v. Find y, given that k(y) = 0.
-5, 1/4, 1
Let m(r) be the second derivative of 0 - 1/6*r**4 + 0*r**3 - 2*r + 1/10*r**5 + 0*r**2. Factor m(h).
2*h**2*(h - 1)
Let k(w) be the first derivative of w**4/2 - w**2 + 2. Suppose k(y) = 0. What is y?
-1, 0, 1
Let i(s) be the third derivative of 1/672*s**8 + 0 - 1/420*s**7 + 1/60*s**5 + 1/48*s**4 - 1/12*s**3 + 0*s - 1/120*s**6 - 2*s**2. Factor i(x).
(x - 1)**3*(x + 1)**2/2
Let k(r) = 8*r**2 + 10*r + 7. Let c(z) = z**2 + z + 1. Let m(t) = 14*c(t) - 2*k(t). Factor m(i).
-2*i*(i + 3)
Let d(x) = x + 9. Let l be d(-6). Find q, given that -q + 1 - q**3 - 2*q**l + 4*q**3 - q**2 = 0.
-1, 1
Let h(c) be the third derivative of -c**6/160 - c**5/20 - c**4/8 + 16*c**2. Determine j, given that h(j) = 0.
-2, 0
Let l = 8 - 7. Suppose 5*b = m + 13, 2*b - 4*m - 15 = l. Factor -10/3*x**b + 16/3*x - 8/3 + 2/3*x**3.
2*(x - 2)**2*(x - 1)/3
Let h(m) be the first derivative of 1/15*m**3 + 1/5*m + 1 - 1/5*m**2. What is u in h(u) = 0?
1
Factor 2/3*w**2 + 0 - 2/9*w**4 - 4/9*w + 0*w**3.
-2*w*(w - 1)**2*(w + 2)/9
Let u(y) be the first derivative of 32/27*y**3 + 7/27*y**6 - 4/9*y - 3 + 17/9*y**4 - 1/9*y**2 + 52/45*y**5. Factor u(o).
2*(o + 1)**4*(7*o - 2)/9
Let i(y) be the second derivative of -y**6/135 + y**5/10 - 14*y**4/27 + 4*y**3/3 - 16*y**2/9 + 25*y. Let i(b) = 0. Calculate b.
1, 2, 4
Suppose -2*s - 2 = 2*r, s + 2 = -5*r - 11. Factor -h**s + 1/4 - 3/4*h.
-(h + 1)*(4*h - 1)/4
Let v(h) = 5*h**2. Let i(k) be the second derivative of k**4/12 + k**3/6 - k**2/2 + 3*k. Let w(a) = -12*i(a) + 3*v(a). Determine n, given that w(n) = 0.
2
Let k(r) be the third derivative of r**6/600 - r**5/60 + r**4/30 + 34*r**2. Factor k(v).
v*(v - 4)*(v - 1)/5
Let s(p) = -7*p**4 - 8*p**3 + 7*p**2 + 12*p. Let b(l) = -15*l**4 - 15*l**3 + 15*l**2 + 25*l. Let j(d) = 2*b(d) - 5*s(d). Factor j(f).
5*f*(f - 1)*(f + 1)*(f + 2)
Suppose -90 = -4*i - 2*i. Let o be (-33)/i + 1 - -2. Determine y so that -o*y**3 - y**2 - 1/5*y + 0 = 0.
-1, -1/4, 0
Let v(n) = -n + 10. Let a be v(8). Let c(b) = b**2 - 2*b. Let w be c(3). Factor -2*p + 7*p**2 + a*p**w + 4*p - 3*p**2.
2*p*(p + 1)**2
Let u(l) = -25*l**2 + 235*l - 130. Let c(t) = -2*t**2 + 18*t - 10. Let k(m) = 40*c(m) - 3*u(m). Factor k(n).
-5*(n - 2)*(n - 1)
Let g(m) be the second derivative of 0 - 2*m - 3/4*m**4 + 0*m**2 + m**3 + 3/20*m**5. Factor g(p).
3*p*(p - 2)*(p - 1)
Let x(d) = 3*d**4 - 8*d**3 + 5*d**2. Let k(f) = -6*f**4 + 16*f**3 - 9*f**2 - f. Let c(i) = 2*k(i) + 5*x(i). Factor c(j).
j*(j - 1)**2*(3*j - 2)
What is c in 8*c**3 + 0*c**4 + 0*c**4 + c**4 + 16*c**2 + 0*c**3 = 0?
-4, 0
Find m, given that 2*m**2 + 109 - 2*m - 109 = 0.
0, 1
Suppose 9*w + 10 = 11*w. Solve 0 + 8/9*r**4 + 2/3*r**3 - 8/9*r**w - 8/9*r**2 + 2/9*r = 0.
-1, 0, 1/2, 1
Let g(w) be the second derivative of 1/4*w**5 + 0 + 1/6*w**3 + 1/15*w**6 + 1/3*w**4 + 0*w**2 + 5*w. Solve g(z) = 0 for z.
-1, -1/2, 0
Let p(c) be the first derivative of 2 + 0*c**3 - 1/18*c**4 + 1/9*c**2 + 0*c. Find x, given that p(x) = 0.
-1, 0, 1
Let v(r) = r**2 - 6*r - 6. Let z be v(8). Let b = z + -8. Determine h so that -1/2*h + 3/2*h**b + 0 = 0.
0, 1/3
Let h(q) be the second derivative of 0*q**2 + 2/135*q**6 + 1/90*q**5 + 0 - 5*q + 0*q**4 + 0*q**3 + 1/189*q**7. Factor h(a).
2*a**3*(a + 1)**2/9
Let f(q) = 5*q**3 + q**2 + q - 1. Let m be f(1). Let z be 2*(-5)/m*-3. Suppose 0*b + 0*b**3 - 2/9*b**z + 0*b**2 + 2/9*b**4 + 0 = 0. What is b?
0, 1
Let -20*w**3 + 44*w + 5*w**4 + 45 - 15*w - 20*w - 10*w**2 + 51*w = 0. What is w?
-1, 3
Let z(g) be the third derivative of g**9/211680 - g**7/5880 - g**6/1260 - g**5/30 - 3*g**2. Let f(d) be the third derivative of z(d). Factor f(c).
2*(c - 2)*(c + 1)**2/7
Let p(g) be the first derivative of -g**4/48 + g**3/12 + 3*g**2/8 - 3*g + 1. Let f(v) be the first derivative of p(v). Factor f(i).
-(i - 3)*(i + 1)/4
Let x be (-63)/(-30) - (-6)/(-4). Let t(d) be the first derivative of -2*d**3 - 3/5*d + 3/2*d**2 + 1/10*d**6 - x*d**5 - 1 + 3/2*d**4. Factor t(z).
3*(z - 1)**5/5
Suppose 0 = -5*w - b + 22, -5*b + 0*b - 6 = -4*w. Let o be ((-2)/w)/(13/(-78)). What is j in 0 + 0*j**4 + 1/2*j**5 + 0*j**2 + 0*j - 1/2*j**o = 0?
-1, 0, 1
Suppose 0 = -3*q - 2*q + 10. Suppose 3 + o + 5*o**q - 2*o**2 + 0*o**2 - 7*o = 0. Calculate o.
1
Let m(i) = -i**2 + 13*i + 16. Let x be m(14). Determine p so that -7*p**3 - 8*p**x - 2*p + 3*p + 23*p**3 = 0.
0, 1/4
Factor 1/2*w**2 + 0 - w.
w*(w - 2)/2
Let h be 3/7 + (-6)/63. Find x such that 5/6*x**4 - 1/3*x - 5/6*x**2 + h*x**3 + 0 = 0.
-1, -2/5, 0, 1
Let s be 1/4 + 7/4. Solve -s*w**3 + 7*w**4 - 4*w**4 - 6*w**2 + 5*w**3 = 0.
-2, 0, 1
Let t be (119/(-14))/((-1)/2). Suppose 3*r**4 - 4*r - 5*r**2 - 13*r**3 + r**4 + r**3 + t*r**2 = 0. What is r?
0, 1
Let u(h) = -h**3 + h**2 - 2*h - 2. Let q(l) = 6*l**3 - 6*l**2 + 10*l + 11. Let d(i) = 2*q(i) + 11*u(i). Factor d(a).
a*(a - 2)*(a + 1)
Let p(j) be the first derivative of 2*j**3/15 - 2*j**2/5 + 2*j/5 - 6. Let p(r) = 0. What is r?
1
Let y(h) be the first derivative of h**4/4 + h**3/3 - 14. Factor y(o).
o**2*(o + 1)
Let s(r) be the second derivative of 11/42*r**4 + 1/14*r**5 + 1/3*r**3 + 0 + 1/7*r**2 - 7*r. Solve s(o) = 0 for o.
-1, -1/5
Let t(r) be the second derivative of 3*r + 0*r**2 + 1/12*r**4 + 1/6*r**3 + 0. Factor t(j).
j*(j + 1)
Let m(q) be the third derivative of q**7/630 - q**6/180 + q**5/180 + 12*q**2. Solve m(d) = 0.
0, 1
Let r(x) be the second derivative of -x**6/60 + x**5/40 - 8*x. Factor r(p).
-p**3*(p - 1)/2
Let n(j) = -j**3 + 11*j**2 + 9*j + 38. Let k be n(12). Let -3/2*i**k - 3/2 - 3*i = 0. Calculate i.
-1
Suppose -59*d = -63*d. Find q such that d*q + 4/5*q**2 - 2/5*q**4 + 2/5*q**3 + 0 = 0.
-1, 0, 2
Solve 2/9*t**2 - 1/9 + 1/9*t + 1/9*t**5 - 1/9*t**4 - 2/9*t**3 = 0.
-1, 1
Let s(n) be the second derivative of 1/6*n**3 - 1/42*n**7 - 1/6*n**4 + 0 + 0*n**5 + 0*n**2 + 3*n + 1/15*n**6. Solve s(f) = 0.
-1, 0, 1
Let h(l) be the third derivative of -l**2 + 0*l**3 + 0*l + 0*l**4 + 1/60*l**5 + 0 - 1/210*l**7 + 0*l**6. Solve h(w) = 0.
-1, 0, 1
Factor 0 + s - 3/2*s**2.
-s*(3*s - 2)/2
Let i(t) = t**2 + t + 1. Let x(d) = 20 + 17*d + 19*d + 24*d**2 - 8*d. Let l(h) = 20*i(h) - x(h). Factor l(q).
-4*q*(q + 2)
Let t(c) = 16*c**4 - 3*c**3. Let b be (-44)/10 + 8/20. Let a(z) = -15*z**4