- 1/240*h**6. Let p(b) be the second derivative of a(b). Factor p(o).
-o**3/2
Let q(u) = -u**2 + u + 1. Let t(p) = p**2 - 32*p - 32. Let k(l) = -11*l - 11. Let d(y) = -17*k(y) + 6*t(y). Let v(b) = 2*d(b) + 10*q(b). Factor v(a).
2*a**2
Let h(k) be the first derivative of 2*k - 1 - 1/2*k**2 - 1/3*k**3. Factor h(b).
-(b - 1)*(b + 2)
What is j in 4/5*j**2 + 2/5*j**3 + 0 + 2/5*j = 0?
-1, 0
Suppose -4*x = -3*x - 8. Suppose 3 - x = -f. Suppose -4*m**2 - m + 11*m**4 + m**4 - 11*m**5 + 2*m**3 + 2*m**f = 0. Calculate m.
-1/3, 0, 1
Let g(k) be the first derivative of k**5/10 + k**4/8 - k**3/6 - k**2/4 + 23. Find p, given that g(p) = 0.
-1, 0, 1
Let z be 3/(-15)*1 + (-80)/(-150). Let l(f) be the first derivative of -z*f**2 - 1 + 2/9*f**3 + 0*f. Factor l(p).
2*p*(p - 1)/3
Let p(t) = t**4 - 10*t**3 - 15*t**2 - 17*t - 7. Let j(b) = 5*b**4 - 40*b**3 - 59*b**2 - 69*b - 29. Let o(n) = -6*j(n) + 26*p(n). Factor o(g).
-4*(g + 1)**3*(g + 2)
Suppose -3*o = -5*o + 4. Let v(r) be the second derivative of -2*r - 2/15*r**6 + 0*r**o - 1/10*r**5 + 1/6*r**4 + 0 + 0*r**3. Factor v(n).
-2*n**2*(n + 1)*(2*n - 1)
Let z = -114/11 - -1379/132. Let o(t) be the second derivative of z*t**4 + 0*t**3 + 0 + 1/20*t**5 - 2*t + 0*t**2. Factor o(w).
w**2*(w + 1)
Let p be (-8 + 1)/(5 + 170/(-20)). Factor -2/3*x + 2/15 + 8/15*x**p.
2*(x - 1)*(4*x - 1)/15
Let l(p) = 33*p**2 + 70*p - 13. Let i(z) = 16*z**2 + 35*z - 6. Let v(k) = 7*i(k) - 4*l(k). Factor v(t).
-5*(t + 2)*(4*t - 1)
Let h(l) = -l**2 - 71*l - 128. Let g(c) = -36*c - 64. Let v(x) = -7*g(x) + 4*h(x). Find m, given that v(m) = 0.
-4
Determine a so that 0 + 0*a**2 + 0*a + 2/13*a**3 + 2/13*a**4 = 0.
-1, 0
Let q(y) be the first derivative of y**9/3024 - y**7/420 + y**5/120 - 5*y**3/3 - 2. Let c(i) be the third derivative of q(i). Factor c(o).
o*(o - 1)**2*(o + 1)**2
Let l(y) be the third derivative of 1/18*y**4 + 0*y + 7*y**2 + 0 + 1/120*y**6 + 1/18*y**5 - 4/9*y**3. Determine u, given that l(u) = 0.
-2, 2/3
Let x(d) = -2*d**3 - d**2 + d - 3. Let g(u) = u**3 + u**2 + 2. Suppose -4*w + 24 = -6*n + 4*n, 24 = 5*w - n. Let k(a) = w*x(a) + 6*g(a). Factor k(i).
-2*i*(i - 2)*(i + 1)
Let o = 11 + -9. Let m(j) be the second derivative of o*j + 0 + 1/27*j**3 - 1/54*j**4 - 1/90*j**5 + 1/9*j**2. Solve m(l) = 0.
-1, 1
Let u(k) be the first derivative of k**7/280 - k**5/40 + 4*k**3/3 - 4. Let g(c) be the third derivative of u(c). Factor g(h).
3*h*(h - 1)*(h + 1)
Factor -3*r**2 + 28*r**2 + 20 + 40*r + 5*r**3 + 0*r**3.
5*(r + 1)*(r + 2)**2
Let t be (2/(-10))/((-24)/20). Let p(d) be the third derivative of 0 - t*d**3 - 1/12*d**4 - 1/60*d**5 + 2*d**2 + 0*d. Determine q, given that p(q) = 0.
-1
Let g(l) be the third derivative of l**6/1320 - l**4/264 + 11*l**2. Suppose g(n) = 0. Calculate n.
-1, 0, 1
Suppose 0 - 2*q**3 + 3/4*q**5 + q**2 + 1/4*q**4 + 0*q = 0. What is q?
-2, 0, 2/3, 1
Solve -2*o**4 - 2*o**3 + 3*o**5 + 6*o**2 - o**5 - 4*o**2 = 0.
-1, 0, 1
Let d be ((-1)/3)/(2/(-18)). Find u, given that -7*u**d + 3*u**3 + 6*u**3 = 0.
0
Let o(t) be the second derivative of -1/18*t**4 + 1/30*t**5 + 1/45*t**6 - 1/9*t**3 - 6*t + 0 + 0*t**2. Find n such that o(n) = 0.
-1, 0, 1
Suppose -6 = -5*w + 2*t - 2, 2*w - 3*t = -5. Let a(m) be the first derivative of 3/4*m**w + 1/6*m**3 + m - 1. Let a(k) = 0. What is k?
-2, -1
Let i(d) be the first derivative of -112*d**3/3 + 26*d**2 + 24*d + 13. Let i(y) = 0. Calculate y.
-2/7, 3/4
Factor 1/9*w**5 + 0 + 0*w**3 - 2/9*w**4 + 2/9*w**2 - 1/9*w.
w*(w - 1)**3*(w + 1)/9
Solve -3*x**3 - x**5 - 18*x**4 - 13*x**4 + 0*x**5 + 27*x**4 = 0.
-3, -1, 0
Let g be (-726)/(-770) - (-4)/(-5). Determine s so that -g*s**4 + 0*s + 2/7*s**2 + 0*s**3 - 1/7 = 0.
-1, 1
Let s be 2/(-6) + (-245)/21. Let q be (2/(-6))/(1/s). Determine d, given that d**3 + q*d - 2*d**2 - 2*d - d = 0.
0, 1
Let x(j) = 4*j**4 + 24*j**3 + 17*j**2 + 5*j - 5. Let y(f) = 9*f**4 + 48*f**3 + 33*f**2 + 9*f - 9. Let c(b) = 9*x(b) - 5*y(b). Find q, given that c(q) = 0.
-2, -2/3, 0
Let q(t) be the third derivative of -25*t**8/336 + 13*t**7/42 - 3*t**6/8 - t**5/12 + 5*t**4/12 - 3*t**2 + 2*t. Let q(s) = 0. What is s?
-2/5, 0, 1
Let c be 4/10 - 161/(-35). Determine n so that -n**3 + 0*n**c + n**5 - n**3 + n**4 + 0*n**3 = 0.
-2, 0, 1
Let x(o) be the second derivative of o**7/105 - o**6/30 + o**5/30 + 2*o**2 + 5*o. Let v(f) be the first derivative of x(f). Factor v(p).
2*p**2*(p - 1)**2
Let m(q) be the second derivative of 3*q**5/100 - q**4/20 - q**3/5 - 23*q. Factor m(o).
3*o*(o - 2)*(o + 1)/5
Let s(m) be the third derivative of m**7/245 + m**6/210 + 10*m**2. Determine h, given that s(h) = 0.
-2/3, 0
Let a(n) be the first derivative of -4/9*n**3 - 1/30*n**5 - 1/3*n**2 - 5/24*n**4 + 4 + 0*n. Factor a(r).
-r*(r + 1)*(r + 2)**2/6
Let k(y) be the first derivative of -y**6/6 + 4*y**5/5 - 5*y**4/4 + 2*y**3/3 + 11. What is t in k(t) = 0?
0, 1, 2
Let g(l) = 4*l**3 + 6*l + 4. Let h(w) = -3*w**3 - w**2 - 5*w - 3. Let z(r) = -2*g(r) - 3*h(r). Factor z(o).
(o + 1)**3
Let h = 65/213 + 2/71. Find q, given that -h*q**2 + 2/3*q - 1/3 = 0.
1
Let f = -118 + 475/4. Suppose -3/4*g**4 + 0*g + 0 - f*g**5 + 0*g**2 + 0*g**3 = 0. Calculate g.
-1, 0
Let y(t) be the first derivative of -t**8/240 - 2*t**7/105 - 11*t**6/360 - t**5/60 + 4*t**3/3 - 5. Let m(o) be the third derivative of y(o). Factor m(q).
-q*(q + 1)**2*(7*q + 2)
Factor 0*a - 1/4*a**2 + 1/4*a**3 + 0 - 1/4*a**5 + 1/4*a**4.
-a**2*(a - 1)**2*(a + 1)/4
Let n(g) be the second derivative of g**9/7560 - g**7/1050 + g**5/300 - 7*g**3/6 - 5*g. Let j(i) be the second derivative of n(i). Determine s so that j(s) = 0.
-1, 0, 1
Let y(k) = -k**3 + 3*k**2 + k - 1. Let r be y(3). Let 7*c**2 - r*c - 9*c**2 + c**2 + 3 = 0. What is c?
-3, 1
Let o(p) be the third derivative of 2*p**8/1155 - 2*p**7/1155 + p**6/1980 + p**3/6 + p**2. Let t(x) be the first derivative of o(x). Factor t(i).
2*i**2*(4*i - 1)**2/11
Let g be (2 - 48/21)*-7 - -1. Let x(h) be the second derivative of 0*h**2 - 1/70*h**5 - h - 1/105*h**6 + 0 + 1/21*h**g + 1/42*h**4. Factor x(z).
-2*z*(z - 1)*(z + 1)**2/7
Let -2/11*q**2 + 2/11*q - 2/11*q**3 + 2/11 = 0. Calculate q.
-1, 1
Suppose -7*a + 5*a + 4 = 0. Suppose 0 = 2*h - 0 - 4. Factor -a*c**h + 2*c**4 - c**5 + 0*c**4 + 0*c + c.
-c*(c - 1)**3*(c + 1)
Determine o so that -4/3 - 2/3*o**4 + 14/3*o + 10/3*o**3 - 6*o**2 = 0.
1, 2
Let a(j) = 5*j**3 + 5*j**2 + 4*j. Let p(r) = 4*r**3 + 4*r**2 + 3*r. Let l(n) = 3*a(n) - 4*p(n). Solve l(f) = 0 for f.
-1, 0
Find p, given that 0 - 2/21*p**2 + 8/21*p = 0.
0, 4
Factor 2*z**5 - 7 + 9*z**4 + 25 + 60*z**3 + 92*z**2 + 66*z + 9*z**4.
2*(z + 1)**3*(z + 3)**2
Let h(d) be the second derivative of 0*d**4 + 0*d**3 - 4*d + 1/120*d**5 + 1/252*d**7 - 1/90*d**6 + 0 + 0*d**2. Factor h(r).
r**3*(r - 1)**2/6
Let h(q) be the third derivative of -1/315*q**7 + 0*q**4 + 0*q + 2*q**2 + 1/180*q**5 + 1/672*q**8 - 1/720*q**6 + 0 + 0*q**3. Factor h(p).
p**2*(p - 1)**2*(3*p + 2)/6
Let q(r) = r**3 - 8*r**2 + 7*r + 2. Let w be q(7). Factor -11*x**2 + 3*x**2 - 2*x**w - 5*x**2 + 6*x.
-3*x*(5*x - 2)
Let u(o) = -2*o**2 - 8*o + 1 + 9*o - o**3 + 1. Let q be u(-2). Factor -1/2*i**2 + q*i + 0.
-i**2/2
Let t = 13 + -13. Suppose 6*n = 4*n + 6. Factor -1/4*o**n + 0*o**2 + t + 0*o.
-o**3/4
Factor 2/7*b + 4/7 - 2/7*b**2.
-2*(b - 2)*(b + 1)/7
Let n be 36/8 + 2/4. Let j(k) = k - 5. Let u be j(n). Factor u + 0 - 2*f - 4*f**2 + 4*f**4 + 2*f**5.
2*f*(f - 1)*(f + 1)**3
Let m(b) be the first derivative of -1/3*b + 1/9*b**3 + 1/12*b**4 - 1/6*b**2 - 3. Factor m(n).
(n - 1)*(n + 1)**2/3
Let p(m) be the first derivative of m**5/5 - m**4 - 2*m**3/3 + 6*m**2 + 9*m - 26. Factor p(w).
(w - 3)**2*(w + 1)**2
Let u(w) be the second derivative of w**6/1620 - w**5/540 - w**3/3 + 2*w. Let y(r) be the second derivative of u(r). Let y(i) = 0. Calculate i.
0, 1
Let m(q) be the second derivative of 0*q**3 + 0*q**2 + 1/12*q**4 - 5*q + 0. Factor m(r).
r**2
Let f = 6535/2106 + -215/81. Let j = 2/39 + f. Factor -1/2*q**3 + 0*q - j*q**2 + 0.
-q**2*(q + 1)/2
Let j(y) be the first derivative of -5/33*y**3 - 1/110*y**5 + 2*y + 2 + 2/33*y**4 + 2/11*y**2. Let o(x) be the first derivative of j(x). Factor o(k).
-2*(k - 2)*(k - 1)**2/11
Let k(h) be the first derivative of -1/14*h**4 - 4/21*h**3 - 1/7*h**2 + 0*h - 1. Factor k(r).
-2*r*(r + 1)**2/7
Suppose 0*m + 4 = 2*m. Factor -4*b - 3*b**2 + 3 + 