or 1/4*m**2 + 1/4*m + 0.
m*(m + 1)/4
Let h(b) be the first derivative of -b**2/2 - b + 1. Let o be h(-3). Factor 0*y**4 - y**2 + 4*y - y**2 + 2*y**3 + o*y**4 - 6*y.
2*y*(y - 1)*(y + 1)**2
Suppose -14 = 2*o - o. Let g be 4/o - (-142)/56. Solve -g*l**5 - l + 13/4*l**3 + 1 + 9/4*l**4 - 13/4*l**2 = 0.
-1, -2/3, 2/3, 1
Let n(c) be the second derivative of -1/50*c**5 - 1/5*c**2 + 1/15*c**3 + 6*c + 1/30*c**4 + 0. Factor n(z).
-2*(z - 1)**2*(z + 1)/5
Let y(j) be the second derivative of j**7/210 - j**6/50 + 3*j**5/100 - j**4/60 + 5*j. Determine s so that y(s) = 0.
0, 1
Let g(a) be the first derivative of 2/7*a**4 + 10/21*a**3 + 2/35*a**5 + 2/7*a**2 + 0*a + 6. Factor g(d).
2*d*(d + 1)**2*(d + 2)/7
Let z be ((-90)/25)/6 - -1. Suppose 4/5 - z*n**2 - 2/5*n = 0. Calculate n.
-2, 1
Determine z so that -4/11 - 2/11*z + 2/11*z**2 = 0.
-1, 2
Suppose 3 = 3*t - 3. Let f(x) = -1. Let d = -17 + 7. Let k(u) = -u**2 - 2*u - 6. Let h(a) = d*f(a) + t*k(a). Let h(q) = 0. What is q?
-1
Find f, given that -8/5*f - 6/5 - 2/5*f**2 = 0.
-3, -1
Let v(k) be the first derivative of 1/14*k**4 + 1/7*k**2 - 4/21*k**3 - 5 + 0*k. Solve v(f) = 0.
0, 1
Let z = 166 - 1160/7. Let k(o) be the first derivative of -2/35*o**5 + 1/7*o**2 - 1/14*o**4 + z*o**3 - 4/7*o - 2. Find r such that k(r) = 0.
-2, -1, 1
Let x be (0 + -1)*30/(-6). Let m(j) = -j**2 - j - 1. Let z(n) = -6*n**2 - 3*n - 6. Let d(c) = x*m(c) - z(c). Find a, given that d(a) = 0.
1
Factor 16/5*r**2 + 4/5*r**5 + 24/5*r**3 + 4/5*r + 16/5*r**4 + 0.
4*r*(r + 1)**4/5
Let m(l) = l**2 - 9*l + 22. Let a be m(3). Factor 10*x**3 - 25/3*x**a + 12*x**2 + 8/3*x + 0.
-x*(x - 2)*(5*x + 2)**2/3
Let b(y) = -y - 4. Let z be b(-7). Let g be (4/(-6))/((-1)/6). Suppose -5*t**4 + t**2 - z*t**2 + 3*t**4 - g*t**3 = 0. What is t?
-1, 0
Let c(x) be the second derivative of 0 + 1/7*x**3 - 4*x - 3/70*x**5 - 1/105*x**6 - 1/42*x**4 + 2/7*x**2. Determine f, given that c(f) = 0.
-2, -1, 1
Suppose -8 = -2*u - 0*u. Factor n**u + 1/2*n + 1/2 - 3/2*n**2 - 1/2*n**3.
(n - 1)**2*(n + 1)*(2*n + 1)/2
Determine n, given that 8/5*n + 2/5 + 6/5*n**2 = 0.
-1, -1/3
Suppose 0 = 2*b + 2 - 6. Suppose 0 = b*n - 3 - 3. Suppose -2/3 - 2*x**2 + 2/3*x**n + 2*x = 0. Calculate x.
1
Factor -2/3*s**3 + 0*s + 0 + 0*s**2.
-2*s**3/3
Let n(w) be the second derivative of 8*w**6/15 - 11*w**5/5 + 3*w**4 - 2*w**3/3 - 2*w**2 - 6*w. Factor n(q).
4*(q - 1)**3*(4*q + 1)
Let h(c) be the first derivative of -7*c**5/270 + 5*c**4/108 + 2*c**3/27 + c**2 - 2. Let y(f) be the second derivative of h(f). Solve y(m) = 0 for m.
-2/7, 1
Let p(w) be the second derivative of 0 + 2*w - 1/6*w**4 - w**2 - 2/3*w**3. Factor p(y).
-2*(y + 1)**2
Let s = -8 - -10. Let g(m) be the third derivative of 1/30*m**5 + 2*m**s + 1/6*m**4 + 0 + 0*m + 1/3*m**3. Solve g(c) = 0.
-1
Let d(t) be the third derivative of t**6/720 - t**5/120 + t**4/72 - 12*t**2. Factor d(m).
m*(m - 2)*(m - 1)/6
Let j(i) be the second derivative of 1/40*i**6 + 1/4*i**4 + 0*i**2 + 3/20*i**5 + 0*i**3 + 11*i + 0. Factor j(g).
3*g**2*(g + 2)**2/4
Factor 0 - 2/5*y**4 + 6/5*y**2 + 0*y**3 - 4/5*y.
-2*y*(y - 1)**2*(y + 2)/5
Let t = -5/149 - -641/1341. Let m(w) be the second derivative of t*w**3 - 2/9*w**4 + 0*w**2 + 1/30*w**5 + w + 0. Factor m(y).
2*y*(y - 2)**2/3
Let u(h) be the second derivative of -3*h**5/100 + 31*h + 2. Factor u(l).
-3*l**3/5
Let w(y) be the second derivative of -y**6/90 - y**5/30 + y**4/36 + y**3/9 - 2*y. Factor w(m).
-m*(m - 1)*(m + 1)*(m + 2)/3
Let i(q) be the first derivative of q**5/60 + q**4/12 + q**3/6 - q**2 + 2. Let c(w) be the second derivative of i(w). Factor c(a).
(a + 1)**2
Let z(v) be the third derivative of v**5/30 + v**4/12 + v**3/2 - v**2. Let k(q) = 2*q**2 + 2*q + 4. Let s(b) = 3*k(b) - 4*z(b). Factor s(c).
-2*c*(c + 1)
Let v(l) = 4*l**2 - 90*l + 46. Let p be v(22). Factor 2/5*u**4 - 2/5 + 4/5*u - 4/5*u**3 + 0*u**p.
2*(u - 1)**3*(u + 1)/5
Let m be (3/(-2))/(-149 + 5). Let u(q) be the third derivative of 0 - 1/240*q**5 + 4*q**2 + m*q**4 + 1/12*q**3 + 0*q. Factor u(y).
-(y - 2)*(y + 1)/4
Let -27*o**3 - 13*o**3 + 1 - 5 + 46*o**2 - 3*o + o = 0. What is o?
-1/4, 2/5, 1
Let i(b) be the second derivative of b**4/24 - b**2/4 - 4*b. Find a, given that i(a) = 0.
-1, 1
Let 72*t**3 - 147*t**5 + 27*t**4 - 22*t**4 - 12*t**2 - 68*t**4 = 0. Calculate t.
-1, 0, 2/7
What is p in -96*p**3 - 2139*p**4 + 2103*p**4 - 8*p**2 - 4*p**5 - 56*p**2 = 0?
-4, -1, 0
Let s(f) = -4*f**4 + 6*f**3 + 14*f**2 - 18*f. Let z(d) = 8*d**4 - 13*d**3 - 27*d**2 + 37*d. Let u(l) = -5*s(l) - 2*z(l). Factor u(o).
4*o*(o - 2)*(o - 1)*(o + 2)
Let p = 11/18 - 23/45. Let o(j) be the second derivative of 0*j**2 + 0 + 3/10*j**5 + 0*j**3 - p*j**6 + 4*j - 1/4*j**4. Factor o(l).
-3*l**2*(l - 1)**2
Let x(u) = u**2 - 1. Let j(l) = l**2 + 7*l + 2. Let q be j(-6). Let r = q - 0. Let z(d) = -6*d**2 + 4*d + 4. Let n(p) = r*x(p) - z(p). Factor n(f).
2*f*(f - 2)
Factor 0*w + 19*w**3 - 4*w - 12*w**2 - 12*w**3.
w*(w - 2)*(7*w + 2)
Let h be (-9)/6*16/(-24) - 1. Suppose 8/5*o**3 + 0 + h*o + 4/5*o**2 + 4/5*o**4 = 0. What is o?
-1, 0
Let m(j) be the first derivative of 3*j**5/5 + 15*j**4/4 + 6*j**3 - 6*j**2 - 24*j - 2. Suppose m(t) = 0. Calculate t.
-2, 1
Let o = 8 - 4. Suppose 20 = -4*l - 4*b, l - 9 = b - o. Factor -2*d**5 + d**4 + 3*d**4 + l*d**3 - 2*d**3.
-2*d**3*(d - 1)**2
Suppose 3*m + 15 = -4*j, 3*m = -m + 2*j + 2. Let o(f) = -1. Let v(w) = w**2 - 2*w + 5. Let t(p) = m*v(p) - 4*o(p). Factor t(q).
-(q - 1)**2
Suppose 5*x = 3*b + 11, -3*x - 2 - 5 = 5*b. Let f be x*(-2 + (2 - 0)). Solve a**4 + f*a**4 + 0*a**2 + 0*a**2 = 0 for a.
0
Let c(d) be the first derivative of -d**4/4 + 3*d**2/2 + 2*d + 1. Factor c(b).
-(b - 2)*(b + 1)**2
Let n(c) be the second derivative of c**6/30 - c**5/20 - c**4/12 + c**3/6 - 16*c. Solve n(d) = 0.
-1, 0, 1
Let u = 8 - 3. Suppose 0 = 2*w + 2, -w = -u*x + 2*w + 18. Factor -5*b**4 - 6*b**2 + 11*b**4 - 3*b + 0*b + 3*b**x.
3*b*(b - 1)*(b + 1)*(2*b + 1)
Let z(t) = 4*t**4 - t**2 - 3*t + 3. Let m(p) = 9*p**4 - 2*p**2 - 7*p + 7. Let i be (-1)/(-4) - 58/8. Let w(n) = i*z(n) + 3*m(n). Factor w(d).
-d**2*(d - 1)*(d + 1)
Let k be (-1)/(-3)*0 + 4. Solve -7*w**2 - 2*w**k - 2*w - 6*w**3 + w**2 + 0*w + 0*w = 0.
-1, 0
Factor 0 - 1/4*d**2 + 1/4*d.
-d*(d - 1)/4
Let k(h) = h**3 + h + 1. Suppose 0 = 3*u + 15 + 21. Let c(j) = 3*j**4 + 9*j**3 - 3*j**2 + 15*j + 12. Let s(n) = u*k(n) + c(n). Find g, given that s(g) = 0.
-1, 0, 1
Let z(y) be the third derivative of -y**7/8820 - y**6/630 - y**5/140 - y**4/24 - 6*y**2. Let h(n) be the second derivative of z(n). Factor h(j).
-2*(j + 1)*(j + 3)/7
Suppose 7 = 3*s + 1. Let 0*c**2 + 3 - c**2 - 7 + 3*c + s = 0. Calculate c.
1, 2
Let r be (5/(-10))/(5/10). Let d be r/(-3)*(13 - 12). Determine w, given that -d + 2/3*w**2 - 1/3*w = 0.
-1/2, 1
Factor -27/8*s**3 + 0 + 9/4*s**2 + 3/2*s**4 - 3/8*s.
3*s*(s - 1)**2*(4*s - 1)/8
Let v(s) = s**3 - 3*s**2 + s - 1. Suppose -y = -5*x + 20, 5*x = -y - 0 + 10. Let l be v(x). Factor 3*d**3 + 4*d - 3*d**2 - 2*d**3 - l*d.
d*(d - 2)*(d - 1)
Suppose -1 - 11 = -2*t. Let o(f) = -f**2 - 3. Let p(k) = -2*k**2 - 5. Let l(z) = t*p(z) - 10*o(z). Let l(b) = 0. What is b?
0
Let j(g) be the first derivative of g**6/4 - 11*g**5/5 + 13*g**4/2 - 7*g**3 + 9*g**2/4 - 7. Suppose j(x) = 0. Calculate x.
0, 1/3, 1, 3
Let s be 2 + -1 + 0/(-13). Let z(n) be the first derivative of 0*n - 1/6*n**4 + 2/3*n**2 + 2/9*n**3 + s. Factor z(p).
-2*p*(p - 2)*(p + 1)/3
Let x be 3/(-4) - (-45)/60. Factor -1/3*i**4 - 1/3*i**3 + x + 1/3*i + 1/3*i**2.
-i*(i - 1)*(i + 1)**2/3
Let g(k) be the first derivative of -2*k**3/3 - 3*k**2 - 4*k - 10. What is t in g(t) = 0?
-2, -1
Let z(h) be the second derivative of 0*h**3 + 0 + 1/30*h**4 - 1/150*h**5 + h - 3/2*h**2. Let u(s) be the first derivative of z(s). Factor u(j).
-2*j*(j - 2)/5
Let j(f) = 17*f**3 + 43*f**2 + 31*f - 9. Let u(m) = -8*m**3 - 21*m**2 - 15*m + 5. Let d(s) = -3*j(s) - 7*u(s). Factor d(z).
(z + 2)**2*(5*z - 2)
Let j(m) = 2*m**4 - 12*m**3 + 22*m**2 + 25*m + 3. Let w(x) = -x**4 + 11*x**3 - 21*x**2 - 25*x - 4. Let k(q) = 6*j(q) + 7*w(q). Let k(r) = 0. What is r?
-1, 2
Let -4/3*l - 8/3 + 4/3*l**2 = 0. Calculate l.
-1, 2
What is c in -3*c - 2*c**2 - 4*c + 6*c - c**3 = 0?
-1, 0
Let v(c) be the second derivative of -c**5/4 - 5*c**4/12 + 5*c**3/6 + 5*c**2/2 - 32*c. Factor v(h).
-5*(h - 1)*(h + 1)**2