-1/2*l**3 + 1/4*l + 0*l**c + 1/4*l**5 + 0*l**2 + 0.
l*(l - 1)**2*(l + 1)**2/4
Find g such that 5*g + 13*g**2 + g**2 + 2*g**4 + 1 + 7*g**3 - 5*g**2 = 0.
-1, -1/2
Let v(k) be the second derivative of k**6/105 - 9*k**5/35 + 97*k**4/42 - 48*k**3/7 + 64*k**2/7 + 3*k. Factor v(y).
2*(y - 8)**2*(y - 1)**2/7
Let h(s) = -s**3 + 2*s**2 - 2*s - 2. Let j(w) = 2*w**3 - 3*w**2 + 3*w + 3. Let v(p) = -10*h(p) - 6*j(p). Suppose v(t) = 0. What is t?
-1, 1
Let y = -16 - -3. Let m be (-25 - y)*(-2)/42. Factor -m*z - 2/7 - 2/7*z**2.
-2*(z + 1)**2/7
Let n(b) be the second derivative of b**4/30 - b**2/5 + 4*b. Factor n(k).
2*(k - 1)*(k + 1)/5
Let m be (522/315)/((-12)/(-2)). Let h = 2/35 + m. Let 1/3*q**3 + 0*q + h*q**2 + 0 = 0. What is q?
-1, 0
Let y = -7 + 12. Suppose 9 = 2*m + y. Find v, given that 1/4 + 1/2*v + 1/4*v**m = 0.
-1
Let j(b) = b**2 - 2. Let o be j(-2). Let n be 3/(-6)*-2 + o. Factor -2*f + 6*f**3 - f**5 - 3*f**3 - f**5 + f**n.
-2*f*(f - 1)**2*(f + 1)**2
Let p = -121 - -123. Let j(m) be the second derivative of 0*m**2 - 1/72*m**4 + 0*m**3 - p*m + 0. Factor j(b).
-b**2/6
Suppose k = u + 6, -4*k - u = -5 - 14. Let 1/2*n**4 - n**3 - n**2 + 1/2 + 1/2*n**k + 1/2*n = 0. Calculate n.
-1, 1
Let s(n) be the first derivative of 3*n**4/32 + n**3/8 - 3*n**2/16 - 3*n/8 + 4. Determine c so that s(c) = 0.
-1, 1
Suppose f**5 + 2*f**5 - f**3 - f**5 - 5*f**3 + 4*f**2 = 0. Calculate f.
-2, 0, 1
Let h = 5 - 3. Let k = 12/5 - 2. Solve -k*l**h + 0*l + 2/5 = 0 for l.
-1, 1
Let s = -26 - -29. Let w(m) be the first derivative of 2/3*m**s + 1 + 0*m - m**2. Factor w(o).
2*o*(o - 1)
Determine y, given that y + 1/2 + 1/2*y**2 = 0.
-1
Let s(i) = -i**2 - 6*i + 19. Let o be s(-8). Suppose g + 14 = 4*p, 4*g = o*p - p. What is k in 3/4*k**p + 0 - 3/2*k**3 + 0*k + 3/4*k**2 = 0?
0, 1
Suppose r = -5*j + 30, 11*j = 14*j + 4*r - 35. Find c such that 0*c**4 + 0 + 3/4*c**j + 0*c**2 + 3/4*c - 3/2*c**3 = 0.
-1, 0, 1
Let n(t) be the third derivative of 6*t**7/35 - 7*t**6/40 - 11*t**5/20 + 7*t**4/8 - t**3/2 - 9*t**2. Suppose n(p) = 0. Calculate p.
-1, 1/4, 1/3, 1
Let y(h) be the third derivative of h**7/56 - h**6/24 - h**5/48 + 5*h**4/48 + h**2. Determine s, given that y(s) = 0.
-2/3, 0, 1
Let f(a) be the second derivative of 2*a + 2/3*a**3 - a**2 + 0 - 1/6*a**4. Factor f(s).
-2*(s - 1)**2
Let y(r) be the second derivative of 4/5*r**2 + 9*r + 1/30*r**4 + 4/15*r**3 + 0. Factor y(z).
2*(z + 2)**2/5
Let p(g) be the first derivative of -g**8/1176 + g**7/735 - g**2/2 - 2. Let y(b) be the second derivative of p(b). Solve y(w) = 0 for w.
0, 1
Suppose 2*w**3 - 2/3*w**5 - 2/3*w**4 - 4/3*w + 0 + 2/3*w**2 = 0. What is w?
-2, -1, 0, 1
Let p(x) = x - 4. Let a be p(6). Let g be (3 - a)*0/3. Factor g + 0*n**2 - 1/4*n**3 + 1/4*n.
-n*(n - 1)*(n + 1)/4
Let k = 4 - -6. Suppose k = -h + 6*h. Factor 1 - 4*m**3 - m**h + 5*m**3 - 2*m**3 + m.
-(m - 1)*(m + 1)**2
Let d(o) be the second derivative of -o**4/3 + 4*o**3/3 + 6*o**2 + o. Factor d(n).
-4*(n - 3)*(n + 1)
Let m(u) be the second derivative of u**5/70 + u**4/21 - u**3/21 - 2*u**2/7 - 2*u. Suppose m(o) = 0. Calculate o.
-2, -1, 1
Let f(t) = 3*t**4 + 3*t**3 + 3*t - 3. Let x(u) = -u**3 - u + 1. Let r(y) = f(y) + 3*x(y). Suppose r(j) = 0. Calculate j.
0
Let z(x) be the second derivative of -x**4/12 + 5*x**3/6 - 2*x**2 - 5*x. Factor z(g).
-(g - 4)*(g - 1)
Suppose 113*p + o = 109*p + 16, p + 5*o + 15 = 0. Find a such that -3*a**p + 0 + 27/4*a**2 + 3/2*a + 3/2*a**3 - 27/4*a**4 = 0.
-2, -1, -1/4, 0, 1
Let d(u) be the second derivative of -u**5/30 + u**4/9 - 7*u. Find j such that d(j) = 0.
0, 2
Factor -20*p**3 + 3*p**2 + 10*p**4 - 5*p**4 - 3*p**2.
5*p**3*(p - 4)
Let u(t) = -t + 4 - t**2 - t - 4*t. Let y be u(-6). Determine h so that 0 + h**3 + 0 - 2*h**y + h**2 = 0.
-1/2, 0, 1
Let t = 5 + -9. Let r(g) = -2*g**2 + 8*g - 2. Let q(a) = -3*a**2 + 9*a - 3. Let j(n) = t*q(n) + 5*r(n). Factor j(v).
2*(v + 1)**2
Let b(h) be the third derivative of -h**7/420 - h**6/40 - h**5/10 - h**4/6 + 7*h**2. Suppose b(k) = 0. Calculate k.
-2, 0
Suppose s - 20 = -4*r, s = -3*r - 0 + 16. Determine n, given that -17*n + 6*n**r + 3 - 3*n**4 + 13*n**2 + 5*n**2 + 5*n - 12*n**3 = 0.
1
Let o(g) = 2*g**2 - 6*g + 6. Let s be o(3). Factor 3*d**2 + 4*d - 4*d + s*d + 3.
3*(d + 1)**2
Let l(d) = d**2 - 12*d + 4. Let b be l(8). Let f be (-8)/28 - 15/b. Factor 1/4*v**2 + 0 + f*v.
v*(v + 1)/4
Let n(m) = -3*m**3 + 2*m**2 - 10*m + 6. Let c(p) = 2*p**3 - 2*p**2 + 10*p - 6. Let t(y) = -5*c(y) - 4*n(y). Factor t(h).
2*(h - 1)**2*(h + 3)
Let z(q) be the second derivative of -q**7/210 - 7*q**6/360 - q**5/60 + q**4/24 + q**3/2 - 3*q. Let x(o) be the second derivative of z(o). Factor x(w).
-(w + 1)**2*(4*w - 1)
Let f(w) be the second derivative of -w**6/90 + w**5/60 + w**4/12 - 5*w**3/18 + w**2/3 - 6*w. Solve f(v) = 0 for v.
-2, 1
Factor 6 - h**2 - 10 + 5.
-(h - 1)*(h + 1)
Let w be 5 - (1 + 1) - 0. Let y = 1 + w. Factor 2*u**2 + u**5 - 1 - 2*u**3 + 0*u**4 - u**y + 0 + u.
(u - 1)**3*(u + 1)**2
Let s(h) be the first derivative of -2*h**5/5 + 6*h**4/7 - 2*h**3/7 - 2*h**2/7 - 15. Find z such that s(z) = 0.
-2/7, 0, 1
Let i(j) be the first derivative of -3 + 1/16*j**4 + 0*j + 1/20*j**5 - 1/8*j**2 - 1/12*j**3. Suppose i(h) = 0. Calculate h.
-1, 0, 1
Let s be -6 + -15*16/(-36). Solve 4/3 - 2/3*j**3 + 2/3*j**4 + s*j - 2*j**2 = 0 for j.
-1, 1, 2
Let p(y) = -y**3 - 7*y**2 - 9*y - 14. Let j be p(-6). Let 16*k**3 + k - 49*k**4 - 4*k**2 + 61*k**j - 9*k = 0. Calculate k.
-1, 0, 2/3
Let b(d) be the second derivative of d**8/8400 - d**6/900 + d**4/120 + d**3/2 - d. Let f(v) be the second derivative of b(v). Factor f(l).
(l - 1)**2*(l + 1)**2/5
Factor 10*r + 12*r**5 - 5*r - 4*r - 2*r**3 - 11*r**5.
r*(r - 1)**2*(r + 1)**2
Suppose 5*m = 21 - 1. Suppose 24 = 4*r - 24. Factor -6*i + 4 + 4*i**m + r*i**3 - 3*i - 3*i + i**2.
(i + 2)**2*(2*i - 1)**2
Let h be 12/(-7) + 8 + -6. Let h + 4/7*o + 2/7*o**2 = 0. What is o?
-1
Suppose -c - 2 = 5*a, -c - 4 = -5*a + c. Suppose 2/7*i**2 + a + 2/7*i = 0. What is i?
-1, 0
Let k(g) be the second derivative of 1/24*g**4 - 1/60*g**5 - 3*g - g**2 + 0*g**3 + 0. Let r(m) be the first derivative of k(m). Factor r(y).
-y*(y - 1)
Suppose -4*n + 2*n + 13 = -3*w, -2*w - 12 = -3*n. Let j = -12 - -21. Factor 0*m - m + 5*m**3 + 24*m**4 + 8*m**n - 27*m**3 - j*m**5.
-m*(m - 1)**2*(3*m - 1)**2
Let k(w) be the second derivative of w**7/28 + 2*w**6/5 + 9*w**5/5 + 17*w**4/4 + 23*w**3/4 + 9*w**2/2 + 2*w - 1. What is o in k(o) = 0?
-3, -2, -1
Let w(u) be the first derivative of 0*u**4 + 0*u**3 + 0*u + 1/3*u**6 - 2/5*u**5 + 0*u**2 - 5. Factor w(k).
2*k**4*(k - 1)
Let r(b) be the first derivative of 0*b**4 + 0*b**2 + 2/3*b**3 + 0*b**5 + 0*b - 1/180*b**6 - 1. Let m(y) be the third derivative of r(y). Solve m(c) = 0.
0
Suppose -4*h = -0*h - 8. Factor 0 + 1/3*x**h + 0*x.
x**2/3
Let c = -46 + 51. Find a, given that -50/9*a**c + 0 - 20/3*a**4 - 8/9*a + 8/3*a**2 + 22/9*a**3 = 0.
-1, 0, 2/5
Let w(r) be the third derivative of r**6/200 + r**5/50 - r**4/40 - r**3/5 - 8*r**2. Factor w(b).
3*(b - 1)*(b + 1)*(b + 2)/5
Let v(n) be the third derivative of n**9/9072 - n**8/1680 + n**7/840 - n**6/1080 - 2*n**3/3 - 7*n**2. Let o(i) be the first derivative of v(i). Factor o(x).
x**2*(x - 1)**3/3
Factor -5*q**4 - 1875*q + 20*q**2 + 1875*q.
-5*q**2*(q - 2)*(q + 2)
Let h(o) be the second derivative of -o**6/150 - o**5/100 - 11*o. Suppose h(y) = 0. What is y?
-1, 0
Factor -v**3 - 3/7*v**2 + v + 5/7*v**4 - 2/7.
(v - 1)**2*(v + 1)*(5*v - 2)/7
Let y(j) be the second derivative of -j**6/200 - j**5/100 + j**4/40 + j**3/10 - j**2/2 - 2*j. Let w(f) be the first derivative of y(f). Factor w(d).
-3*(d - 1)*(d + 1)**2/5
Suppose 0 = 3*w + m + 3*m, m = w. Suppose -12 = z - w*z - 3*n, 2*z - n = -4. Determine l, given that 2/5 - 2/5*l**2 + z*l = 0.
-1, 1
Let f be 18/8 - ((-55)/20 + 2). Let g(b) be the first derivative of 12*b**2 + 3 + 3/4*b**4 + 5*b**f + 12*b. Solve g(p) = 0.
-2, -1
Let h(x) be the third derivative of x**6/40 - x**5/20 - 17*x**2. Determine g so that h(g) = 0.
0, 1
Let k(w) = w**3 - 10*w**2 - 10*w - 9. Let c be k(11). Suppose 2*p + 2 = m + 1, 3*p = -c*m + 16. Factor -v - 2*v**3 + 2*v**p + 1/5 + v**4 - 1/5*v**5.
-(v - 1)**5/5
Suppose 2*t = -4*x + 2, -3*t = -5*x + 4*x + 18. Determine b so that x*b**4 - 2*b - 13/3*b**2 + 4/3 + 7/6*b**3 + 5/6*b**5 =