2*l**3/3 - 2*l**2. Let t(q) be the first derivative of k(q). Factor t(w).
w**3*(w + 1)
Let r(i) be the first derivative of 1/105*i**5 + 0*i**3 - 1/84*i**4 - 1/420*i**6 - 1 + 0*i + 3/2*i**2. Let n(f) be the second derivative of r(f). Factor n(t).
-2*t*(t - 1)**2/7
Let l(c) be the third derivative of 0*c**4 + 1/160*c**6 + 0 - 1/40*c**5 - 2*c**2 + 0*c + 0*c**3. Factor l(g).
3*g**2*(g - 2)/4
Let i(t) be the third derivative of t**8/2520 + 2*t**7/1575 - t**6/300 - 4*t**5/225 - t**4/45 - 14*t**2. Let i(w) = 0. What is w?
-2, -1, 0, 2
Suppose 3 - 15 = -4*l. Let r(t) be the first derivative of 0*t - l - t**2 + 4/3*t**3 - 1/2*t**4. Solve r(b) = 0 for b.
0, 1
Factor -4/9*b - 2/3*b**2 - 1/9*b**4 + 8/9 + 5/9*b**3.
-(b - 2)**3*(b + 1)/9
Let c(l) be the third derivative of -7*l**2 - 1/120*l**5 + 0*l + 0 + 0*l**3 + 1/420*l**7 - 1/192*l**4 + 1/960*l**6. Factor c(i).
i*(i - 1)*(i + 1)*(4*i + 1)/8
Let q = -2176/9 - -242. Factor 0 + 2/3*k**3 - 2/3*k**4 + 0*k + 2/9*k**5 - q*k**2.
2*k**2*(k - 1)**3/9
Let c(o) = 11*o**4 - 12*o**3 + o**2 + 5*o - 5. Let l(g) = 5*g**4 - 6*g**3 + g**2 + 2*g - 2. Let n(s) = 2*c(s) - 5*l(s). Factor n(q).
-3*q**2*(q - 1)**2
Let f(w) = 7*w**3 + 28*w**2 + 60*w + 42. Let b(v) = -29*v**3 - 111*v**2 - 240*v - 169. Let o(x) = 2*b(x) + 9*f(x). Let o(d) = 0. What is d?
-2
Let j = 20 - 7. Factor j*d**2 - 5*d**2 + 0*d**2 + 4*d**5 - 4*d - 8*d**4.
4*d*(d - 1)**3*(d + 1)
Let a(l) = 6*l**5 + 4*l**4. Let t(m) = 11*m**5 + 12*m**4 + 12*m**5 - 5*m**5. Let h(d) = -8*a(d) + 3*t(d). Let h(n) = 0. What is n?
-2/3, 0
Let n = -5/63 + 298/2961. Let q = 99/235 - n. Factor q + 2/5*w**4 - 4/5*w**3 - 4/5*w**2 + 2/5*w**5 + 2/5*w.
2*(w - 1)**2*(w + 1)**3/5
Let u(k) = k**3 + 6*k**2 - 3*k - 3. Let j be u(-6). Let 2*h**3 - j*h**4 - 2*h + 0*h**3 + 14*h**4 + 1 = 0. Calculate h.
-1, 1
Let k(s) be the third derivative of 1/24*s**4 + s**2 + 0*s + 0*s**3 - 1/60*s**5 + 0. Solve k(j) = 0 for j.
0, 1
Let z(g) be the third derivative of -g**7/1260 - g**6/240 - g**5/120 - g**4/144 + 7*g**2. Factor z(m).
-m*(m + 1)**3/6
Suppose -15 = -3*m - 69. Let k be ((-6)/(-8))/(m/(-16)). What is o in -2/3 + 4/3*o**2 + 2/3*o + k*o**5 - 2/3*o**4 - 4/3*o**3 = 0?
-1, 1
Let c(j) = -j**3 + 9*j**2 - 2*j + 11. Let o be c(9). Let b = o + 11. Factor b*v**2 - 3*v**2 + 2*v - v.
v*(v + 1)
Let t(b) be the first derivative of 12*b**5/5 - 4*b**4 + 4*b**3/3 - 3. Solve t(y) = 0.
0, 1/3, 1
Let w(j) = -3*j**4 + 6*j**3 + 11*j**2 + 2*j. Let c(q) = 5*q**4 - 9*q**3 - 17*q**2 - 3*q. Let t(m) = 5*c(m) + 8*w(m). What is k in t(k) = 0?
-1, 0
Factor 0 + 2/5*b**3 - 2/5*b**4 - 2/5*b + 2/5*b**2.
-2*b*(b - 1)**2*(b + 1)/5
Let t(i) be the third derivative of 0 - 2/3*i**3 - 1/6*i**5 - 7/12*i**4 + 0*i + 4*i**2. Solve t(r) = 0.
-1, -2/5
Let v be 6/(-10) - 78/(-30). Find n such that -10 + 12 - n**v + 2*n**2 + 3*n = 0.
-2, -1
Let w = 28 - 28. Suppose s + 3*s = w. Solve 0*i**3 - 2/3*i**4 + 0 + 0*i + s*i**2 = 0 for i.
0
Let y(d) be the third derivative of -d**5/60 - 5*d**4/24 - d**3/3 + 2*d**2. Let z be y(-4). What is p in 2*p**4 - p**5 - 2*p**z + 5*p - 4*p + 0*p**4 = 0?
-1, 0, 1
Let l(p) be the first derivative of 2*p**3/63 - 16*p**2/21 + 128*p/21 + 15. Factor l(u).
2*(u - 8)**2/21
Suppose 5*k + 5*p - 17 = 13, 3*k - 4*p + 10 = 0. Let w be (-1)/(-1 + 0)*4. Factor 4*b + k*b**3 - 3*b**2 - w*b + b.
b*(b - 1)*(2*b - 1)
Suppose 7*t = 2*t. Factor -3/5*b**5 + 6/5*b**4 - 3/5*b**3 + t*b**2 + 0*b + 0.
-3*b**3*(b - 1)**2/5
Solve 12*a**3 + 5*a - 8*a - 13*a - a**5 - 32*a**2 + 28*a**4 + 9*a**5 = 0.
-2, -1/2, 0, 1
Let w(c) be the second derivative of c**5/110 - c**4/66 - 2*c**3/33 + 16*c. Solve w(g) = 0 for g.
-1, 0, 2
Let w(c) be the third derivative of -c**6/540 + c**5/45 - 11*c**4/108 + 2*c**3/9 - 18*c**2. Find v, given that w(v) = 0.
1, 2, 3
Suppose q - 1 = -4*a, -5*q + 12 = 4*a - 9. Let w(s) = 8*s**2 + 10*s + 8. Let o(y) = y**2 + y + 1. Let r(z) = a*w(z) + 6*o(z). Factor r(u).
-2*(u + 1)**2
Let h(w) = -8*w**4 + 5*w**3 + 3*w**2 + 3*w. Let c(l) = 17*l**4 - 10*l**3 - 7*l**2 - 7*l. Let a(n) = -3*c(n) - 7*h(n). Let a(m) = 0. What is m?
0, 1
Let n(a) = -a - 1. Let r(p) = p**2 - 1. Let b(v) = 8*v**2 - 14*v + 8. Let h(c) = b(c) + r(c). Let f(t) = h(t) + n(t). Solve f(s) = 0 for s.
2/3, 1
Let c be -2 - (-10 - (2 + -1)). Let a be ((-2)/(-6))/(1/c). Determine q so that -q**4 - q**2 + q**4 - 2*q**a - q**4 + 0*q**3 = 0.
-1, 0
Let m(x) = -9*x + 3*x**2 - 9*x**2 - 4*x**2 + 0 - x**3 + 2. Let o be m(-9). Let -8/7*p**5 + 16/7*p**3 - 2/7*p**4 - 2/7 + 4/7*p**o - 8/7*p = 0. Calculate p.
-1, -1/4, 1
Let a be (5/3)/(17/51). Let r be 26/10 + (-1)/(-1). Factor -r*w**4 - 8/5*w**2 + 2/5 + w**a + 22/5*w**3 - 3/5*w.
(w - 1)**4*(5*w + 2)/5
Suppose -g + 7 = o - 0*o, 3*g = 12. Let h be (1 - (-3)/(-4))*2. Factor 0*z + h*z**o - 1/2*z**4 + 0 + z**2.
-z**2*(z - 2)*(z + 1)/2
Factor -2*q - q - 3*q**2 - 3 - 4*q + q.
-3*(q + 1)**2
Let f = 71/111 - -1/37. Factor 0 - f*q**3 + 2/3*q - 2/3*q**2 + 2/3*q**4.
2*q*(q - 1)**2*(q + 1)/3
Let o(j) be the third derivative of j**9/20160 + j**8/30240 - j**5/30 + 3*j**2. Let g(i) be the third derivative of o(i). Factor g(m).
m**2*(9*m + 2)/3
Let o(n) be the second derivative of 3/70*n**5 + 0*n**2 - 5*n - 1/35*n**6 + 0 - 1/42*n**4 + 1/147*n**7 + 0*n**3. Suppose o(x) = 0. What is x?
0, 1
Let s(t) = t**2 + 8*t - 2. Let g be s(-6). Let c be ((-3)/(-21))/((-6)/g). Factor -10/3*d**2 - 1/3*d**5 - 10/3*d**3 - 5/3*d**4 - 5/3*d - c.
-(d + 1)**5/3
What is i in -12/7*i + 0 + 15/7*i**4 - 36/7*i**2 - 9/7*i**3 = 0?
-1, -2/5, 0, 2
Factor -f**2 - 9*f**3 + 4*f**3 - 9*f**2.
-5*f**2*(f + 2)
Let d(j) = -j**2 - j - 1. Let w(y) = 3*y**2 + y + 2. Let b(c) = -4*d(c) - w(c). Factor b(p).
(p + 1)*(p + 2)
Suppose 8 - 2 = 3*o. Let p be o/(-8)*1*-8. Determine h so that 2/5*h**3 + 4/5*h**p + 0 + 2/5*h = 0.
-1, 0
Let w = -17 + 30. Let v = w + -38/3. Factor -v*d**3 + 0 - 1/3*d + 2/3*d**2.
-d*(d - 1)**2/3
Let x = 110/3 + -36. Factor -2/3*o**3 + 2/3 - 2/3*o**2 + x*o.
-2*(o - 1)*(o + 1)**2/3
Let x(s) be the first derivative of s**4/2 + 2*s**3 + 3*s**2 + 2*s - 1. Suppose x(c) = 0. Calculate c.
-1
Let s(n) be the second derivative of -5*n**7/84 - n**6/4 - n**5/8 + 5*n**4/8 + 5*n**3/6 + 26*n. Let s(z) = 0. Calculate z.
-2, -1, 0, 1
Let x(l) be the second derivative of l**6/150 - l**5/50 - l**4/15 + l**3/15 + 3*l**2/10 + 11*l. Factor x(j).
(j - 3)*(j - 1)*(j + 1)**2/5
Suppose -2*k + 0 + 6 = -2*r, -4*r = 5*k - 15. Let o = -176/3 - -178/3. Factor 13/3*t + k*t**3 - o - 20/3*t**2.
(t - 1)**2*(9*t - 2)/3
Let n(k) be the first derivative of k**6/40 - k**5/20 - k**4/48 + k**3/12 + 2*k - 6. Let j(t) be the first derivative of n(t). Factor j(l).
l*(l - 1)**2*(3*l + 2)/4
Solve 4*u - 1/3*u**5 + 4/3 + 1/3*u**3 + 11/3*u**2 - u**4 = 0.
-2, -1, 2
Let l be (8/6)/(-8 - -10). Factor -l*y**2 + 0 + 0*y.
-2*y**2/3
Factor -1/5*i**4 + 0 + i**3 + 0*i - 4/5*i**2.
-i**2*(i - 4)*(i - 1)/5
Let p(b) be the first derivative of b**4/10 - 2*b**3/15 + 6. Find x, given that p(x) = 0.
0, 1
Let l be 4*(1 - 1 - -1). Factor 0*p**4 - 3*p**l + 2*p**4 + 2*p**2 - 1.
-(p - 1)**2*(p + 1)**2
Factor 45*w**3 + 1 + 8*w**2 + 12*w - 12*w**4 + 3 - 4*w**5 - 53*w**3.
-4*(w - 1)*(w + 1)**4
Let r be (-4)/6*45/(-2). Determine m, given that -12*m**3 + r*m**2 + 3 + 6*m**4 - 3 - 6*m - 3*m**4 = 0.
0, 1, 2
Let u(q) be the first derivative of 81*q**4/32 - 3*q**3/2 + q**2/4 + 12. Solve u(d) = 0.
0, 2/9
Let j be 2 - (-2894)/(-1320) - (-5)/25. Let l(w) be the third derivative of -j*w**4 + 0*w + 0 + 2*w**2 - 1/330*w**5 + 0*w**3. Suppose l(s) = 0. Calculate s.
-1, 0
Find w such that -5/4*w**4 + 0*w**3 + 10*w + 15/2*w**2 + 15/4 = 0.
-1, 3
Let i(g) be the second derivative of -g**7/1260 - g**6/1080 - g**4/12 - 4*g. Let l(n) be the third derivative of i(n). Factor l(a).
-2*a*(3*a + 1)/3
Suppose 3*n - 5*n = -4. Suppose n*p - 3 = k - 0*k, -p + 5*k = 3. Factor -2*f**3 + 0 + 8/5*f - 16/5*f**p.
-2*f*(f + 2)*(5*f - 2)/5
Suppose 0 = -t - 12*z + 14*z + 8, 5*z = -2*t - 11. Factor 0 + 2/15*y - 8/15*y**3 + 2/5*y**t.
-2*y*(y - 1)*(4*y + 1)/15
Let b(g) be the third derivative of -343*g**6/780 + 49*g**5/130 - 7*g**4/52 + g**3/39 + 6*g**2. Factor b(k).
-2*(7*k - 1)**3/13
Let w(g) be the third derivative of g**5/20 - g**4/4 + g**3/2 + 19*g**2. Find a, given that w(a) = 0.
1
Let c(v) = -2*v - v - 4*v + 6*v - 7. Let s be c(-9). Find t, given that -5*t**5 + 3 - 3 - s*t**3 