*n**2 - 25*n. Let q(k) = k**3 + 4*k**2 - 3*k. Let w(j) = 6*m(j) - 51*q(j). Suppose w(l) = 0. Calculate l.
-1, 0, 1/2, 1
Let y(i) be the third derivative of i**6/1080 - i**5/270 + i**4/216 - 15*i**2. Let y(a) = 0. What is a?
0, 1
Let v = -56/5 - -188/15. Let c be (-1)/(2/(-4)*2/4). Solve 2/3 + 0*l**3 + 2/3*l**c - v*l**2 + 0*l = 0.
-1, 1
Let u = 945/16 + -59. Let p(z) be the first derivative of u*z**4 + 0*z - 3 - 1/12*z**3 + 0*z**2. Factor p(w).
w**2*(w - 1)/4
Let z(i) be the first derivative of -i**4/42 - i**3/7 - 2*i**2/7 - 5*i + 3. Let o(c) be the first derivative of z(c). Factor o(t).
-2*(t + 1)*(t + 2)/7
Factor 2/5*m**2 - 4*m + 10.
2*(m - 5)**2/5
Suppose -3*c + 6*c - 117 = 0. Let x = c - 116/3. Find b such that 4/3*b**2 + x*b**3 + 2/3 + 5/3*b = 0.
-2, -1
Let u = 9 - 9. Let b be 4/10 - 40/225. Factor 0*l - b + u*l**3 + 4/9*l**2 - 2/9*l**4.
-2*(l - 1)**2*(l + 1)**2/9
Let p(x) = -2*x**4 + 14*x**3 - 31*x**2 + 40*x - 21. Let u(j) = j**4 - 7*j**3 + 15*j**2 - 20*j + 11. Let l(k) = -3*p(k) - 5*u(k). Suppose l(b) = 0. Calculate b.
1, 2
Factor 10/7 - 8/7*j - 2/7*j**2.
-2*(j - 1)*(j + 5)/7
Let j(y) be the second derivative of -1/120*y**5 - 1/18*y**4 + 0*y**2 - 1/12*y**3 + y + 0. Factor j(h).
-h*(h + 1)*(h + 3)/6
Let u(n) = n**3 - n + 2. Suppose 2*l = 4*l. Let g be u(l). Factor 6*r**2 + 2*r**5 - 6*r**4 - 2*r**3 + r**3 - g*r**3 + r**5.
3*r**2*(r - 2)*(r - 1)*(r + 1)
Let l(v) be the second derivative of -v**5/100 - v**4/60 + v**3/30 + v**2/10 - 2*v. Factor l(d).
-(d - 1)*(d + 1)**2/5
Let m(a) be the second derivative of -a**7/112 + a**6/60 + a**5/20 - 3*a**4/16 + 11*a**3/48 - a**2/8 + 11*a - 1. What is f in m(f) = 0?
-2, 1/3, 1
Let n be 3/6*32/(-30)*-5. Find r, given that 8/3*r + 2/3*r**2 + n = 0.
-2
Suppose -2*o + 5*o - 6 = 0. Find w, given that -2 + 2*w - 1/2*w**o = 0.
2
Let m(n) be the third derivative of n**6/40 - n**5/5 + 3*n**4/8 + 12*n**2. Determine j so that m(j) = 0.
0, 1, 3
Suppose -49 + 39 = -2*g. Let t(w) be the third derivative of -1/3*w**4 + 0 + 0*w - 2*w**2 + 4/3*w**3 - 1/10*w**g. Factor t(r).
-2*(r + 2)*(3*r - 2)
Suppose -2*q + 10 = 2*z, 3*z = -3*q + 5*z + 35. Find j such that -2*j**2 + 4*j**3 + 16*j**2 - q*j**4 + j**4 - 6*j**4 - 4*j = 0.
-1, 0, 2/7, 1
Suppose 3*b = 5*b - 2. Determine j so that -4*j + b + 0 + j**2 + 3 = 0.
2
Let l(b) = 27*b**3 - 6*b**2 - 9*b - 3. Let w(y) = -13*y**3 + 3*y**2 + 5*y + 1. Let f(x) = -4*l(x) - 9*w(x). Factor f(z).
3*(z - 1)*(z + 1)*(3*z - 1)
Suppose 2 = -4*d - 6. Let k = 5 + d. Factor -4*j**3 + 5*j**k - 2*j**5 + 4*j**3 + 2*j**4 - 3*j**3 - 2*j**2.
-2*j**2*(j - 1)**2*(j + 1)
Factor 0*k**2 + 14*k**2 - 5*k**3 + 7*k**2 + 5*k - 10 - 11*k**2.
-5*(k - 2)*(k - 1)*(k + 1)
Find w such that 2/5*w**4 - 1/5*w + 2/5*w**3 - 4/5*w**2 + 2/5 - 1/5*w**5 = 0.
-1, 1, 2
Determine t so that 3/5*t**4 + 9*t**3 + 111/5*t + 36/5 + 117/5*t**2 = 0.
-12, -1
Let f(x) be the second derivative of -3*x + 0*x**2 - 1/21*x**3 - 1/147*x**7 + 2/21*x**4 - 3/35*x**5 + 0 + 4/105*x**6. Factor f(t).
-2*t*(t - 1)**4/7
Let b(q) = q**2 + q + 1. Suppose 0 = -2*o + 7*o - 30. Let z(c) = 1 - 12 + o - 2*c - 3*c - 2*c**2. Let f(v) = 5*b(v) + z(v). Factor f(t).
3*t**2
Suppose -17*x = -13*x. Let z(i) be the third derivative of x*i**3 - 1/240*i**5 + 1/840*i**7 + 3*i**2 + 0*i + 0*i**4 + 0*i**6 + 0. What is u in z(u) = 0?
-1, 0, 1
Suppose 4*a - 5 - 11 = 0. Let j(n) be the second derivative of -3/4*n**a - 11/30*n**6 + 0*n**2 - 1/14*n**7 + 0 + 2*n - 1/3*n**3 - 3/4*n**5. Solve j(v) = 0.
-1, -2/3, 0
Let w(z) be the second derivative of 5*z**4/12 + 5*z**3 - 35*z**2/2 - 3*z - 4. Factor w(q).
5*(q - 1)*(q + 7)
Let k(s) be the third derivative of s**8/50400 - s**7/3150 + s**6/600 + 7*s**5/60 + s**2. Let b(m) be the third derivative of k(m). Let b(r) = 0. What is r?
1, 3
Factor 2/7*t**3 + 0 + 2/7*t + 4/7*t**2.
2*t*(t + 1)**2/7
Let r(i) be the third derivative of -i**8/24 + 10*i**7/63 - 11*i**6/60 + i**4/9 - i**2. Solve r(n) = 0 for n.
-2/7, 0, 2/3, 1
Suppose 0 = -5*j - 9 - 6. Let r = -3 - j. Factor -7*n**3 + 8*n**3 + n**2 + r*n**2.
n**2*(n + 1)
Factor -517*d**3 + 91*d**4 - 158*d**3 + 990*d**2 + 46 - 580*d + 44*d**4 + 74.
5*(d - 3)*(3*d - 2)**3
Let t(w) = w**4 + w + 1. Let l(v) = v**4 + 6*v**3 - 6*v**2 + 5*v + 3. Suppose 0 = 5*c + 5 - 0. Let k(q) = c*l(q) + 3*t(q). Factor k(z).
2*z*(z - 1)**3
Let c(i) = -i**2 - i - 1. Let u(r) = -4*r - 3*r + 6*r. Let h = -2 + -1. Let t(z) = h*u(z) + c(z). Factor t(m).
-(m - 1)**2
Let r(d) = -d**2 + 13*d - 7. Let p be r(12). Let f(c) = -c**2 + 6*c - 1. Let g be f(p). Factor 0*t + 0*t**3 + 1/5 - 2/5*t**2 + 1/5*t**g.
(t - 1)**2*(t + 1)**2/5
Factor 27 - 15*u - 15 - 12 + 5*u**2.
5*u*(u - 3)
Find y, given that -10*y**4 + 3 + 6*y**2 + y**4 - 3*y**5 + 2*y**3 - 8*y**3 + 9*y = 0.
-1, 1
Let i = 195 - 389/2. Factor -i + 3/4*t - 1/4*t**2.
-(t - 2)*(t - 1)/4
Let j = 5 + -4. Suppose -j = -3*a + 5. Factor -1/4*c**3 + 0*c**a + 0 + 0*c.
-c**3/4
Let p(u) = 6*u**3 - 7*u**2 + 4*u - 3. Let f(y) = y**3 - y**2 + y - 1. Let g(d) = 5*f(d) - p(d). What is o in g(o) = 0?
-1, 1, 2
Let g = 15 + -12. Let x(u) be the first derivative of -2/3*u**g - 8*u + 1 - 4*u**2. Factor x(t).
-2*(t + 2)**2
Let t(o) = -o - 11. Let r be t(-14). Let z(q) be the first derivative of 2/9*q**r - 2/9*q + 1 + 2/9*q**2. Suppose z(a) = 0. Calculate a.
-1, 1/3
Suppose 9 = 2*v + v. Factor -2*l**v + 9*l**2 + 1 - 1 - 7*l**2.
-2*l**2*(l - 1)
Let b(l) be the third derivative of l**7/840 - l**6/120 + l**5/80 - 4*l**2. Find i, given that b(i) = 0.
0, 1, 3
Factor -2/3*i**3 - 8/3 - 8*i + 2/3*i**5 + 2*i**4 - 22/3*i**2.
2*(i - 2)*(i + 1)**3*(i + 2)/3
Let z(c) = 10*c**2 + 5*c - 5. Let v(b) = -5*b**2 - 3*b + 2. Let t(g) = 5*v(g) + 3*z(g). Determine d so that t(d) = 0.
-1, 1
Let n(l) = -l**3 + 2*l**2 - 2*l + 1. Suppose 5*b = -3*m + 7*m + 1, -4*m + 9 = 5*b. Let v be n(b). Let -j + v - 1/2*j**2 = 0. What is j?
-2, 0
Let l(m) be the third derivative of 1/336*m**8 + 0 + 0*m + 0*m**5 + 0*m**4 - 3*m**2 + 0*m**6 + 1/105*m**7 + 0*m**3. Factor l(i).
i**4*(i + 2)
Let l(d) be the first derivative of -2 + 2/7*d**2 + 2/3*d**3 + 5/14*d**4 + 0*d. Factor l(x).
2*x*(x + 1)*(5*x + 2)/7
Let b(q) = -3*q**2 - q + 4. Let a(u) = -u**2 - u + 1. Let j(p) = 6*a(p) - 3*b(p). Let j(m) = 0. What is m?
-1, 2
Let o(w) = -w. Let v = -4 - -8. Let y(z) = -z**3 - z**2. Let x(b) = 4*b**3 + 4*b**2. Let m(d) = x(d) + 3*y(d). Let g(i) = v*o(i) + 2*m(i). Factor g(u).
2*u*(u - 1)*(u + 2)
Let v(s) = 8*s**2 - 7*s - 2. Let p(g) be the third derivative of 2*g**2 + 0 + 0*g + 1/24*g**4 + 0*g**3. Let j(o) = p(o) + v(o). Determine n so that j(n) = 0.
-1/4, 1
Let i(s) be the first derivative of 4*s**3/21 - 18*s**2/7 - 40*s/7 - 31. Factor i(w).
4*(w - 10)*(w + 1)/7
Let n(g) = g**4 - 3*g**3 + 3*g**2 + g - 4. Let p(w) = -5*w**4 + 13*w**3 - 12*w**2 - 4*w + 17. Let h(t) = 9*n(t) + 2*p(t). Factor h(l).
-(l - 1)**2*(l + 1)*(l + 2)
Suppose -2*o = 5 - 9. Solve -3/4*k + 3/4*k**4 - 1/2*k**o + 1/4*k**5 + 1/2*k**3 - 1/4 = 0 for k.
-1, 1
Factor -21*k**2 - 6*k - k**3 + 30*k**2 - 2*k**3.
-3*k*(k - 2)*(k - 1)
Let i be 2/20*1092/14. Determine o so that -48/5*o**4 + i*o - 24*o**3 - 6/5 - 27/5*o**2 = 0.
-2, -1, 1/4
Factor 2 - 2*j - 3*j**2 + 4*j**2 + 2 - 3.
(j - 1)**2
Let m be (3/2)/((-2)/(-2)) - 1. Suppose 3/2*n + m*n**2 + 1/2 - n**4 - 3/2*n**3 = 0. What is n?
-1, -1/2, 1
Let j(z) be the third derivative of -361*z**6/540 - 19*z**5/135 - z**4/108 - 3*z**2 - 4. Determine a, given that j(a) = 0.
-1/19, 0
Let d(c) = -c**3 + 5*c**2 + 11*c - 9. Let n be d(7). Let f = 278/9 + n. Determine o so that 8/3*o**3 - f*o**5 + 0 - 4/9*o - 10/9*o**2 - 2/9*o**4 = 0.
-2, -1/4, 0, 1
Let u(j) be the first derivative of j**4/12 + 4*j**3/9 - 16. Factor u(h).
h**2*(h + 4)/3
Let g be (-46)/138 + 20/6 + -1. Let p be (-3)/4*2/(-3). Let 1/6 + 1/2*t**g - 1/6*t**3 - p*t = 0. What is t?
1
Let d(y) be the first derivative of -3*y**4/8 + y**3/2 + 3*y**2/4 - 3*y/2 - 8. Factor d(b).
-3*(b - 1)**2*(b + 1)/2
Factor -4/13*i**2 - 6/13*i**3 + 0*i**4 + 0*i + 0 + 2/13*i**5.
2*i**2*(i - 2)*(i + 1)**2/13
Suppose 3*f + 5*q = 6, 3*f - 5*q - 10 = -2*f. Solve 3*d**3 + 0*d**f - d**3 - d**4 - d**2 = 0.
0, 1
Let h(i) = 40*i**3 - 80*i**2 + 48*i + 4. Let x(p) = -p**4 - 79*p**3 + 161*p**2 - 95*p - 7. Let d(w) = -7*h(w) - 4*x(w). Factor d(z).
4*z*(z - 1)**2*(z + 11)
Let h = -1 - -6. Suppose u - 20*u**2 + 7*u + 16*u**3 + h*u**4 - 5*