Factor -190/3*p**3 - 23/3*p**4 - 1/3*p**5 - 833/3*p - 658/3*p**2 - 343/3.
-(p + 1)**2*(p + 7)**3/3
Let d(u) be the second derivative of -u**7/168 + u**6/30 - u**5/16 + u**4/24 + 4*u. Determine r, given that d(r) = 0.
0, 1, 2
Let k = -3/20 - -19/20. Factor -2/5 + k*t - 2/5*t**2.
-2*(t - 1)**2/5
Let j(y) = -y**3 - 6*y**2 + 3. Let c be j(-6). Find o, given that -5*o**c - 4*o + 6*o**2 + 5*o**3 + o + 3*o**3 - 6 = 0.
-2, -1, 1
Factor q**3 + 4 - 4*q**2 - 9*q**3 + 2*q**5 + 28*q - 6*q - 16*q.
2*(q - 2)*(q - 1)*(q + 1)**3
Let n be (-34)/12 - (-2)/(-12). Let k be (n/(-9))/(2/3). Factor 1/4*r**2 - k*r + 1/4.
(r - 1)**2/4
Let q(k) be the third derivative of -k**7/5040 + k**6/1440 - k**4/8 + k**2. Let j(a) be the second derivative of q(a). Solve j(f) = 0.
0, 1
Let i(v) be the second derivative of -3*v**5/20 + v**4/4 + v**3/2 - 3*v**2/2 - 16*v. Factor i(u).
-3*(u - 1)**2*(u + 1)
Suppose -3*f - 2*i = -2 - 68, -f + 27 = -3*i. Suppose 2*b - 5*o = f, 7*o - 2*o + 30 = 5*b. Factor 8/9*x**2 - 8/3*x**4 + 2/9*x + b*x**5 + 0 - 4/9*x**3.
2*x*(x - 1)**2*(3*x + 1)**2/9
Factor -u + 5*u**2 - 323 - 24*u + 343.
5*(u - 4)*(u - 1)
Let o(x) be the first derivative of -x**3/18 + x/6 - 8. Factor o(k).
-(k - 1)*(k + 1)/6
Let a(b) = b**3 + 22*b**2 + 126*b - 5. Let f(l) = -l + 1. Let d(u) = -a(u) - 5*f(u). Find x such that d(x) = 0.
-11, 0
Let b(r) = r**2. Let g(v) = 19*v**2 - 24*v + 9. Let l(h) = 3*b(h) - g(h). What is j in l(j) = 0?
3/4
Let v(m) be the second derivative of -25*m**7/56 + 9*m**6/8 - 9*m**5/10 + m**4/4 + 6*m. Factor v(c).
-3*c**2*(c - 1)*(5*c - 2)**2/4
Let f(b) = b**3 - 7*b**2 + 7*b - 5. Let d be f(6). Let j be 54/45 - (0 + d). Solve 0 - 1/5*a**2 - j*a + 1/5*a**4 + 1/5*a**3 = 0.
-1, 0, 1
Let u(b) be the first derivative of 49*b**5/150 - 4*b**3/15 - 2*b**2 + 4. Let z(y) be the second derivative of u(y). Factor z(p).
2*(7*p - 2)*(7*p + 2)/5
Suppose 3*q - 3*x = 4*q - 9, 19 = 5*q + 2*x. Factor -2*d**2 - d - 5/4*d**q - 1/4*d**4 + 0.
-d*(d + 1)*(d + 2)**2/4
Let m be (432/84)/((-2)/(-21)). Let i be (1/3)/(21/m). Suppose -2/7*h**3 - i*h - 6/7*h**2 - 2/7 = 0. What is h?
-1
Let t(v) = -v**3 + 18*v**2 - 17*v + 5. Let h(f) = 3*f**3 - 63*f**2 + 60*f - 18. Let p(d) = 5*h(d) + 18*t(d). Suppose p(x) = 0. Calculate x.
0, 1, 2
Suppose -x - f + 11 = x, -5*f = -x - 11. Determine s so that -6*s**x - 3*s**4 + 2*s**3 - 2*s**5 + 9*s**4 = 0.
-1, 0, 1
Factor -2/11*b**3 + 26/11*b - 14/11 - 10/11*b**2.
-2*(b - 1)**2*(b + 7)/11
Let y(z) be the second derivative of z**4/42 + 20*z**3/21 + 100*z**2/7 + 3*z. Find i such that y(i) = 0.
-10
Let d(o) be the first derivative of 0*o + 1/12*o**4 - 4 + 0*o**2 + 2/15*o**5 + 0*o**3. Factor d(u).
u**3*(2*u + 1)/3
Let g(o) be the third derivative of 3/112*o**8 + 0*o - 11/70*o**7 + 11/20*o**5 + 0 - 4*o**2 + 19/120*o**6 + 2/3*o**3 - o**4. Suppose g(l) = 0. What is l?
-1, 1/3, 2
Suppose o = -4*p + 4, -2*o + p - 1 + 0 = 0. Find h such that o*h - 1/2*h**5 - 3/2*h**3 - 1/2*h**2 + 0 - 3/2*h**4 = 0.
-1, 0
Let i(c) be the third derivative of -c**6/240 - c**5/24 - c**4/12 + 14*c**2. Find r such that i(r) = 0.
-4, -1, 0
Determine q, given that -2*q**4 - 10*q + 3 + 12*q**4 - 1 - 5*q**5 + 3*q**5 - 20*q**3 + 20*q**2 = 0.
1
Let m(w) = w**3 + 31*w**2 + 21*w - 20. Let b(t) = 6*t**2 + 4*t - 4. Let c(x) = -11*b(x) + 2*m(x). Find r such that c(r) = 0.
-1, 1, 2
Let s = -33 + -17. Let g be 16/s*(-30)/12. Factor 2/5 + 6/5*i + g*i**2.
2*(i + 1)*(2*i + 1)/5
Suppose -f = 16*l - 18*l + 4, 0 = 4*f - 16. Determine g, given that 0*g**2 + 1/2*g**5 + 0*g - g**3 + 0 + 1/2*g**l = 0.
-2, 0, 1
Let h(s) = s**2 + s - 2. Suppose 0 = 3*a - 5 - 1. Let r(w) = 3*w**2 + w - 4. Let t(c) = a*r(c) - 5*h(c). Factor t(n).
(n - 2)*(n - 1)
Let p(g) be the third derivative of -g**5/15 - 4*g**4/3 - 32*g**3/3 - 4*g**2. Factor p(n).
-4*(n + 4)**2
Solve 2/23*h**3 + 0*h**2 + 0 + 2/23*h**4 + 0*h = 0.
-1, 0
Factor -27/2 - 3/2*b**4 + 6*b**3 + 3*b**2 - 18*b.
-3*(b - 3)**2*(b + 1)**2/2
Let d(l) be the second derivative of 1/12*l**4 + 5*l - l**2 + 1/6*l**3 + 0. Factor d(r).
(r - 1)*(r + 2)
Let c = -14 - -18. Find v, given that 0*v - 2*v**3 - c*v**4 + 2*v**2 - 4*v + 6*v**3 + 2*v**2 = 0.
-1, 0, 1
Let f(p) be the third derivative of -p**6/180 - p**5/30 - p**4/12 - p**3/2 + 3*p**2. Let j(r) be the first derivative of f(r). Factor j(u).
-2*(u + 1)**2
Let h(o) be the first derivative of 0*o**3 + 3 + 0*o**2 + 2/5*o**5 + 0*o**4 - 1/6*o**6 + 0*o. What is x in h(x) = 0?
0, 2
Let v(i) be the first derivative of -i**5/210 + i**4/42 - i**3/21 - 4*i**2 + 4. Let x(g) be the second derivative of v(g). Let x(z) = 0. What is z?
1
Let h(g) be the second derivative of -1/100*g**5 - 2/15*g**3 + 1/15*g**4 - 2*g + 0 + 0*g**2. Factor h(a).
-a*(a - 2)**2/5
Let a(h) = 17*h**4 - 58*h**3 + 53*h**2 - 15*h. Let p(z) = -35*z**4 + 115*z**3 - 105*z**2 + 30*z. Let f(k) = 5*a(k) + 3*p(k). Find n such that f(n) = 0.
0, 3/4, 1
Let z(k) = k**3. Let s = 4 - 0. Let t(v) = 2*v + 11*v**3 - s*v**2 - v**3 - 4*v. Let r(n) = -t(n) + 12*z(n). Let r(c) = 0. What is c?
-1, 0
Let w(k) be the third derivative of -k**7/3780 + k**5/540 - k**3/3 - 5*k**2. Let s(x) be the first derivative of w(x). Factor s(o).
-2*o*(o - 1)*(o + 1)/9
Let u(r) be the second derivative of 2*r**7/21 - 2*r**5/5 + 2*r**3/3 + 8*r. Solve u(j) = 0.
-1, 0, 1
Let v(x) be the second derivative of x**5/150 - x**4/90 - 4*x**3/45 + 4*x**2/15 + 31*x. Factor v(d).
2*(d - 2)*(d - 1)*(d + 2)/15
Determine n, given that -2/7*n**5 + 2/7*n - 20/7*n**2 + 8/7*n**4 + 12/7 + 0*n**3 = 0.
-1, 1, 2, 3
Let m(u) = -14*u**3 + 20*u**2 - 32*u + 9. Let l(w) = -5*w**3 + 7*w**2 - 11*w + 3. Let v be ((-20)/(-25))/(2/(-15)). Let i(c) = v*m(c) + 17*l(c). Solve i(a) = 0.
-3, 1
Determine h, given that 2*h**4 + 32*h + 7*h**4 - 9*h**2 + 0*h**2 - 29*h - 3*h**3 = 0.
-1, 0, 1/3, 1
Let r(h) = -3*h**5 - 6*h**4 + 9*h**3 + 19*h**2 - 5*h - 7. Let o(y) = -3*y**5 - 6*y**4 + 9*y**3 + 18*y**2 - 6*y - 6. Let d(v) = 7*o(v) - 6*r(v). Factor d(n).
-3*n*(n - 1)**2*(n + 2)**2
Let x be -13 + -1 - (-2 - 0). Let s be 10/3 - 8/x. Factor 0*b**3 + 14*b**3 - s - 32*b**2 - 8*b + 30*b.
2*(b - 1)**2*(7*b - 2)
Let w be (11 + -5)/((-8)/(-6)). Let i = -4 + w. Factor i*b**4 - 1/2 + b - b**3 + 0*b**2.
(b - 1)**3*(b + 1)/2
Let u(g) be the first derivative of g**3/6 + g**2 + 3*g/2 - 16. Factor u(r).
(r + 1)*(r + 3)/2
Let c = 13/5 - 29/15. Let j = -28 + 32. Determine t, given that 2/3*t**j + c*t**3 - 2/3*t**2 + 0 - 2/3*t = 0.
-1, 0, 1
Let 0 + 0*z + 21/4*z**3 + 3/2*z**2 + 15/4*z**4 = 0. Calculate z.
-1, -2/5, 0
Let b(j) be the first derivative of -j**6/24 - 4. Determine z so that b(z) = 0.
0
Let l(a) be the second derivative of -a**7/21 + a**6/5 - 3*a**5/10 + a**4/6 + 12*a. Factor l(x).
-2*x**2*(x - 1)**3
Let p be (-9)/(-4)*(-1)/(-3)*4. Let s(w) be the first derivative of -3 + 5/12*w**4 + 1/3*w**2 + 0*w - 7/9*w**p. Suppose s(y) = 0. What is y?
0, 2/5, 1
Let p(g) = -2*g**4 + 14*g**3 + g**2 - 5*g - 5. Let j(k) = k**4 - k**3 + k**2 + k + 1. Let l(t) = -5*j(t) - p(t). Suppose l(s) = 0. What is s?
-2, -1, 0
Let c = 136 - 131. Let o(p) be the third derivative of -5/24*p**4 + 0 + 1/20*p**c - 4*p**2 + 0*p - 1/3*p**3. Suppose o(y) = 0. Calculate y.
-1/3, 2
Suppose -2*s = -0 - 2. Suppose 4*c - s = 11. Solve 0*f + f**4 + 0 + 1/3*f**2 + 4/3*f**c = 0.
-1, -1/3, 0
Let i(m) be the third derivative of -m**6/30 + m**5/15 + m**4/6 - 2*m**3/3 + 23*m**2. Factor i(r).
-4*(r - 1)**2*(r + 1)
Let t(g) = -4*g**4 - 12*g**3 - 7*g**2 - 9*g + 5. Let q(s) = 10*s**4 + 30*s**3 + 18*s**2 + 22*s - 12. Let p(k) = -5*q(k) - 12*t(k). Factor p(a).
-2*a*(a + 1)**3
Factor -7/8*o**3 + 1/8*o**5 + 15/8*o**2 + 9/4*o - 3/8*o**4 + 0.
o*(o - 3)**2*(o + 1)*(o + 2)/8
Let b(s) be the third derivative of -s**7/8820 + s**6/840 - s**5/210 - s**4/8 - 2*s**2. Let l(k) be the second derivative of b(k). Solve l(w) = 0 for w.
1, 2
Let r be (-1)/(2 - 228/116). Let o = r + 89/3. Factor -2/3 + 4/3*f - o*f**2.
-2*(f - 1)**2/3
Let k(s) = 2*s**2 - 2*s - 1. Let a be k(2). Let m = 1339/4 + -334. Determine w, given that 0*w**a + 0*w - 3/4 + 3/2*w**2 - m*w**4 = 0.
-1, 1
Let y(c) = -155*c**4 + 95*c**3 - 20*c**2 + 25*c - 25. Let s(z) = -39*z**4 + 24*z**3 - 5*z**2 + 6*z - 6. Let h(f) = -25*s(f) + 6*y(f). Factor h(q).
5*q**2*(3*q - 1)**2
Let t(l) = -l**5 + l**3 - l + 1. Let y(g) = -6*g**5 - 8*g**4 - 4*g**3 + 4*g**2 + 6*g + 8. Let s be 1/(