k + 1/2*k**3 + 0 - 1/2*k**4 = 0.
-1, 0, 1
Factor 8/3*m + 2/3*m**3 + 0 + 8/3*m**2.
2*m*(m + 2)**2/3
Let s(v) be the second derivative of -7*v**4/60 - 19*v**3/30 + 3*v**2/5 + v. Factor s(q).
-(q + 3)*(7*q - 2)/5
Let q(l) be the second derivative of -l**7/11340 + l**6/1080 - l**5/270 - l**4/6 - 3*l. Let i(h) be the third derivative of q(h). Factor i(o).
-2*(o - 2)*(o - 1)/9
Let o be 0/(-5 - (-14 + 7)). Suppose 4 - 7 = -y. Factor o*j**y - 1/3*j**2 - 1/6*j + 1/3*j**4 + 0 + 1/6*j**5.
j*(j - 1)*(j + 1)**3/6
Let p(y) be the first derivative of -7 - 6*y - 9/2*y**2 - y**3. Let p(c) = 0. What is c?
-2, -1
Let n(k) be the first derivative of -3*k**5/5 + 3*k**4/4 + k**3 - 3*k**2/2 + 5. Factor n(j).
-3*j*(j - 1)**2*(j + 1)
Let q = 709/55 + -122/11. Suppose 3/5*t**2 + q*t + 6/5 = 0. Calculate t.
-2, -1
Suppose -12 = 3*s - 9*s. Solve -4*j - 2*j**3 + 4*j**s + 6*j**3 - 4 - j**2 + j**4 = 0.
-2, -1, 1
Let m(u) = -11*u**4 + 6*u**2 - 5*u. Let g(o) = 20*o - 2*o + 24*o**4 - 21*o**2 + 15*o**4. Let v(y) = -5*g(y) - 18*m(y). Solve v(i) = 0.
-1, 0, 1
Let w(m) be the second derivative of m**4/3 - 8*m**3/3 - 3*m. Factor w(g).
4*g*(g - 4)
Suppose 3*w + n = 4, 7*w + 4*n + 8 = 3*w. Factor 6/5*a + 3/5 - 6/5*a**w - 3/5*a**4 + 0*a**2.
-3*(a - 1)*(a + 1)**3/5
Let u = -3 - -5. Let h(p) = -4*p**2 - p + 8. Let w(j) = -2*j**2 + 4. Let s(v) = u*h(v) - 5*w(v). Factor s(f).
2*(f - 2)*(f + 1)
Let w(n) be the second derivative of n**7/1365 - n**6/780 - n**5/390 + n**4/156 + n**2 + 3*n. Let h(d) be the first derivative of w(d). Factor h(v).
2*v*(v - 1)**2*(v + 1)/13
Let z(t) = -4*t**3 + 8*t**2 - 4*t - 6. Let c(v) = 11*v**3 - 23*v**2 + 12*v + 17. Let b(y) = 6*c(y) + 17*z(y). Determine k, given that b(k) = 0.
-2, 0, 1
Factor -2*z**4 + 8/5*z**3 + 0*z**2 + 0*z + 0 + 2/5*z**5.
2*z**3*(z - 4)*(z - 1)/5
Factor -2/5*a**4 - 2/5 + 0*a**3 + 0*a + 4/5*a**2.
-2*(a - 1)**2*(a + 1)**2/5
Let s(q) be the third derivative of -q**5/135 + 2*q**4/27 - 8*q**3/27 - 47*q**2. Factor s(z).
-4*(z - 2)**2/9
Let d be 3 + (-3)/(-6)*0. Factor 4*l**2 + 0*l**4 + 15*l**d - 13*l**3 - 6*l**4.
-2*l**2*(l - 1)*(3*l + 2)
Let j be 3/((-49)/(-2) + -2). Let l(n) be the first derivative of -j*n**5 + 0*n**4 + 1 - 2/3*n + 0*n**2 + 4/9*n**3. Factor l(a).
-2*(a - 1)**2*(a + 1)**2/3
Let j(v) be the first derivative of 0*v + 0*v**2 - 2/11*v**4 + 4 - 2/11*v**3 - 2/55*v**5. Solve j(b) = 0.
-3, -1, 0
Let v = -67 - -69. Let o(t) be the second derivative of -1/80*t**5 + 0*t**v + 1/60*t**6 + 0*t**3 - 1/168*t**7 + 2*t + 0*t**4 + 0. Factor o(n).
-n**3*(n - 1)**2/4
Let f(m) = -13*m**3 - 19*m**2 + 53*m + 69. Let k(n) = 20*n**3 + 28*n**2 - 80*n - 104. Let l(u) = -8*f(u) - 5*k(u). Solve l(g) = 0.
-4, -1, 2
Let z = -1 + 1. Let c(g) be the first derivative of 1 + 1/20*g**5 + 1/4*g**2 - 1/4*g + z*g**3 - 1/8*g**4. Factor c(x).
(x - 1)**3*(x + 1)/4
Let q(h) be the third derivative of h**7/420 - 7*h**6/240 + 3*h**5/40 + 9*h**4/16 - 9*h**3/2 - 24*h**2. Factor q(j).
(j - 3)**3*(j + 2)/2
Let a(j) be the second derivative of 5*j**4/12 + 5*j**3/2 + 5*j**2 - 12*j. What is f in a(f) = 0?
-2, -1
Let w(r) be the third derivative of 1/180*r**6 - 7/144*r**4 - 1/18*r**3 + 0*r + 6*r**2 + 1/72*r**5 + 0. Let w(n) = 0. Calculate n.
-2, -1/4, 1
Suppose -b + 3*p + 28 = -2*p, 0 = -3*b + 4*p + 29. Suppose 0 = 2*k + t - 9, -b*k + 5*t - 1 - 5 = 0. What is h in 2*h**k - 2*h**2 + 0 - 2/3*h**4 + 2/3*h = 0?
0, 1
Let l be ((-42)/60 + 1)*8/6. Factor -4/5 - l*h + 2/5*h**3 + 4/5*h**2.
2*(h - 1)*(h + 1)*(h + 2)/5
Let c be ((-6)/(-4))/(2/8). Suppose -c = -s - s. Factor n**3 + n - 2*n**4 - 2*n**s - 2*n**3.
-n*(n + 1)**2*(2*n - 1)
Factor 10/3*i**3 + 1/3*i**4 + 0 + 0*i + 3*i**2.
i**2*(i + 1)*(i + 9)/3
Let j(n) be the second derivative of -n**4/6 - 4*n**3/3 + 5*n**2 + 20*n. Factor j(v).
-2*(v - 1)*(v + 5)
Let g(u) = -u**2 + u - 1. Let p(x) = 16*x**2 - 28*x + 16. Let n(r) = -20*g(r) - p(r). Find z such that n(z) = 0.
-1
Let c(u) be the third derivative of 0*u**4 + 0*u**3 + 0*u + 0 + 1/100*u**6 - 4*u**2 - 1/75*u**5. Solve c(q) = 0.
0, 2/3
Let c(k) be the first derivative of k**8/10080 + k**7/720 + k**6/144 + k**5/80 + k**3/3 - 6. Let a(t) be the third derivative of c(t). What is w in a(w) = 0?
-3, -1, 0
Suppose -7 = -2*w + 3. Suppose -3*t + 21 = -2*l + 3, w*l = 3*t - 27. Determine j, given that 0*j**2 - 1/2 + j**3 - j + 1/2*j**t = 0.
-1, 1
Let r be (8/14)/((-20)/(-56)). Determine c, given that r*c**2 + 2/5*c - 4/5*c**3 + 2/5*c**5 - 4/5 - 4/5*c**4 = 0.
-1, 1, 2
Let n = 160 - 158. Let -1/3 + 2/3*r - 1/3*r**n = 0. What is r?
1
Let v = -37 + 112/3. Let p = 0 + 0. Determine l, given that -v*l + 1/3*l**2 + p = 0.
0, 1
Factor -1/5 + 0*c**2 + 2/5*c**3 + 1/5*c**4 - 2/5*c.
(c - 1)*(c + 1)**3/5
Let r(q) be the second derivative of -7*q + 0*q**2 - 1/12*q**4 + 0*q**3 - 1/30*q**6 + 1/10*q**5 + 0. Factor r(o).
-o**2*(o - 1)**2
Let o(x) be the first derivative of -2*x**5/25 + x**4/2 - 16*x**3/15 + 4*x**2/5 - 33. Find s such that o(s) = 0.
0, 1, 2
Let u = -6 - -11. Let i = u - 2. Factor 3*j - i*j**2 - 4*j - 2*j.
-3*j*(j + 1)
Let n(u) be the first derivative of 36*u**5/5 + 21*u**4 + 64*u**3/3 + 8*u**2 + 5. Find z such that n(z) = 0.
-1, -2/3, 0
Let i(j) be the third derivative of 4*j**2 + 0*j + 1/75*j**6 + 0 + 1/15*j**3 + 1/25*j**5 + 1/15*j**4 + 1/525*j**7. Factor i(a).
2*(a + 1)**4/5
Let u(z) be the second derivative of -z**6/420 + 2*z**5/105 - z**4/21 + z**2/2 + 3*z. Let g(x) be the first derivative of u(x). Factor g(n).
-2*n*(n - 2)**2/7
Let r = 8 - 6. Suppose -d**3 + 3*d**2 - 4*d**3 - 3*d**4 + r*d + 2*d + d**2 = 0. What is d?
-2, -2/3, 0, 1
Let d be -6 + (-138)/(-24) + 9/4. Let h(o) be the second derivative of 0 + 0*o**3 + 1/54*o**4 - 1/90*o**5 + 0*o**d + o. Suppose h(k) = 0. Calculate k.
0, 1
Let m(h) = 6*h**3 - 2*h**2 - 4*h - 16. Let o = 2 - -3. Let c(n) = -2*n**3 + n**2 + n + 5. Let v(g) = o*m(g) + 16*c(g). Find b, given that v(b) = 0.
0, 1, 2
Suppose 18 + 3 = 3*s. Let i(u) be the third derivative of -3*u**2 + 0 + 1/540*u**6 + 0*u**5 + 0*u + 0*u**3 - 1/315*u**s + 0*u**4. Factor i(q).
-2*q**3*(3*q - 1)/9
Suppose -2*g**4 - 6*g**2 - 2*g - 8*g**3 + 2*g**3 - 2*g + 2*g = 0. Calculate g.
-1, 0
Suppose 5*t + 35 = 10*t. Let g be t/(-49) - (-11)/28. Find c such that -1/2*c + g + 1/4*c**2 = 0.
1
Factor -2/9*x**2 + 0 + 2/9*x**4 - 2/3*x**3 + 2/3*x.
2*x*(x - 3)*(x - 1)*(x + 1)/9
Let x(b) be the third derivative of -10*b**7/21 + b**6/3 + 8*b**5/5 - 5*b**4/3 + 2*b**3/3 - 7*b**2. Suppose x(y) = 0. Calculate y.
-1, 1/5, 1
Suppose -q + 5 = 3*l - 1, 4*q - 11 = l. Let i(t) be the first derivative of -1/6*t**6 + 0*t**3 - l + 0*t**2 - 1/4*t**4 + 0*t + 2/5*t**5. Factor i(z).
-z**3*(z - 1)**2
Suppose -z = -h - 2 - 4, 24 = 4*z - 2*h. Suppose 3*i = -w - 6, w = z*w - 3*i - 6. Factor w + 2/3*r**2 + 2/3*r.
2*r*(r + 1)/3
Suppose 5*n + 5*p = -25, -6*n + 2*n + 5*p = -25. Suppose n = -c - 0*c + 2. Factor 5*w**c - 45*w**2 + 4 + 16*w**3 - 6 + 17*w.
(w - 2)*(4*w - 1)**2
Factor -42*n**2 - 30*n + 75 + 30*n**3 + n**4 - 48*n**2 + 18*n**2 - 4*n**4.
-3*(n - 5)**2*(n - 1)*(n + 1)
Let p(k) be the third derivative of -3*k**7/560 - 11*k**6/960 - k**5/240 + 15*k**2. Factor p(u).
-u**2*(u + 1)*(9*u + 2)/8
Let l(v) be the second derivative of v**4/42 - 8*v**3/21 + 16*v**2/7 + 12*v. Determine m, given that l(m) = 0.
4
Let l(q) = 4*q**2 - 72*q + 329. Let d(y) = -2*y**2 + 36*y - 165. Let a(w) = -10*d(w) - 6*l(w). Find m such that a(m) = 0.
9
Let v(y) = y**3 - 5*y**2 - 10*y - 1. Let j(l) = l**2 - 3*l**3 + 30*l + l**3 + 15*l**2 + 4. Let o(n) = -3*j(n) - 8*v(n). Let o(p) = 0. Calculate p.
-2, -1
Let f be (-9)/(-21)*14/4. Let d(z) be the first derivative of f*z**3 + 0*z + 1/2*z**2 - 3. Find x such that d(x) = 0.
-2/9, 0
Let h(g) be the third derivative of -g**5/15 + g**4/3 - 2*g**3/3 + 7*g**2. Solve h(q) = 0 for q.
1
Let y = 1 - 3. Let v = 4 + y. Let -4*m**5 + 0*m**3 + 2*m - 6*m**3 + 6*m**4 + 4*m**4 - 2*m**v = 0. Calculate m.
-1/2, 0, 1
Let l(r) be the second derivative of r**7/105 - r**6/24 + r**5/15 - r**4/24 + 3*r**2/2 - 3*r. Let i(m) be the first derivative of l(m). Factor i(k).
k*(k - 1)**2*(2*k - 1)
Let u(z) be the first derivative of -343*z**6/2 + 588*z**5 + 1071*z**4/4 - 706*z**3 + 354*z**2 - 72*z - 25. Determine q so that u(q) = 0.
-1, 2/7, 3
Let b(d) = -d + 4. Let z be b(6). Let k = 0 - z. Factor 0*n**k + 0*n - 2/9*n**5 + 2/9*n**4 + 0*n**3 + 0.