7/42 - n**6/6 - n**5/2 + 5*n**4/6 + 5*n**3/6 - 5*n**2/2 - 8*n. Solve m(y) = 0 for y.
-1, 1
Let q(v) = -7*v**2 - 3*v + 9. Let y(h) = 5*h**2 + 2*h - 9. Let j(s) = -2*q(s) - 3*y(s). Determine l so that j(l) = 0.
-3, 3
Let f be (176/90 + -2)/(3/(-30)). Let k be (-1)/(-2 + (-9)/(-5)). Factor 4/9*v**2 - 2/9*v**k + 2/3*v + 2/9 - f*v**3 - 2/3*v**4.
-2*(v - 1)*(v + 1)**4/9
Let m be -2*(-25)/(-30)*-3. Determine v so that 0 + 3/2*v**3 + v**4 + v**2 + 1/4*v**m + 1/4*v = 0.
-1, 0
Let m(i) be the second derivative of i**4/21 - 6*i**3/7 + 4*i**2 + 3*i + 5. Factor m(g).
4*(g - 7)*(g - 2)/7
Let c(k) be the second derivative of 7*k + 0 + k**2 - 23/18*k**3 + 7/36*k**4. Factor c(h).
(h - 3)*(7*h - 2)/3
Let s be 2/6 + 25/15. Factor -n**5 - n + s*n - 2*n**4 + 0*n**4 + 2*n**2.
-n*(n - 1)*(n + 1)**3
Let y(t) = t**3 + t. Let n(g) = 2*g**3 + 4*g. Suppose 0 = -5*l + 1 + 4. Let f be (-1)/(-2)*3*-2. Let v(q) = f*y(q) + l*n(q). Determine c so that v(c) = 0.
-1, 0, 1
Let i(z) be the third derivative of 0*z - 1/24*z**4 + 1/360*z**6 + z**2 + 0 + 1/3*z**3 + 0*z**5. Let x(s) be the first derivative of i(s). Solve x(c) = 0 for c.
-1, 1
Let u(d) be the second derivative of d**6/90 - d**4/18 + d**2/6 - 7*d. Factor u(z).
(z - 1)**2*(z + 1)**2/3
Let w(c) be the third derivative of 49*c**6/75 - 161*c**5/150 + 11*c**4/15 - 4*c**3/15 - 7*c**2. Let w(g) = 0. What is g?
1/4, 2/7
Let l(h) be the first derivative of -8 - 2/3*h**3 - 32*h - 8*h**2. Factor l(p).
-2*(p + 4)**2
Solve 8*l**3 - 5*l**5 + l**5 - 8*l**4 - 8 - 6*l + 2*l + 16*l**2 = 0 for l.
-2, -1, 1
Let l(x) = 7*x**2 - 9*x + 10. Let f(h) = 15*h**2 - 18*h + 21. Let w(p) = 4*f(p) - 9*l(p). Factor w(y).
-3*(y - 2)*(y - 1)
Factor 0*a + 0*a**2 - 1/6*a**4 + 0 + 1/6*a**3.
-a**3*(a - 1)/6
Factor 0*o + 1/2 - 1/2*o**2.
-(o - 1)*(o + 1)/2
Find i, given that 1/4*i**2 - 3/4 + 1/2*i = 0.
-3, 1
Let o(f) = 9*f**2 + 5*f - 5. Let i(y) = 4*y**2 + 2*y - 2. Let n(u) = 10*i(u) - 4*o(u). Determine r, given that n(r) = 0.
0
Let t be 1 + 2 - -1 - 204/54. Solve t*l**3 + 0*l + 2/9*l**2 - 2/9*l**4 + 0 - 2/9*l**5 = 0.
-1, 0, 1
Factor d - 1/3*d**2 + 4/3.
-(d - 4)*(d + 1)/3
Let b(d) be the first derivative of d**6/3 + 6*d**5/5 + d**4 + 4. Suppose b(m) = 0. What is m?
-2, -1, 0
Factor -4/7*u**2 + 0*u**3 + 2/7 + 2/7*u**4 + 0*u.
2*(u - 1)**2*(u + 1)**2/7
Let a = -19/12 + 65/36. Let x be (3/(-15))/((-36)/40). Suppose -4/9*c**3 + x*c + 0 + a*c**5 + 0*c**4 + 0*c**2 = 0. Calculate c.
-1, 0, 1
Suppose -2*d + 5 = -5. Let k(r) be the second derivative of -1/3*r**2 - 7/9*r**3 + 0 - 5/6*r**4 + 2*r - 3/10*r**d. Factor k(l).
-2*(l + 1)*(3*l + 1)**2/3
Let c(v) be the third derivative of v**8/84 - 8*v**7/105 + v**6/6 - 2*v**5/15 + 22*v**2. Solve c(q) = 0 for q.
0, 1, 2
Let l be (-3 - 349/6)*4. Let r = l + 250. Solve r*y**3 + 2/3*y + 7/3*y**4 + 0 + 11/3*y**2 = 0 for y.
-1, -2/7, 0
Determine i, given that -5/2 - 15/4*i**2 + 5/4*i**3 + 5/4*i**4 - 25/4*i = 0.
-1, 2
Let x(h) be the second derivative of 2/3*h**3 + 1/5*h**5 + 0 + 0*h**2 - 2/3*h**4 - 8*h. Factor x(w).
4*w*(w - 1)**2
Let s(f) be the third derivative of f**7/630 - f**5/180 + 7*f**2. Find i such that s(i) = 0.
-1, 0, 1
Let q(s) be the first derivative of s**6/180 - s**5/90 + 3*s**2/2 - 2. Let i(g) be the second derivative of q(g). Factor i(h).
2*h**2*(h - 1)/3
Factor 5*f**5 - 6*f**5 - 2*f**4 - 10*f + 11*f + 4*f**4 - 2*f**2.
-f*(f - 1)**3*(f + 1)
Let n(o) be the third derivative of 7*o**6/1200 - 4*o**5/75 + 11*o**4/60 - 4*o**3/15 - 2*o**2 + 21*o. Factor n(m).
(m - 2)**2*(7*m - 4)/10
Let u(g) = 2*g**2 - 3*g - 12. Let b(s) = -6*s**2 + 10*s + 36. Let x(r) = -5*b(r) - 16*u(r). Factor x(v).
-2*(v - 2)*(v + 3)
Let r(q) = -15*q**4 + 27*q**3 - 18*q**2 + 15*q + 9. Let a = -6 + 15. Let o(k) = 8*k**4 - 14*k**3 + 9*k**2 - 8*k - 5. Let t(n) = a*o(n) + 5*r(n). Factor t(g).
-3*g*(g - 1)**3
Let u(a) = -a**3 - 9*a**2 - 8*a + 6. Let t be u(-8). Suppose 0 = y - t*y + 10. Determine f, given that -4/3*f**3 + 2/3 - 2/3*f**4 + 4/3*f + 0*f**y = 0.
-1, 1
Let i(o) be the first derivative of 16*o**6/15 - 4*o**5/5 + o**4/6 - 5*o - 5. Let z(f) be the first derivative of i(f). Suppose z(c) = 0. Calculate c.
0, 1/4
Let h(j) = 9*j**2 - 4 + j**3 + 1 + 4 + 1. Let x be h(-9). Factor -5*s - s - 2*s**x + 0*s.
-2*s*(s + 3)
Suppose -2*z - 5*g + 7 = -15, 4*z = -5*g + 24. Let v = 1 + z. Factor 2/3 + 2/3*k - 2/3*k**3 - 2/3*k**v.
-2*(k - 1)*(k + 1)**2/3
Let k(p) be the first derivative of -7*p**4/10 - 4*p**3 - 29*p**2/5 - 12*p/5 - 6. Let k(g) = 0. Calculate g.
-3, -1, -2/7
Let w(c) be the third derivative of 0*c - 3*c**2 + 0 + 0*c**6 - 1/210*c**7 + 0*c**3 + 1/60*c**5 + 0*c**4. Find i, given that w(i) = 0.
-1, 0, 1
Let f(s) be the first derivative of -2/3*s**3 + 2/7*s + 2 - 2/7*s**4 - 2/7*s**2. What is l in f(l) = 0?
-1, 1/4
Suppose 3/5*o**2 + 0 - 1/5*o**3 - 3/5*o**4 - 1/5*o**5 + 2/5*o = 0. What is o?
-2, -1, 0, 1
Let o(x) be the second derivative of 1/6*x**4 + 0*x**3 + 1/5*x**6 - 1/21*x**7 + 2*x + 0*x**2 + 0 - 3/10*x**5. Solve o(n) = 0 for n.
0, 1
Let f(y) be the second derivative of y**6/120 + y**5/80 - y**4/48 - y**3/24 + 3*y. Factor f(j).
j*(j - 1)*(j + 1)**2/4
Let q(h) = h**2 - 7*h + 1. Let m be q(6). Let t = -2 - m. Factor 0*j + 1/2*j**5 - 1/2*j**t + 0 + 0*j**2 + 0*j**4.
j**3*(j - 1)*(j + 1)/2
Let k(o) be the second derivative of o**8/10080 - o**7/3780 - o**6/1080 + o**5/180 + o**4/6 - 3*o. Let n(w) be the third derivative of k(w). Factor n(q).
2*(q - 1)**2*(q + 1)/3
Let c(m) be the second derivative of -m**4/96 - 22*m. Find j such that c(j) = 0.
0
Let f(h) be the third derivative of 3*h**5/20 + 5*h**4/4 - 4*h**3 + 17*h**2. Let f(v) = 0. Calculate v.
-4, 2/3
Let z be (-3)/((-81)/4)*384/256. Determine u so that 0*u + 0 - z*u**2 + 2/9*u**3 = 0.
0, 1
Let c be 12/28*-2*28/(-6). Let r(u) be the third derivative of 4*u**2 - 1/270*u**5 + 0*u**3 - 1/108*u**c + 0 + 0*u. Determine a, given that r(a) = 0.
-1, 0
Let s(f) be the third derivative of -f**5/40 + f**4/4 - 3*f**3/4 + 15*f**2. Find b such that s(b) = 0.
1, 3
Suppose 5*y = -5*f - 0*y + 35, 5*y - 31 = -3*f. Let j(i) be the second derivative of 2/9*i**3 - 1/18*i**4 + 0 - 2*i - 1/3*i**f. Factor j(o).
-2*(o - 1)**2/3
Let v(n) be the first derivative of -2*n**3/9 - 2*n**2/3 - 21. Factor v(q).
-2*q*(q + 2)/3
Let w be (-16)/(-6) + 4/(-6). Suppose 0 = b - 4*n + 1, 3*b + 0*b + w*n - 11 = 0. Factor o + o**3 - o**3 - o**b.
-o*(o - 1)*(o + 1)
Let u(x) be the second derivative of x**5/70 - x**3/7 - 2*x**2/7 - 2*x. Factor u(f).
2*(f - 2)*(f + 1)**2/7
Determine m so that -19/2*m + 28*m**2 + 1 - 24*m**3 = 0.
1/4, 2/3
Let a(k) be the third derivative of -k**7/210 - k**6/120 + k**5/60 + k**4/24 + 14*k**2. Factor a(z).
-z*(z - 1)*(z + 1)**2
Let p be -3*(-2)/9*3. Factor z**3 + 2 - z**4 + z**5 - p - 2*z**4 + 3*z**2 - 2*z.
z*(z - 2)*(z - 1)**2*(z + 1)
Let d(k) = 5*k**2 + 19*k + 18. Let r(m) = -11*m**2 - 37*m - 36. Let b(q) = 5*d(q) + 2*r(q). Determine f, given that b(f) = 0.
-6, -1
Let u be 4/(-3)*4/(8/(-3)). Factor 0 - 3/5*d**u + 0*d.
-3*d**2/5
Let g(m) be the first derivative of 3*m**4/14 - 38*m**3/21 + 3*m**2 - 10*m/7 + 36. Factor g(b).
2*(b - 5)*(b - 1)*(3*b - 1)/7
Let d(b) = b + 3. Let i be d(6). Suppose 0 = -5*s + 4*y + 7, -3*s = -i*y + 4*y + 1. Let -4*c + s*c + c**2 + 0*c**2 = 0. What is c?
0, 1
Let j(c) be the third derivative of -c**5/20 + c**4/2 - 2*c**3 - 11*c**2. Factor j(y).
-3*(y - 2)**2
Let f(b) be the first derivative of b**3 + 6*b**2 + 12*b - 1. Solve f(a) = 0.
-2
Let v(w) be the first derivative of 2*w - 3/2*w**2 + 8 + 1/4*w**4 + 0*w**3. Factor v(z).
(z - 1)**2*(z + 2)
Suppose 0*w + 5 = 4*j + w, 2*w = -3*j. Suppose -q**5 - 10*q**4 + 4*q**3 + 7*q**5 + q**2 - q**j = 0. Calculate q.
0, 2/3, 1
Factor 2*k - 12*k**2 + 16*k**2 - 4*k**3 + 4 + 2*k - 8*k**2.
-4*(k - 1)*(k + 1)**2
Let z(c) be the first derivative of -1/3*c**3 - 3 + 0*c - 1/2*c**2. Factor z(m).
-m*(m + 1)
Let y = 6 - 4. Suppose 5 = y*n - 3. Let 16*f - 3*f**4 - 23*f**2 - 3*f**3 - n + 0*f**2 + 17*f**3 = 0. Calculate f.
2/3, 1, 2
Let s(z) be the first derivative of -2*z**3/15 - z**2/5 + 4*z/5 - 1. Find w, given that s(w) = 0.
-2, 1
Suppose -8 = -2*g + i + 5, 0 = -g - i + 11. Suppose -5*p = -g - 7. Factor -5*y**2 - 1/2*y**5 - 1/2 - 5/2*y - 5*y**p - 5/2*y**4.
-(y + 1)**5/2
Let n(b) be the second derivative of -b**8/2688 + b**7/840 - b**6/960 - 7*b**2/2 + 6*b. Let