4*g - 4*f - 6. Factor -3/4*t**g + 0*t + 3/4.
-3*(t - 1)*(t + 1)/4
Suppose 5*m + 200 = 50. Let j be (-3)/(-5) - (-6)/m. Factor 4/5 - j*n - 2/5*n**2.
-2*(n - 1)*(n + 2)/5
Let s(x) be the first derivative of 7*x**5/25 + 3*x**4/5 + x**3/5 - x**2/5 + 42. Factor s(y).
y*(y + 1)**2*(7*y - 2)/5
Let f(x) be the second derivative of -21/4*x**4 - x - 3*x**2 + 0 + 13/2*x**3. Let f(l) = 0. What is l?
2/7, 1/3
Let w(t) be the third derivative of 5*t**8/336 - t**7/21 + t**6/24 - 4*t**2. Find b, given that w(b) = 0.
0, 1
Factor -2/3*b**2 + 2/3*b + 4/3.
-2*(b - 2)*(b + 1)/3
Let p = 35/2 - 17. Determine g, given that 1/4 + p*g + 1/4*g**2 = 0.
-1
Let r(s) be the first derivative of -1/20*s**4 + 2/5*s - 2 - 2/15*s**3 + 1/10*s**2. Factor r(x).
-(x - 1)*(x + 1)*(x + 2)/5
Let i(h) be the first derivative of 3 + 0*h + 2/3*h**3 + 14/25*h**5 - 1/5*h**2 - 9/10*h**4 - 2/15*h**6. Suppose i(g) = 0. What is g?
0, 1/2, 1
Let z be (-93)/(-7) - 2/7. Solve -18*f**4 - z*f**5 - f**3 - 3*f**3 - f**5 = 0.
-1, -2/7, 0
Suppose -1 = -4*n + 7. Determine i so that -i**3 + 4*i**4 - 17*i**n + 17*i**2 - 2*i**5 - i**5 = 0.
0, 1/3, 1
Let b(u) be the second derivative of -u**7/735 + u**6/420 + u**5/210 - u**4/84 - u**2/2 + 2*u. Let i(t) be the first derivative of b(t). Factor i(s).
-2*s*(s - 1)**2*(s + 1)/7
Let k(a) be the second derivative of a**5/5 + 2*a**4/3 - 8*a**3/3 - 16*a**2 - 11*a. Determine g, given that k(g) = 0.
-2, 2
Let d(z) = 4*z**4 + 8*z**3 - z**2 + 2*z + 7. Let j(c) = c**4 + c**3 + c + 1. Suppose -3*s - a = -4*s + 3, -4*a + 8 = 0. Let r(h) = s*j(h) - d(h). Factor r(o).
(o - 2)*(o - 1)**2*(o + 1)
Let w(b) = -b**2 - 9*b + 12. Let s be w(-10). Factor c**2 + 0*c**s + c - c**2 + c**2.
c*(c + 1)
Let i(y) = -5*y**2 - 2*y + 3. Let u be i(2). Let j = -11 - u. Factor 4*x**4 - j*x**3 - x**5 + 10*x**2 - 4*x + x**4 + 1 - x.
-(x - 1)**5
Let q(n) be the third derivative of 1/315*n**7 - 5*n**2 + 0*n**3 + 0*n**5 + 0*n + 0 + 1/180*n**6 + 0*n**4. Factor q(w).
2*w**3*(w + 1)/3
Let r(n) = 7*n**4 - 9*n**3 - 5*n**2 - 5. Let k(p) = -p**4 + 1. Let o(x) = -5*k(x) - r(x). Solve o(z) = 0.
-1/2, 0, 5
Let f(v) = v**3 + 8*v**2 + 3. Let t be (-7)/((-63)/24)*-3. Let n be f(t). Factor -4/5*h**2 - 2/5*h - 2/5*h**n + 0.
-2*h*(h + 1)**2/5
Let v(y) be the third derivative of -y**7/525 + y**6/75 - 2*y**5/75 + 3*y**2 + 2. Let v(u) = 0. Calculate u.
0, 2
Let p(s) be the third derivative of 1/108*s**4 + 0*s - 2*s**2 + 0*s**3 + 1/135*s**5 + 1/540*s**6 + 0. Let p(c) = 0. What is c?
-1, 0
Let o(a) be the second derivative of -a**5/100 + a**4/15 - a**3/6 + a**2/5 + 37*a. Factor o(f).
-(f - 2)*(f - 1)**2/5
Determine k so that -8/3 - 4/3*k**2 - 4*k = 0.
-2, -1
Suppose 3*s - s - 4 = 0. Let y(t) = 1. Let g(w) = 14*w**2 - 32*w + 10. Let x(p) = s*y(p) - g(p). Factor x(d).
-2*(d - 2)*(7*d - 2)
Let a = -4 + 4. Let q(h) be the third derivative of -2*h**2 - 1/240*h**6 + a + 0*h + 1/48*h**4 - 1/12*h**3 + 1/120*h**5. Let q(r) = 0. What is r?
-1, 1
Let v = -19 + 25. Solve -2 + 4*g**5 + 4 + 6 + v*g**4 - 19*g**3 - 26*g**2 + 3*g**3 = 0.
-2, -1, 1/2, 2
Let p(u) = -8*u - 40. Let a be p(-5). Let w(j) be the second derivative of 4/105*j**6 + 9/70*j**5 + 0 - 3*j + 1/7*j**4 + 1/21*j**3 + a*j**2. Factor w(c).
2*c*(c + 1)**2*(4*c + 1)/7
Let f(b) = 10*b**5 + b**4 + 2*b**3 - b**2. Let j(k) = -19*k**5 - 3*k**4 - 4*k**3 + 2*k**2. Let m(n) = -11*f(n) - 6*j(n). Factor m(y).
y**2*(y + 1)**2*(4*y - 1)
Let t be (3 + -9)/((-3)/(-3)). Let n be (t/2)/(84/(-32)). Factor 10/7*w + 2/7*w**3 + n*w**2 + 4/7.
2*(w + 1)**2*(w + 2)/7
Let v(k) be the first derivative of k**6/10 - 3*k**5/10 + k**3 - 3*k**2/2 - k - 4. Let l(w) be the first derivative of v(w). Factor l(i).
3*(i - 1)**3*(i + 1)
Let j(u) be the first derivative of -4*u**5/45 + u**4/3 + 8*u**3/9 - 56*u**2/9 + 32*u/3 - 61. Determine z, given that j(z) = 0.
-3, 2
Let w be ((-36)/280 - 3/(-15))*8. Solve -2/7*m**2 - 2/7 + w*m = 0.
1
Let t(d) be the second derivative of -d**6/120 - d**5/20 - d**4/12 - 2*d**2 + 3*d. Let u(c) be the first derivative of t(c). Suppose u(q) = 0. What is q?
-2, -1, 0
Let l(v) be the third derivative of -v**7/2520 + v**5/120 - v**4/12 + 4*v**2. Let x(r) be the second derivative of l(r). Solve x(b) = 0.
-1, 1
Factor 2/7*k**2 - 4/21*k + 0.
2*k*(3*k - 2)/21
Let v(r) be the first derivative of -19*r**4/22 - 80*r**3/33 - 23*r**2/11 - 4*r/11 + 42. Determine x so that v(x) = 0.
-1, -2/19
Suppose -4*f + 20 = 2*q, -3*f + 15 = -4*q - q. Factor j**4 + 3*j**5 + 3*j**3 - 7*j**4 - j**5 + j**f.
3*j**3*(j - 1)**2
Suppose -2*g = 2*g. Let p be (0 + (-1)/(-2))*g. Factor -k**2 + k + p*k**2 + 2*k**2.
k*(k + 1)
Let m(d) = -d**3 + 7*d**2 - 4*d. Let p(h) = h**3 - 6*h**2 + 3*h. Let x(b) = 5*m(b) + 6*p(b). Determine k, given that x(k) = 0.
-1, 0, 2
Let a(i) = 4*i - 9. Let w be a(6). Suppose -2*k = -115 + w. Factor 34*v**2 + k*v**5 + 8*v + 138*v**3 - 35*v**2 - 140*v**4 - 55*v**2.
2*v*(v - 1)**2*(5*v - 2)**2
Suppose -4*h - 4 = -5*m, 3*h - m = 2*m. Factor 6*p - 4 - 6*p**3 + p**2 + p**2 + 2*p**h + 0.
2*(p - 2)*(p - 1)**2*(p + 1)
Suppose 24/5*b**4 - 3/5*b - 3*b**2 + 3/5*b**3 + 12/5*b**5 + 3/5 = 0. Calculate b.
-1, 1/2
Let s(c) be the third derivative of c**6/300 - 2*c**5/25 + 4*c**4/5 - 64*c**3/15 + 3*c**2. Factor s(a).
2*(a - 4)**3/5
Let c(f) = -5*f**3 + f**2 - 1. Let o be c(-1). Solve r - 2 + 0*r - o*r - 2*r**2 = 0.
-1
Factor 151*n + 50*n**3 - 22*n - 94 - 5*n**4 - 180*n**2 + 141*n - 41.
-5*(n - 3)**3*(n - 1)
Let n(z) be the third derivative of z**7/525 + z**6/100 + z**5/75 + 11*z**2. Solve n(r) = 0 for r.
-2, -1, 0
Let u(k) = 20*k**3 - 60*k - 40. Let f(b) = 4*b**3 - 12*b - 8. Let v(q) = -16*f(q) + 3*u(q). Let v(m) = 0. What is m?
-1, 2
Let n = 9 - 6. Let 4 + 8*v**2 - n + 2*v + 3 - 20*v = 0. What is v?
1/4, 2
Let d(i) be the third derivative of i**5/60 - i**4/12 - 4*i**3/3 - 21*i**2. Determine t, given that d(t) = 0.
-2, 4
Let n(t) be the third derivative of -7*t**6/30 + 2*t**5 - 6*t**4 + 16*t**3/3 - 9*t**2. Solve n(w) = 0.
2/7, 2
Let v(z) be the second derivative of z**3/6 - z**2 + 2*z. Let j be v(4). What is i in -2*i**3 + 7*i**4 - 2*i**4 - 2*i**j + 2*i**5 - 3*i**4 = 0?
-1, 0, 1
Let k be (-10)/((2 - 2) + -2). Factor 8*s**4 - 2*s**4 - 35*s**2 - 3*s**k + 29*s**2 + 3*s.
-3*s*(s - 1)**3*(s + 1)
Let z(s) be the third derivative of -s**8/35280 - s**7/7056 - s**6/5040 - s**5/10 - 5*s**2. Let u(k) be the third derivative of z(k). Factor u(b).
-(b + 1)*(4*b + 1)/7
Factor 4/9*s**3 + 0 - 14/9*s**2 + 2/3*s.
2*s*(s - 3)*(2*s - 1)/9
Suppose -5*r + v = -6*r, 6 = -3*v. Let u(s) be the second derivative of s**3 - 1/4*s**4 + 0*s**2 + r*s + 0 - 3/20*s**5. Find m such that u(m) = 0.
-2, 0, 1
Let g(f) be the second derivative of f**5/60 + f**4/24 - f**3/3 - f**2/2 - f. Let r(t) be the first derivative of g(t). Factor r(d).
(d - 1)*(d + 2)
Let s(j) = 17*j**3 + 21*j**2 + 6*j + 2. Let o(i) = 35*i**3 + 42*i**2 + 12*i + 5. Let u(y) = -2*o(y) + 5*s(y). Factor u(l).
3*l*(l + 1)*(5*l + 2)
Let s be (0/(-2 - -4))/(-3). Let p(h) be the third derivative of 0*h**4 - 2*h**2 + 1/180*h**5 + 0 + 1/120*h**6 + s*h + 0*h**3. Factor p(j).
j**2*(3*j + 1)/3
Let k(l) be the second derivative of 2*l**7/231 + l**6/33 + 3*l**5/110 - l**4/66 - l**3/33 + 18*l. What is w in k(w) = 0?
-1, 0, 1/2
Suppose -4*c = 5*g - 70, c + 6 = -2*g + 25. Let x be -5 - -7 - 27/c. Find i, given that -x*i**2 + 0 - 1/5*i = 0.
-1, 0
Let p(f) be the second derivative of f**6/40 - 9*f**5/80 - f**4/16 + 3*f**3/8 - 14*f. What is l in p(l) = 0?
-1, 0, 1, 3
Let i(l) = -l + 1. Let o be i(-2). Let v = o - -2. Factor 5 + 2*y**3 - v.
2*y**3
Let s(c) be the third derivative of 0*c - 1/135*c**6 - 1/18*c**4 - 1/20*c**5 + 1/6*c**3 - 3*c**2 + 0. Let y(h) be the first derivative of s(h). Factor y(w).
-2*(w + 2)*(4*w + 1)/3
Let y be 2/7 - (-38)/14. Let x be y + -3 + 1*2. Determine w so that -2*w**2 - 4 - 2*w + 2 - x*w = 0.
-1
Suppose 0*j**2 + 0*j + 0 + 2/9*j**3 - 2/9*j**4 = 0. Calculate j.
0, 1
Suppose 0 = -5*h - 5*q, -q - 17 + 5 = -3*h. Find v, given that 22/9*v**h + 0 - 10/9*v**4 + 2/9*v - 14/9*v**2 = 0.
0, 1/5, 1
Suppose -5*s + 119 = 37*o - 34*o, -5*o - 4*s = -220. Suppose 456/5*i**4 - 84/5*i**2 + o*i**5 + 159/5*i**3 + 6/5 - 21/5*i = 0. Calculate i.
-1, -2/5, 1/4
Let g(p) = -p + 1 - 1. Let w be g(-3). Solve -f - f**2 + f**3 + w + 2*f**2 - 4 = 0 for f.
-1, 1
Let s(n) = 4*n - 24. Let i(c) = 7*c