*5/25 + 103*y**4/20 + 7*y**3 + 499*y. Suppose t(w) = 0. What is w?
-2, -1, 0, 35
Let c(v) be the second derivative of 17*v - 16/15*v**3 + 1/30*v**4 + 64/5*v**2 + 0. Find o such that c(o) = 0.
8
Let j(u) be the first derivative of 35 + 1/3*u**4 + 128/3*u**2 + 64/9*u**3 + 0*u. Solve j(i) = 0.
-8, 0
Let q(n) be the second derivative of n**4/20 - 41*n**3/5 + 5043*n**2/10 - 210*n. Determine i so that q(i) = 0.
41
Factor -12/7*a**2 + 2/7*a**3 + 0 - 2*a.
2*a*(a - 7)*(a + 1)/7
Let b(w) = 4*w + 1. Let g(k) = -3*k - 1. Let o(r) = -4*b(r) - 5*g(r). Let m be o(-2). Factor -2*l**3 - 2*l**m + l**3.
-3*l**3
Find i, given that -5*i + 0*i + 5*i**3 - 252*i**2 - 10 + 267*i**2 - 5*i**4 = 0.
-1, 1, 2
Factor 1590*q - 275*q**2 - 3645 + 5*q**3 + 2762*q - 437*q.
5*(q - 27)**2*(q - 1)
Let v(m) be the third derivative of -m**5/40 + m**4/3 - 5*m**3/12 - 273*m**2. Find o such that v(o) = 0.
1/3, 5
Let x(m) be the first derivative of m**6/33 + 158*m**5/55 + 1599*m**4/22 + 1014*m**3/11 + 314. Find p, given that x(p) = 0.
-39, -1, 0
Let z(v) = -5*v + 9. Let j be z(3). Let u be (-2)/126*-69 - j/(-14). Suppose -u*f**2 + 0 + 2/3*f**3 + 0*f - 1/6*f**4 = 0. What is f?
0, 2
Let o = -1026 + 1028. Factor -1/6*c**5 + 0 - 1/2*c**3 + 0*c - 1/6*c**o - 1/2*c**4.
-c**2*(c + 1)**3/6
Let n = 40 + -38. Let 740 + 2*j**n - 740 = 0. What is j?
0
Suppose 16*z + 324 = 404. Let s(w) be the third derivative of 1/20*w**z + 2*w**3 + 0*w - 5*w**2 + 0 - 1/2*w**4. Factor s(p).
3*(p - 2)**2
Suppose 0 = 4*o - j - 18, 2*j = -2*o - 2*j. Factor 2*a**2 + 0*a**o - 4*a**4 - 26*a**3 + 25*a**3 + 3*a**4.
-a**2*(a - 1)*(a + 2)
Suppose 3*v + b + 10 - 2 = 0, 2*v + 8 = -2*b. Let z be -5 - ((-156)/21 - v). Factor -3/7*s + 0 - 3/7*s**4 + 3/7*s**3 + z*s**2.
-3*s*(s - 1)**2*(s + 1)/7
Let b = 24 - 4. Suppose 2*p - 2 = p. Solve 27*n**p + 24*n**4 - 8*n**2 + 70*n**4 + 53*n**4 + b*n - 4 - 182*n**3 = 0 for n.
-1/3, 2/7, 1
Let i be 1/((-1)/(-6))*(40/(-45) - -1). Determine s, given that -i*s**4 + 4/3*s + 0 - 4/3*s**2 - 7/3*s**3 = 0.
-2, 0, 1/2
Let x(k) be the first derivative of -k**8/112 - k**7/14 - 9*k**6/40 - 7*k**5/20 - k**4/4 - 17*k**2 + 16. Let c(u) be the second derivative of x(u). Factor c(g).
-3*g*(g + 1)**3*(g + 2)
Let v(w) be the first derivative of w**3 + 615*w**2 + 126075*w + 700. Factor v(y).
3*(y + 205)**2
Suppose -5*c - 4*o + 5900 = 0, -c + 5*o + 1151 = -0*o. Solve c*z**2 - 4 + 336*z + 1436*z**3 - 576*z**5 + 0 + 30 + 6 + 96*z**4 = 0 for z.
-2/3, -1/4, 2
Factor 0*i + 2/3*i**4 + 11/3*i**3 + 0 - 2*i**2.
i**2*(i + 6)*(2*i - 1)/3
Let c = 1481/4 - 370. Factor c*k + k**3 + 5/4*k**2 + 0.
k*(k + 1)*(4*k + 1)/4
Let q(n) = n**2 - 11*n + 14. Let l be q(10). Let c be l/2 + 4 + -4. Factor -6/7*m**c + 8/7 + 0*m - 2/7*m**3.
-2*(m - 1)*(m + 2)**2/7
Let f be (4 + -8 - -15) + 0. Suppose 3*g = 5*o - 7, -3*o - 6*g + f = -g. Find h such that -3 - 3/2*h**o + 9/2*h = 0.
1, 2
Let g(n) be the second derivative of -n**6/285 + 3*n**5/190 + 17*n**4/57 + 16*n**3/19 + 198*n. Find r, given that g(r) = 0.
-3, -2, 0, 8
Suppose -17 = -w + 5*f, 0 = -w + 3*w - 3*f - 13. Suppose 7 = -r - 5*v, r + 4 = -4*v - 1. Find n such that 1/3*n**r - 1/3*n + 0 - 1/3*n**4 + 1/3*n**w = 0.
-1, 0, 1
Let p be 9*(-4 + 0 + 5). Let d be (4/(-6))/((-3)/p). Factor 0*x + x - x**3 - 2*x**2 - 1 + 2*x**d + x**2.
-(x - 1)**2*(x + 1)
Factor 2/5*f + 2/3*f**2 + 0 - 4/15*f**3.
-2*f*(f - 3)*(2*f + 1)/15
Let y be (6/(-9))/(1/(-6)). Suppose 45 = 5*q - 0*n - n, 42 = y*q - 2*n. Factor -4*a**4 + 2*a**3 + 2*a**5 - 4*a**5 + q*a**4 - 4*a**3.
-2*a**3*(a - 1)**2
Let w(h) be the first derivative of h**5/140 - h**4/28 + 13*h**2/2 - 3. Let v(i) be the second derivative of w(i). Factor v(l).
3*l*(l - 2)/7
Let o(v) = -10*v**2 + 6*v - 3. Let p be o(2). Let d = p + 34. Solve z**2 + 0 - 1/3*z**d - 2/3*z = 0.
0, 1, 2
Factor -55*i**4 - 2*i**2 - 11*i**3 - 2*i**5 - 5*i**5 + 39*i**4.
-i**2*(i + 1)**2*(7*i + 2)
Let q(t) be the second derivative of 50*t**2 - 20*t + 10*t**3 + 1/5*t**5 + 0 - 3*t**4. What is g in q(g) = 0?
-1, 5
Suppose 25 + 47 = 2*k. Suppose 0 = 2*t - 6*t + k. Factor -3*b**2 - b**3 - 1 + 0*b**2 + 6*b - t*b.
-(b + 1)**3
Suppose y = 4*d, -1253 = 2*d - 3*y - 1233. Solve 1/10*n**d - 1/10*n + 0 = 0.
0, 1
Let s(r) be the first derivative of r**5/60 + 5*r**4/24 + r**3 + 57*r**2/2 + 44. Let c(n) be the second derivative of s(n). Factor c(x).
(x + 2)*(x + 3)
Let w be 21*(-1)/(-6) - (5 + -2)/1. Factor 0*i - w*i**2 - 1/4*i**3 + 0.
-i**2*(i + 2)/4
Determine x, given that -75*x + 27556 - 723*x + 513*x**3 - 27552*x**2 + 151*x**3 + 134*x - 4*x**4 = 0.
-1, 1, 83
Let s = -56640/7 - -8092. Factor s - 4/7*y**4 + 8/7*y**3 - 8/7*y + 0*y**2.
-4*(y - 1)**3*(y + 1)/7
Let m(b) be the third derivative of b**6/720 - b**5/90 - 5*b**4/48 + b**3/2 - 126*b**2 + 2. Determine i, given that m(i) = 0.
-3, 1, 6
Let b(s) = -10*s**3 - 92*s**2 - 6*s + 64. Let j(v) = -10*v**3 - 92*v**2 - 7*v + 66. Let y(l) = 3*b(l) - 4*j(l). Solve y(k) = 0 for k.
-9, -1, 4/5
Let p(q) be the first derivative of 4*q**3/3 + 88*q**2 - 180*q - 240. Factor p(j).
4*(j - 1)*(j + 45)
Factor 4*f**2 + 148 - 4*f**3 - 164 + 11*f + 5*f.
-4*(f - 2)*(f - 1)*(f + 2)
Let o = 28142 + -28137. Determine c, given that 0 - 6/7*c + 2/7*c**o + 4/7*c**3 + 8/7*c**4 - 8/7*c**2 = 0.
-3, -1, 0, 1
Let s(m) be the second derivative of m**4/15 + 24*m**3/5 + 136*m**2/5 - 142*m. Let s(w) = 0. What is w?
-34, -2
Let i(z) = -z**4 - 2*z**3 + 20*z**2 - 18*z + 23. Let y(h) = -3*h**4 - 5*h**3 + 61*h**2 - 53*h + 77. Let l(a) = 28*i(a) - 8*y(a). Factor l(x).
-4*(x - 1)**3*(x + 7)
Find o, given that 4 - 24/5*o - 12/5*o**3 - 61/5*o**2 + o**4 = 0.
-2, -1, 2/5, 5
Let j(q) be the first derivative of 5*q**4/24 + 25*q**3/6 + 45*q**2/4 + 65*q/6 + 76. Find y, given that j(y) = 0.
-13, -1
Suppose 5*r + 57*r = 124. Let 9/2*w**3 + 3/2*w**5 - 6*w**r + 6*w**4 + 0 - 6*w = 0. What is w?
-2, -1, 0, 1
Let c be -5 + -1 - -2 - -6. Factor 4*h**4 - 3*h - 9*h**c + 6 - 4*h**3 - h**4 + 7*h**3.
3*(h - 1)**2*(h + 1)*(h + 2)
Let d be (7/((-560)/(-32)))/(9/30). Determine h so that -1/3*h**4 + 16/3 + d*h**3 + 0*h**2 - 16/3*h = 0.
-2, 2
Determine s, given that -3*s**2 + 0*s + 0 + 1/7*s**3 = 0.
0, 21
Suppose -2*j = -3*a - 7, -5*j + 2*j = -3*a - 12. Let k(w) = -2*w**2 + 6*w + 22. Let c be k(j). Factor 48/17*l**c + 2/17*l**4 - 64/17*l + 32/17 - 16/17*l**3.
2*(l - 2)**4/17
Let k = -641057/1587222 + 7/13338. Let r = -2/17 - k. Factor 8/7*t - 6/7*t**2 - r.
-2*(t - 1)*(3*t - 1)/7
Let u be 15*-8*4/(-96). Let k be 31/2 + (-3)/(-6). Factor 3*f**4 - 8*f**5 + f**2 - f**3 - 9*f**u + k*f**5 - 2*f**3.
-f**2*(f - 1)**3
Let t(b) be the first derivative of b**4 + 8*b**3/3 - 6*b**2 + 6. Factor t(j).
4*j*(j - 1)*(j + 3)
Let b(q) = 16*q + 30. Let x be b(7). Let l = x - 283/2. Factor -1/8 + 1/2*w - 3/4*w**2 - 1/8*w**4 + l*w**3.
-(w - 1)**4/8
Let m be (-2)/8*-2 + 70/(-300). Factor -2/15*d**3 + 14/15*d + m*d**2 + 8/15.
-2*(d - 4)*(d + 1)**2/15
Let z(i) be the first derivative of -i**3/21 + 2*i**2/7 + 3*i + 784. Let z(u) = 0. What is u?
-3, 7
Suppose -2/5*r**4 - 36/5 + 10*r + 6/5*r**2 - 18/5*r**3 = 0. What is r?
-9, -2, 1
Let d(n) = -42*n - 40. Let v be d(-1). Factor -1/4*s**3 + v - 3*s + 3/2*s**2.
-(s - 2)**3/4
Factor -3/4*f**3 - 1/4*f**5 - 5/4*f**4 + 0*f + 0 + 9/4*f**2.
-f**2*(f - 1)*(f + 3)**2/4
Let n(k) = -k**2 + 2*k - 10. Let x(s) = -2*s**2 - 5*s - 5. Let m(z) = 6*z**2 + 14*z + 16. Let i(h) = -6*m(h) - 17*x(h). Let p(c) = 6*i(c) - 7*n(c). Factor p(g).
-(g + 2)*(5*g - 2)
Let p(o) = -o**2. Let v(f) = -f - 2 - 1 + 2 - 1. Let w be v(-1). Let d(h) = -3*h**3 - 3*h**2. Let y(n) = w*d(n) + 3*p(n). What is q in y(q) = 0?
0
Let q(g) be the first derivative of -3/17*g**2 - 4/17*g - 2/51*g**3 - 4. Let q(o) = 0. Calculate o.
-2, -1
Let f(i) be the second derivative of 1/20*i**5 - 1/30*i**6 + 0*i**2 - 6*i + 0 + 1/12*i**4 - 1/42*i**7 + 0*i**3. Factor f(w).
-w**2*(w - 1)*(w + 1)**2
Let z(r) be the first derivative of r**4/2 + 40*r**3/3 + 77*r**2 - 484*r - 30. Let z(q) = 0. What is q?
-11, 2
Let t be -2 - (0 + 2 - (-13)/2). Let z = 15 + t. Suppose 3*n - z - 1/2*n**2 = 0. What is n?
3
Let v = 103 - 411/4. Let w(g) be the second derivative of 0*g**2 + 0 - 4*g + v*g**3 - 1/8*g**4. Factor w(z).
-3*z*(z - 1)/2
Let s be -2*(-81)/(-18) - -11. Let q = 74/69 - -6/23. Factor -q - 4/3*k - 1/3*k**s.
-(k + 2)**2/3
Let h(f) be the third derivative of f**8/336 - f**7/