v(x) = 61*x**2 - 21*x + 5. Let l(s) = 5*t(s) - 3*v(s). Factor l(y).
-4*y*(7*y - 2)
Let a(h) = 3*h**2 - 1. Let d be a(1). Factor 8*v**2 + 2*v**3 - 3*v**3 + d*v**3 - 3*v**3.
-2*v**2*(v - 4)
Let j(r) be the first derivative of 0*r - 1/24*r**4 - 1/30*r**5 - 7 + 1/18*r**3 + 1/12*r**2. Let j(p) = 0. What is p?
-1, 0, 1
Let q(g) be the second derivative of -5*g**7/42 + 23*g**6/3 + g**5/2 - 115*g**4/3 - 5*g**3/6 + 115*g**2 + 492*g. Find z such that q(z) = 0.
-1, 1, 46
Let -2/3 - 46/9*f - 40/9*f**2 = 0. Calculate f.
-1, -3/20
Let b = 965/4 - 4817/20. Factor -b*i**3 - 6/5*i + 2/5 + 6/5*i**2.
-2*(i - 1)**3/5
Let i(m) = -5*m**3 - 310*m**2 + 24. Let c be i(-62). Suppose -22/3*n**2 + c + 16*n + 2/3*n**3 = 0. Calculate n.
-1, 6
Let g(p) be the third derivative of -p**8/140 - 26*p**7/525 - 17*p**6/150 - p**5/25 + 4*p**4/15 + 8*p**3/15 + 224*p**2. Suppose g(n) = 0. What is n?
-2, -1, 2/3
Let r = -9608 + 9610. Factor 1/2*m**3 + 1/6*m**4 + 1/2*m**r + 0 + 1/6*m.
m*(m + 1)**3/6
Let y = 1825/2733 - 1/911. Factor -2*i**3 - y*i**5 + 0 - 2*i**4 - 2/3*i**2 + 0*i.
-2*i**2*(i + 1)**3/3
Let r(x) = 3*x**3 + 40*x**2 + 78*x + 13. Let o be r(-11). Find f such that 3/2*f**o + 3/2*f - 3 = 0.
-2, 1
Let a = -6754 - -81097/12. Let d(x) be the first derivative of -73/6*x**3 + 4 - 8*x**2 - 17/8*x**4 + a*x**6 - 2*x + 77/10*x**5. What is w in d(w) = 0?
-1, -2/7, 1
Factor 72/17*b + 122/17*b**3 + 0 + 168/17*b**2 + 28/17*b**4 + 2/17*b**5.
2*b*(b + 1)**2*(b + 6)**2/17
Let z(r) be the second derivative of -r**4/54 - 55*r**3/27 - 6*r**2 + 44*r + 2. Factor z(k).
-2*(k + 1)*(k + 54)/9
Let k(r) = r**3 - r**2 - r + 2. Let v(x) = -28*x**2 - 82*x + 4. Let u(y) = 4*k(y) - 2*v(y). Solve u(a) = 0 for a.
-8, -5, 0
Let u(j) = j**3 - 2*j**2 - 2. Let r(z) = 27*z**2 - 54*z + 6. Let h(t) = -r(t) - 3*u(t). Determine x, given that h(x) = 0.
-9, 0, 2
Suppose -797*t = -801*t + 12. Let y(r) be the first derivative of t*r**3 - 12/5*r**2 + 4/5*r - 5/4*r**4 - 5. Find c, given that y(c) = 0.
2/5, 1
Factor -1/6*b**3 + 0 + 0*b - 7/3*b**2.
-b**2*(b + 14)/6
Let i(p) be the third derivative of -p**5/160 + 27*p**4/64 - 25*p**3/8 + 2*p**2 - 229. Factor i(j).
-3*(j - 25)*(j - 2)/8
Let r(u) be the second derivative of u**6/15 + 9*u**5/10 + 9*u**4/2 + 9*u**3 - 5*u + 1. Let r(d) = 0. Calculate d.
-3, 0
Let y(s) be the second derivative of s**6/15 + s**5/2 - 7*s**4/6 - 5*s**3/3 + 6*s**2 - 2*s - 53. Suppose y(p) = 0. What is p?
-6, -1, 1
Let x(n) = -3*n**2 + 2*n + 2. Let l be x(2). Let i(r) = -r**2 - 7*r - 3. Let h be i(l). Solve -3*a**4 - 3*a**3 + 3*a**5 + 22*a + h*a**2 - 22*a = 0.
-1, 0, 1
Let s(l) = 19*l**2 - 4*l + 7. Let o be s(2). Let c be (-5)/(o/(-2))*(3 - -7). Suppose -4/3*m + 8/3 + c*m**3 - 8/3*m**2 = 0. What is m?
-1, 1, 2
Factor 12*g - 350 + 178 + 20*g**2 + 172.
4*g*(5*g + 3)
Let p(k) = -2*k**2 - 30*k - 64. Let q(g) = 10*g**2 + 148*g + 322. Let c(b) = 28*p(b) + 6*q(b). Factor c(z).
4*(z + 5)*(z + 7)
Determine p, given that p**3 - 16*p + 1130 - 1144 + 2*p**4 + 15*p**3 + 12*p**2 = 0.
-7, -1, 1
Factor -2/3*c**3 - 64/3*c - 22/3*c**2 - 56/3.
-2*(c + 2)**2*(c + 7)/3
Let k(y) = -25*y**2 - 174*y + 10. Let d be k(-7). Factor 0*c - 1/4*c**d + 1/2*c**2 + 0.
-c**2*(c - 2)/4
Let z(x) be the first derivative of 0*x**4 + 10 - 6*x + 1/4*x**3 + 0*x**2 - 3/40*x**5. Let j(o) be the first derivative of z(o). Solve j(w) = 0 for w.
-1, 0, 1
Let b = 5527/2 - 2763. Find w such that b*w**2 + 5/2*w + 3 = 0.
-3, -2
Let s(v) be the first derivative of v**4/18 - 16*v**3/27 - v**2 + 175. Find f, given that s(f) = 0.
-1, 0, 9
Let v(z) = z**2 - 17*z + 68. Let x be v(6). Factor 0*j - 2*j**2 - 3*j**2 + x*j**2 + j**3 + 2*j.
j*(j - 2)*(j - 1)
Let l(h) be the third derivative of -h**7/3780 - h**6/810 - h**5/540 + h**3/6 - 5*h**2. Let m(v) be the first derivative of l(v). Determine q so that m(q) = 0.
-1, 0
Let w(h) be the second derivative of 5*h**4/12 - 55*h**3/6 + 70*h**2 - 266*h. Factor w(d).
5*(d - 7)*(d - 4)
Suppose -4*k + 3*k - 3*m = 9, -5*m - 13 = 2*k. Let p be ((-15)/k + 2)*-6. Factor 8*t**4 - t**3 - 3*t**p + 7*t**5 - 8*t**2 - 3*t**5.
4*t**2*(t - 1)*(t + 1)*(t + 2)
Let v(n) = 8*n**5 - 9*n**4 + 8*n**3 + 7*n**2 - 7. Let s(q) = 4*q**5 - 4*q**4 + 4*q**3 + 4*q**2 - 4. Let a(y) = 7*s(y) - 4*v(y). Factor a(m).
-4*m**3*(m - 1)**2
Let r(g) = -g**3 + 2*g. Let n be r(-2). Let f = -2 + n. Factor 6*s**f + 4*s**2 - 6*s**2 + 2*s**4 - 6*s**3 + 0*s**4.
2*s**2*(s - 2)*(s - 1)
Let z(b) be the second derivative of -b**9/3780 + b**8/1680 + 11*b**4/6 - 49*b. Let s(h) be the third derivative of z(h). Factor s(q).
-4*q**3*(q - 1)
Suppose -4*m - 2*s - 9 = -39, -5*s = 2*m - 35. Suppose -12 + 37 = m*l. Suppose 2*r - 6*r - 2*r**2 + l*r**2 + 2 - r**2 = 0. Calculate r.
1
Let s be ((-4)/9)/((-420)/378)*(-1 + 2). Suppose -s*f**2 - 4 - 14/5*f = 0. What is f?
-5, -2
Let f(i) be the first derivative of 48 - 1/4*i**2 - 1/18*i**3 + 0*i. Factor f(z).
-z*(z + 3)/6
Let u(x) = 9*x**2 + 8*x. Suppose 2*r - p - 11 = -0*p, 4*p + 29 = 5*r. Let c(l) = 5*l**2 + 4*l. Let b(d) = r*c(d) - 3*u(d). Factor b(o).
-2*o*(o + 2)
Let j(v) be the third derivative of -v**6/40 - 2*v**5/5 - 2*v**4 - 91*v**2. Find t such that j(t) = 0.
-4, 0
Let a(u) = 3*u - 38. Let y be a(13). Let z be 5 + (-2 - y/1). Let -1/3*w - 2/3 + 1/3*w**z = 0. Calculate w.
-1, 2
Let q be 65/26 + 2/(-4). Factor 3 + 9*u**2 - 4*u**q + 2 + 10*u.
5*(u + 1)**2
Suppose 0 = -3*a - 5 - 7. Let r = 7 + a. Let 3*x - 2*x**r - x - 2*x + x**5 + x = 0. Calculate x.
-1, 0, 1
Let q(p) be the third derivative of -p**3 + 0 - 1/5*p**5 - 1/40*p**6 + 0*p - 5/8*p**4 - 2*p**2. Solve q(s) = 0.
-2, -1
Let t(v) be the second derivative of -v**7/84 + 2*v**6/15 - v**5/2 + 2*v**4/3 - v - 85. Determine d so that t(d) = 0.
0, 2, 4
Let a(f) be the third derivative of 0*f**3 + 1/42*f**4 + 1/420*f**6 - 20*f**2 - 1/70*f**5 + 0 + 0*f. Factor a(x).
2*x*(x - 2)*(x - 1)/7
Suppose 237/5*g - 657/5*g**2 + 267/5*g**3 - 9/5*g**4 + 162/5 = 0. What is g?
-1/3, 1, 2, 27
Let a(w) = -25*w**2 + 275*w - 205. Suppose 0 = 10*n - 11*n - 3. Let g(f) = 2*f**2 - 23*f + 17. Let v(q) = n*a(q) - 35*g(q). Suppose v(z) = 0. What is z?
2
Suppose 9*f = 13*f. Let s = -221/5 - -2441/55. Determine i so that f*i**2 + 4/11 - 6/11*i + s*i**3 = 0.
-2, 1
Let v(d) be the third derivative of d**8/336 + d**7/3 + 187*d**6/12 + 1156*d**5/3 + 122825*d**4/24 + 83521*d**3/3 + 307*d**2. Find t, given that v(t) = 0.
-17, -2
Suppose -317 - 107 = -156*u + 44. Factor 0*c**u + 0 - 4/9*c**2 + 4/9*c**4 - 2/9*c**5 + 2/9*c.
-2*c*(c - 1)**3*(c + 1)/9
Suppose -2*j - 12 = -8*j. Suppose -9*r - 3*r + 2*r - 2*r**3 - 7*r**j + 19*r**2 = 0. What is r?
0, 1, 5
Let w = -35 + 39. Suppose -n**3 + 5*n**3 + 2*n**w - 2*n - 2 - 2*n + 0 = 0. What is n?
-1, 1
Let j = 162 + -142. Find d, given that 43*d**3 + 5*d**4 - j*d**2 - 23*d**3 - 5*d**5 + 0*d**4 = 0.
-2, 0, 1, 2
Let m be -12 - (-2)/((-4)/8 + 1). Let z be m - -8 - ((-7)/5 - -1). What is y in 4/5 - 2/5*y**2 - z*y = 0?
-2, 1
Let r be (-116)/(-3) + (-11 - -7) + 4. Let z = r + -38. Factor -z*m**3 - 4/3*m**2 - 2/3*m + 0.
-2*m*(m + 1)**2/3
Let w(a) be the second derivative of -2*a**6/3 - 3*a**5/5 + 2*a**4/3 - 698*a. Factor w(v).
-4*v**2*(v + 1)*(5*v - 2)
Let q(z) = -z**4 + 18*z**3 + 98*z**2 - 2*z - 2. Let l(a) = -2*a**4 + 17*a**3 + 97*a**2 - 3*a - 3. Let n(w) = 2*l(w) - 3*q(w). Suppose n(s) = 0. Calculate s.
-10, 0
Let c(y) be the third derivative of -y**7/70 - y**6/40 + 113*y**2. Find u such that c(u) = 0.
-1, 0
Let p(o) be the third derivative of -2*o**7/105 + o**6/5 - 3*o**5/5 + 2*o**4/3 - 47*o**2 - 1. Factor p(l).
-4*l*(l - 4)*(l - 1)**2
Let n(v) be the first derivative of -v**7/60 + v**6/3 - 19*v**5/35 + 8*v**4/21 - v**3 + 3*v**2 + 24. Let g(x) be the third derivative of n(x). Factor g(d).
-2*(d - 8)*(7*d - 2)**2/7
Let j(p) be the first derivative of -p**3/8 - 147*p**2/16 + 117*p/2 + 509. Solve j(h) = 0.
-52, 3
Suppose -536*o**2 + 535*o**2 + 0*o - 9*o + 136 = 0. Calculate o.
-17, 8
Let t be (-63)/81 + 1 + (-2)/9. Let h(j) be the third derivative of 0 + j**2 + 0*j + 0*j**4 + t*j**3 - 1/20*j**5 - 1/40*j**6. Factor h(z).
-3*z**2*(z + 1)
Let w be (-130)/10*(-1)/(-9). Let j = -73/63 - w. Find t such that -j*t**2 - 4/7*t + 0 = 0.
-2, 0
Let v = 23700/7 - 3380. Factor 12/7*o**2 + v*o + 12/7.
4*(o + 3)*(3*o + 1)/7
Suppose f + 5*a - 16 - 6 = 0, -5*a = -5*f - 10. Let u(j) be the first derivativ