4*r**3 + r**2 - 1. Let c = 13 - 11. Let y(u) = -u**4 + u**2 - 1. Let x(k) = c*y(k) - 2*o(k). Factor x(f).
4*f**3*(f + 2)
Let f be -1 + 2 + 0/1. Suppose 5*a - v - 13 = 4, -3*a + f = 4*v. Factor -4 + 3 - i**2 - a*i - 1.
-(i + 1)*(i + 2)
Let g(l) be the first derivative of 3*l**4/28 - 24*l**3/7 - 153*l**2/14 - 78*l/7 - 377. Find y, given that g(y) = 0.
-1, 26
Factor -147*s**3 - 34*s**3 - 5*s**4 - 21*s**3 - 33*s**3.
-5*s**3*(s + 47)
Factor 6*g**3 - g**2 - 19*g**3 + 12*g**3.
-g**2*(g + 1)
Let q be (-62)/(-40) + (-20)/25. Solve 0 + 3/2*v + q*v**2 = 0 for v.
-2, 0
Let f(g) be the second derivative of 1/27*g**4 + 0 + 0*g**3 - 2/9*g**2 - 9*g. What is q in f(q) = 0?
-1, 1
Let h(p) be the first derivative of p**5/60 + 23*p**2 - 18. Let l(i) be the second derivative of h(i). Solve l(m) = 0.
0
Let n = -8178 - -8179. Let -n + 3/2*q + 0*q**2 - 1/2*q**3 = 0. What is q?
-2, 1
Suppose 15*i - 7*i = 6*i. Let x(y) be the third derivative of -1/70*y**5 - 1/56*y**4 + 0*y - 1/280*y**6 + i*y**3 + 6*y**2 + 0. Factor x(l).
-3*l*(l + 1)**2/7
Let h(l) = -l**4 - 7*l**3 - 11*l**2 + 7*l + 10. Let p(z) = -3*z**4 - 14*z**3 - 23*z**2 + 14*z + 21. Let b(v) = -5*h(v) + 2*p(v). Factor b(a).
-(a - 8)*(a - 1)*(a + 1)**2
Let y(l) be the first derivative of 3*l**5/25 - 23*l**4/20 + 28*l**3/15 + 6*l**2/5 + 243. Let y(x) = 0. What is x?
-1/3, 0, 2, 6
Suppose 0 = -4*o + 5*f + 13, -10*o + 15*o + 4*f = 6. Factor -2/7*n**4 - 8/7*n**3 - 4/7*n - 10/7*n**o + 0.
-2*n*(n + 1)**2*(n + 2)/7
Factor -16/5*x - 1/5*x**2 - 3.
-(x + 1)*(x + 15)/5
Let k(m) be the third derivative of 0 - 25*m**2 + 0*m + 5/12*m**6 - 7/6*m**5 + 11/12*m**4 - 1/3*m**3. Suppose k(v) = 0. Calculate v.
1/5, 1
Let x(p) be the first derivative of p**4/6 + 20*p**3/9 + 11*p**2 + 24*p + 19. Suppose x(g) = 0. What is g?
-4, -3
Let q(i) = i**2 + 1. Let j(s) = -6*s**2 - 7*s - 4. Let d(x) = j(x) + 5*q(x). Let a(m) = m**2 + 6*m - 1. Let h(p) = -7*a(p) - 6*d(p). Find r such that h(r) = 0.
-1, 1
Let p(a) be the first derivative of 0*a + 1/5*a**3 + 3/20*a**4 - 20 + 0*a**2. Solve p(k) = 0.
-1, 0
Let j be 4/(-24)*3*-4*-1. Let b(u) = 4*u**3 + 12*u**2 - 9*u. Let g(n) = n**3 + 2*n**2 + 2*n + 0*n + n**2 - 4*n. Let l(h) = j*b(h) + 9*g(h). Factor l(r).
r**2*(r + 3)
Let k(p) be the first derivative of -p**3/4 + 6*p**2 - 165*p/4 + 85. Let k(y) = 0. Calculate y.
5, 11
Suppose -90 = 220*r - 248*r - 34. Find m, given that -2/5*m**r - 40 - 8*m = 0.
-10
Suppose 0*y + y = 5*j + 26, 22 = y - 4*j. Let u(s) = -9*s**3 + 14*s**2 - 10*s + 6. Let l(q) = -q**2 - q + 1. Let g(w) = y*l(w) - u(w). Factor g(f).
f*(f - 2)*(9*f - 2)
Let y be (6 - ((-2)/2 + 5)) + 2. Suppose -3*n - 2*j + 16 = 0, y*n - 5 = -2*j + 13. Let -16/5 - 12/5*x - 4/5*x**4 + 12/5*x**3 + 4*x**n = 0. What is x?
-1, 1, 4
Solve 16/13*t**4 - 28/13*t**2 + 10/13*t**5 + 14/13*t + 12/13 - 24/13*t**3 = 0.
-2, -1, -3/5, 1
Let x(a) be the third derivative of -6*a**7/35 + 17*a**6/15 - 37*a**5/15 + 4*a**4/3 + 8*a**3/3 - 887*a**2. Let x(o) = 0. What is o?
-2/9, 1, 2
Let x = 63198/19 - 3324. What is q in -36/19 - x*q - 2/19*q**3 - 16/19*q**2 = 0?
-3, -2
Let c be 288/(-1944)*(-9)/6. Factor c*n**3 + 4/9*n**2 + 0 + 2/9*n.
2*n*(n + 1)**2/9
Suppose 7*k - 54 = -6*k - 28. Solve -108/7 - 3/7*f**k - 36/7*f = 0.
-6
Let c(f) = 7*f**3 + f**2 - 3*f - 5. Let l(z) = 16*z**3 - 4*z + z**2 - 8 - 6*z**3 + 1. Let x(j) = -7*c(j) + 5*l(j). What is g in x(g) = 0?
0, 1
Let v be (2/4)/((-4)/(-40)). Suppose -v*n + 8 = -2. Let r**2 + r**4 - n*r + 0*r - 4*r**2 + 4*r = 0. What is r?
-2, 0, 1
Suppose 0 - r**3 + 6*r**2 - 4*r - 3/2*r**4 + 1/2*r**5 = 0. What is r?
-2, 0, 1, 2
Let i be ((-1856)/1160)/((-13)/3 + 3). Solve -1/5*z**4 - i*z**2 + 0 + z**3 + 0*z = 0 for z.
0, 2, 3
Let a(z) = z - 14. Let t be a(16). Let c be (-11)/(-2) - (-2)/(-4). Solve t*u - 3*u**3 + 12*u**2 - c*u**4 - u - 5*u = 0.
-2, 0, 2/5, 1
Let l(c) be the first derivative of -1/2*c**3 + 1/4*c**4 + 5 - 3*c**2 - 3*c. Let v(h) be the first derivative of l(h). Determine w so that v(w) = 0.
-1, 2
Let n(k) be the first derivative of -k**6/2880 + k**5/320 - 23*k**3/3 - 7. Let q(p) be the third derivative of n(p). Suppose q(c) = 0. Calculate c.
0, 3
Factor -3/7*g**2 - 75/7 - 30/7*g.
-3*(g + 5)**2/7
Let t(a) = 10*a**3 + 2 + 0*a**2 - 11*a**3 + 6*a**2. Let j be t(6). Solve j*g - 5*g**2 + 0*g**2 + 4*g**2 + 2*g**2 = 0 for g.
-2, 0
Let m be ((-209)/38 - (-6 + 1))*-8. Let 3/4*r**3 - 3/4*r**5 + 0 + 0*r + 0*r**2 + 0*r**m = 0. Calculate r.
-1, 0, 1
Let p(s) = s**2 - s. Let l(q) = -4*q**2 - 54*q - 18. Let j(w) = -l(w) - p(w). Determine z, given that j(z) = 0.
-18, -1/3
Let m = 71/3432 + 3/143. Let g(b) be the second derivative of 1/40*b**5 + 0*b**2 - m*b**6 + b + 0 - 1/12*b**3 + 5/48*b**4. Factor g(v).
-v*(v - 1)*(v + 1)*(5*v - 2)/4
Let k(n) be the first derivative of -1/9*n**4 + 2/9*n + 0*n**3 - 2/45*n**5 + 7 + 2/9*n**2. Suppose k(q) = 0. What is q?
-1, 1
Let d be (-2)/6*(-5 - 1). Suppose 30 + 111*b + 119*b - 225*b - 5*b**d = 0. Calculate b.
-2, 3
Let c(x) be the second derivative of 0 + 1/2*x**2 + x - 13/48*x**4 + 19/80*x**5 - 1/6*x**3 - 1/20*x**6. Suppose c(p) = 0. What is p?
-1/2, 2/3, 1, 2
Let v(l) = -l - 1. Let j be v(-6). Suppose s**3 + 6*s**3 - 12*s**3 + j*s**4 = 0. What is s?
0, 1
Factor -3/4*f**3 - 3*f**2 + 3/4*f + 3.
-3*(f - 1)*(f + 1)*(f + 4)/4
Suppose 0 = 4*z - 5*l + 17, 3*z + 9 = -2*l + 5*l. Suppose -4*g = -12, 6 = -5*f - g + 3*g. Factor -n + f*n - 3*n**z - 3*n - n**2.
-4*n*(n + 1)
Suppose -5*m - 50 = -3*x - 2*x, m + x + 12 = 0. Let i = -6 - m. Let j**5 - 33 + 87 + 22*j**4 - 3*j**i + 180*j**2 - 162*j - 92*j**3 = 0. What is j?
1, 3
Let x(v) be the second derivative of -v**6/80 - 3*v**5/40 + v**3 + 5*v**2 + 31*v. Let d(m) be the first derivative of x(m). Solve d(l) = 0 for l.
-2, 1
Let w(h) be the second derivative of h**5/10 + 2*h**4 + 11*h**3/3 - 176*h. Factor w(s).
2*s*(s + 1)*(s + 11)
Let g(b) be the third derivative of -b**8/2016 + b**7/315 + b**6/120 - b**5/90 - 5*b**4/144 - 476*b**2. Suppose g(y) = 0. Calculate y.
-1, 0, 1, 5
Let k(l) be the first derivative of l**4/32 + 19*l**3/8 + 783*l**2/16 - 841*l/8 + 179. What is u in k(u) = 0?
-29, 1
Let n(i) be the second derivative of i**6/240 - i**5/10 + i**4 - 9*i**3/2 + 26*i. Let h(m) be the second derivative of n(m). Factor h(x).
3*(x - 4)**2/2
Suppose 21 = 5*j + 6. Suppose 0 = -4*r - y + 48, 9*r - 6*r - 17 = 4*y. Factor 12 + 11 - 6*s**2 + 3*s**3 - 15 - r*s**j + 8*s - 2*s**4.
-2*(s - 1)*(s + 1)*(s + 2)**2
Let c be (10/14 + -1)*(-462)/1056. Let x(l) be the third derivative of c*l**4 + 0*l**3 + 0 + 0*l + 4*l**2 - 1/20*l**5. Factor x(u).
-3*u*(u - 1)
Let c(t) be the third derivative of t**7/1470 + t**6/84 + 23*t**5/420 + t**4/12 - 18*t**2. Factor c(h).
h*(h + 1)*(h + 2)*(h + 7)/7
Let u(f) = -46*f**2 + 139*f - 69. Let y(w) = -24*w**2 + 70*w - 35. Let o(a) = -6*u(a) + 11*y(a). Factor o(k).
(2*k - 1)*(6*k - 29)
Let l(b) = -9*b**3 + 16*b**2 + 34*b + 6. Let w(x) = -18*x**3 + 32*x**2 + 67*x + 12. Let h(z) = -5*l(z) + 3*w(z). Factor h(t).
-(t - 3)*(t + 1)*(9*t + 2)
Suppose 8 = 2*x - 2*m, -3*x - 6*m + 7*m + 8 = 0. Factor -v - 1/2 - 1/2*v**x.
-(v + 1)**2/2
Let t(k) be the third derivative of k**8/168 + k**7/420 - k**6/20 + k**5/24 + k**4/24 - 118*k**2. What is n in t(n) = 0?
-2, -1/4, 0, 1
Let o(f) = -4*f**3 - 115*f**2 - 230*f - 113. Let y(d) = -5*d**3 - 115*d**2 - 231*d - 113. Let x(w) = 4*o(w) - 3*y(w). Factor x(c).
-(c + 1)**2*(c + 113)
Let o(i) be the third derivative of i**6/780 + 54*i**5/65 + 2916*i**4/13 + 419904*i**3/13 + i**2 + 105. Find w, given that o(w) = 0.
-108
Let h(m) = -m**3 - 12*m**2 - 21*m - 11. Let n be h(-10). Let k = n + 3. Let 4*l**4 - 2*l + 6*l**2 + 0*l + k*l**2 - 10*l**3 = 0. Calculate l.
0, 1/2, 1
Determine m so that -4/7*m - 48/7 + 4/7*m**2 = 0.
-3, 4
Suppose 17*n + 4*n**2 + 5*n**2 - 9*n - 4*n**2 - 48*n = 0. Calculate n.
0, 8
Let u(x) = -10*x**2 + 15*x + 60. Let f(n) = -9*n**2 + 15*n + 52. Let m(d) = -5*f(d) + 4*u(d). Factor m(j).
5*(j - 4)*(j + 1)
Factor j**4 - 20*j**5 + 32 + 4*j**5 - 9*j**4 + 64*j + 6*j**5 - 13*j**3 + 26*j**2 + 9*j**5.
-(j - 2)*(j + 1)**2*(j + 4)**2
Let h = 3539/16 + -221. Let l(v) be the second derivative of 5/8*v**3 - 3/4*v**2 + 7*v + 0 - h*v**4. Solve l(d) = 0.
2/3, 1
Let n(o) = o + 17. Let h be n(-9). Determine g, given that -12*g + 2*g**3 + 0 + 2*g**3 + h = 0.
-2, 1
Let 2*o - 3*o - 5*o**2 + 7