 1
Factor 0*r**3 - 4*r**4 - 5*r**3 + 4*r**2 - 3*r**3 - 4*r + 12*r.
-4*r*(r - 1)*(r + 1)*(r + 2)
What is r in -16*r**2 + 47*r**5 + 41*r**5 - 84*r**5 + 12*r**4 = 0?
-2, 0, 1
Let b(z) be the first derivative of z**3/9 - 11*z**2/6 - 4*z + 45. Let b(n) = 0. What is n?
-1, 12
Let x = -3 - -6. Suppose 5*u + x*u - 3*u - 3*u + 2*u**2 = 0. What is u?
-1, 0
Factor -9*k**3 - 5*k**2 + k**4 - 6*k**4 - k**3.
-5*k**2*(k + 1)**2
Let s(g) = g**2 - 2. Let j be ((-3)/(-9))/((-1)/6). Let x be s(j). Let -1/4*z - 1/4*z**3 + 0 - 1/2*z**x = 0. What is z?
-1, 0
Let h(j) = -j**2 - 2*j + 3. Let w be h(1). Let i(v) be the second derivative of 3/4*v**4 + v**2 + 11/6*v**3 + 2*v + w. Factor i(n).
(n + 1)*(9*n + 2)
Let g = -16 - -17. Find b, given that b - b - 3*b - b**2 - g - 1 = 0.
-2, -1
Suppose 10 = 5*a - 45. Find p, given that -p**4 + 5*p**3 + 4*p**5 - a*p**4 + 3*p**3 + 0*p**3 = 0.
0, 1, 2
Let j be ((-198)/(-40) - 5)*-4. Find g such that -2/5*g + 0 - j*g**2 = 0.
-2, 0
Let z be (17/(510/(-12)))/(12/(-70)). Let -2*r - 10*r**3 + 29/3*r**2 + z*r**4 + 0 = 0. Calculate r.
0, 2/7, 1, 3
Let m(l) be the first derivative of -6 + 0*l**5 - 1/9*l**2 + 0*l + 0*l**3 + 1/9*l**4 - 1/27*l**6. Solve m(b) = 0 for b.
-1, 0, 1
Let p be -2 - (-1*502 - -4). Let n = -3456/7 + p. Suppose 6/7*d**2 + n*d + 8/7 = 0. Calculate d.
-2, -2/3
Let 2/13*k**2 + 12/13 + 14/13*k = 0. What is k?
-6, -1
Determine g, given that 0*g + 3/2*g**3 + 0 + 0*g**2 = 0.
0
Let n(r) be the second derivative of -3*r**5/80 - r**4/16 - 2*r. Factor n(k).
-3*k**2*(k + 1)/4
Factor -3*f**4 - 6*f**2 + 21/2*f**3 - 6*f + 0.
-3*f*(f - 2)**2*(2*f + 1)/2
Let z(x) be the third derivative of x**5/60 - 7*x**4/72 + x**3/9 - 3*x**2. Factor z(c).
(c - 2)*(3*c - 1)/3
Suppose -5*t + 90 = -90. Factor 79*s**2 + 2*s**2 + t*s - 8*s + 4 + 8*s.
(9*s + 2)**2
Let l(g) be the first derivative of -g**6/15 + 2*g**5/25 + 2*g**4/5 - 8*g**3/15 + 41. What is m in l(m) = 0?
-2, 0, 1, 2
Let t(x) = 3*x + 20. Let y be t(-6). Let a(c) be the second derivative of 1/42*c**4 + 1/7*c**2 + 0 - 2/21*c**3 - y*c. Factor a(q).
2*(q - 1)**2/7
Solve 4/13 + 2/13*d**2 - 6/13*d = 0.
1, 2
Let s(z) = z**3 - 3*z**2 - 4. Let h(t) = t**3 - 4*t**2 - 4. Let x(y) = -6*h(y) + 7*s(y). Suppose x(i) = 0. Calculate i.
-2, 1
Factor 0*z**3 - 6*z + 2 + 5 + 2*z**3 - 3.
2*(z - 1)**2*(z + 2)
Let 2/3 + 4/3*c**2 - 5/3*c - 1/3*c**3 = 0. What is c?
1, 2
Let y = 15 - 43/3. Determine z, given that 10/3*z + 16/3*z**2 + y + 8/3*z**3 = 0.
-1, -1/2
Let z(w) = -w**5 + 12*w**4 - 5*w**3 - 4*w**2 + 2*w. Let q(l) = -4*l**5 + 61*l**4 - 24*l**3 - 20*l**2 + 9*l. Let h(b) = -6*q(b) + 33*z(b). What is a in h(a) = 0?
-2/3, 0, 1, 2
Solve -1/3 + 1/3*o - 1/3*o**3 + 1/3*o**2 = 0 for o.
-1, 1
Factor 1/7*l**3 + 0*l + 0 + 2/7*l**2.
l**2*(l + 2)/7
Let r(h) = h**2 - h - 1. Suppose -w = -2 - 0. Let v(x) = x**3 - 5*x**2 + 5*x + 1. Let t(o) = w*r(o) + v(o). Factor t(n).
(n - 1)**3
Let z(l) be the first derivative of -l**3/15 - 4*l**2/5 - 16*l/5 + 10. What is c in z(c) = 0?
-4
Let f = 41 + -23. Let x = -16 + f. Suppose 0*k + 0*k**2 + 4/3*k**3 + 0 - x*k**4 = 0. What is k?
0, 2/3
Let m = 799/1960 + -3/392. Factor 0 - 2/5*k**4 + 0*k + m*k**3 + 0*k**2.
-2*k**3*(k - 1)/5
Suppose 2*t - 19 = -11. Suppose 0*x + 1/2*x**t + 0*x**2 + 0 + 0*x**3 + 1/2*x**5 = 0. What is x?
-1, 0
Let m(i) be the first derivative of i**4/36 + 2*i**3/9 + i**2/2 - 12. Factor m(x).
x*(x + 3)**2/9
Let n(o) be the second derivative of -3/10*o**5 + 0 + 0*o**4 + o**3 - 1/10*o**6 + 3/2*o**2 - 3*o. Find l, given that n(l) = 0.
-1, 1
Let j(q) = 15*q**2 + 85*q + 55. Let u(p) = p**2 + 6*p + 4. Let v(o) = 4*j(o) - 55*u(o). Factor v(y).
5*y*(y + 2)
Find r, given that 8/9*r**2 - 4/3*r**3 + 2/9*r + 10/9*r**5 + 0 - 8/9*r**4 = 0.
-1, -1/5, 0, 1
Let l be 48 - (-2 + -1 + 2). Suppose 0*t**2 + 8*t**2 + 13*t**2 + l*t**3 - 24*t + 4 = 0. What is t?
-1, 2/7
Solve 0 + 0*g - 2/3*g**2 + 2/3*g**3 = 0.
0, 1
Let y(u) = -9*u**3 - 17*u**2 - 4*u + 4. Let x(v) = 2*v**3 - v**3 + 3*v**3 + 8*v**2 + 2*v + 0*v**3 - 2. Let w(l) = -13*x(l) - 6*y(l). Solve w(p) = 0.
-1, 1
Let a = -16 - -18. Suppose -a*g = g - 6. Determine s, given that 2/3*s**g + 4/3*s + 2/3 = 0.
-1
Let x = -608/35 - -130/7. Factor 3/5*w**2 - 3/5*w**3 + 0 + x*w.
-3*w*(w - 2)*(w + 1)/5
Let v be -10 + (-3)/6*0. Let c be 1/1 - (-2)/v. Suppose 0 - 2/5*h**2 + c*h = 0. Calculate h.
0, 2
Let z(u) be the first derivative of -u**5/5 - u**4/2 - u**3/3 + 8. Factor z(m).
-m**2*(m + 1)**2
Suppose 16 = -f + 3*f + 5*j, -24 = 4*f - 4*j. Let u = 4 + f. Determine t so that 2/3*t**u + 0 + 0*t - 2/3*t**3 = 0.
0, 1
Let g be ((-54)/(-8))/9 + 2/(-4). Factor 0 - 1/4*r - g*r**2.
-r*(r + 1)/4
Suppose s = 4*t - 8, 9*t = 11*t + 2*s - 4. Factor 0 + 0*c - 2/3*c**t.
-2*c**2/3
Let y(t) be the first derivative of t**3/3 + t**2 - t - 1. Let u be y(1). Find z such that 0*z**2 + 4 + 3*z + u*z**2 - 9*z = 0.
1, 2
Let k be 2/1 + -2 + 1. Let r be (-7)/(2*k/(-2)). Let 4*l - r*l**2 - l**2 - l**2 - l**2 = 0. What is l?
0, 2/5
Let s(p) be the second derivative of -7*p**6/6 - 59*p**5/20 - 7*p**4/3 - 2*p**3/3 + 14*p. Solve s(l) = 0 for l.
-1, -2/5, -2/7, 0
Let c(n) be the second derivative of 0*n**2 - 1/210*n**7 + 1/30*n**4 + 0 - 1/75*n**6 - 3*n + 0*n**5 + 1/30*n**3. Suppose c(a) = 0. What is a?
-1, 0, 1
Factor -6 + s**2 - s**3 + 2*s**2 + 2*s**3 + 2.
(s - 1)*(s + 2)**2
Let c(r) be the first derivative of 0*r**2 + 2/15*r**3 - 8/5*r - 3. Factor c(g).
2*(g - 2)*(g + 2)/5
Let d be (-8)/(-14) + (-4)/14. Let o(h) = 32*h - 93. Let i be o(3). Solve 0 - d*k**i - 2/7*k - 4/7*k**2 = 0 for k.
-1, 0
Let f(n) = n**3 - 4*n**2 - 2*n - 12. Let s be f(5). Factor 2/3*u**2 - 1/3*u**5 - 1/3*u**4 + 2/3*u**s - 1/3*u - 1/3.
-(u - 1)**2*(u + 1)**3/3
Suppose 2*h + 10 = 4*h. Determine u so that -u**3 + h*u**3 - 2*u**4 + 2 + 4*u**2 - 4*u - 4*u**2 = 0.
-1, 1
Let r(u) be the third derivative of u**5/180 - u**4/18 + u**3/6 + 4*u**2. Solve r(k) = 0 for k.
1, 3
Let k(y) be the third derivative of y**7/280 + y**6/30 + y**5/10 - 2*y**3/3 + 4*y**2. Let n(j) be the first derivative of k(j). Factor n(g).
3*g*(g + 2)**2
Let c be 1/(2 + 21/(-12)). Factor 0*z**4 - 5*z**4 + 2*z**4 + 0*z**c.
-3*z**4
Let g(n) = n + 7. Let p be g(-3). Factor -2*v - 3*v**2 - 3*v**2 + p*v**2 + 0*v.
-2*v*(v + 1)
Let f(u) = u + 9. Let m be f(-7). Let z be (3/(84/16))/m. Find k, given that z*k**2 - 8/7*k + 8/7 = 0.
2
Let m(x) = -5*x**3 - 12*x**2 - 21*x - 19. Let g(d) = -4*d + 47*d + 24*d**2 - 3*d**3 + 37 + 12*d**3. Let t(u) = -3*g(u) - 5*m(u). Factor t(i).
-2*(i + 2)**3
Let a(u) be the first derivative of u**5 - 5*u**4 + 25*u**3/3 - 5*u**2 + 20. Factor a(c).
5*c*(c - 2)*(c - 1)**2
Let t(q) be the second derivative of 3*q**5/80 + q**4/8 - q**3/8 - 3*q**2/4 + 4*q. Factor t(i).
3*(i - 1)*(i + 1)*(i + 2)/4
Suppose 3 = 5*b + 4*x - 11, 0 = -3*b - 5*x + 11. Let z be (3 + -4)*(b - 2). Factor z*c**2 + 4/7*c**3 + 0*c + 0 - 6/7*c**4.
-2*c**3*(3*c - 2)/7
Suppose 0 = -9*l + 6*l. Let w(x) be the first derivative of -1 + 1/5*x**2 - 14/15*x**3 + 3/2*x**4 + l*x + 4/15*x**6 - 26/25*x**5. Factor w(u).
2*u*(u - 1)**3*(4*u - 1)/5
Solve 4*g**4 - 6*g**3 - 2*g**4 + 3*g**5 + 0*g**3 - 5*g**4 = 0 for g.
-1, 0, 2
Factor 0*d - 26*d**3 + 29*d**3 + 6*d**2 + 3*d.
3*d*(d + 1)**2
Let y be -8*(3 - (-3)/2). Let f = 184/5 + y. Let -f*j + 0 + 2/5*j**2 = 0. What is j?
0, 2
Let s(d) = -2*d**4 + 6*d**3 + 10*d**2 - 16*d - 14. Let v(i) = -5*i**4 + 17*i**3 + 29*i**2 - 48*i - 41. Let k(g) = -7*s(g) + 2*v(g). Let k(l) = 0. What is l?
-1, 2
Let s(v) be the third derivative of v**6/120 - v**5/40 + v**3/2 + v**2. Let f(o) be the first derivative of s(o). Factor f(q).
3*q*(q - 1)
What is w in 8/5 + 1/5*w**4 - 6/5*w**2 - 4/5*w + 1/5*w**3 = 0?
-2, 1, 2
Let v be (-125)/(-45) - 2/(-9). Suppose -6*g**4 + v*g**2 + 21*g + 6*g**3 + 21*g**2 + 6 - 3*g**5 + 0*g**4 = 0. Calculate g.
-1, 2
Let a(h) = -4*h**2 + 4*h - 2. Let t(n) = n**3 + 12*n**2 - 13*n + 7. Suppose -3*x + x = -28. Let w(m) = x*a(m) + 4*t(m). Factor w(p).
4*p*(p - 1)**2
Factor -5 + 1 - 52*u + 44*u - 4*u**2.
-4*(u + 1)**2
Let o = 33 + -33. Let b(z) be the second derivative of o + 3*z + 0*z**3 - 1/12*z**4 + 1/2*z**2. Factor b(s).
-(s - 1)*(s + 1)
Let t(b) = -b**3 - 10*b**2 - 2*b - 10. Let u be t(-10). Let x = u + -10. Factor x*i - 1/3*i**2 + 1/3.
-(i - 1)*(i + 1)/3
Let g = 43 + -39. Let o(u) be the third derivative of 0*u**5 + 0*u**3 + 0*u - 