Suppose -x = -4*y + y. Factor -2/3*t**4 - 2*t**y + 2*t**3 + 2/3*t + 0.
-2*t*(t - 1)**3/3
Let h = 13 + -10. Determine m, given that -2*m**2 - 5 + 0 + 4*m + h = 0.
1
Let f = 7 - 5. Let k be 0 + f + (1 - -2). Factor u**2 - k + 5 + u.
u*(u + 1)
Suppose 2*z - 17 + 5 = 0. Let 4*t**2 + 6*t**4 - t - 2*t**4 + 3*t**5 - z*t**3 - 4*t**5 = 0. Calculate t.
0, 1
Let d(b) = b. Let m(r) = r**3 + 2*r**2 + 9*r. Let u(q) = 24*d(q) - 3*m(q). Suppose u(n) = 0. What is n?
-1, 0
Let t(r) be the first derivative of r**7/210 - r**6/150 - r**5/100 + r**4/60 - 2*r + 3. Let l(h) be the first derivative of t(h). Determine g so that l(g) = 0.
-1, 0, 1
Let y(o) be the third derivative of 0*o**4 + 1/270*o**6 + 1/945*o**7 + 0*o**3 + 0*o + 5*o**2 + 0 + 1/270*o**5. Find z, given that y(z) = 0.
-1, 0
Let z(m) be the second derivative of m**9/52920 + m**8/11760 + m**7/8820 + m**4/4 + 2*m. Let r(l) be the third derivative of z(l). What is g in r(g) = 0?
-1, 0
Let g(u) be the first derivative of -u**4/4 + u**3 - 3*u**2/2 + 3*u + 1. Let m(j) be the first derivative of g(j). Factor m(q).
-3*(q - 1)**2
Let n be 2 + 80/(-45) - 2/36. Find k, given that 1/6*k**2 + 0 + n*k = 0.
-1, 0
Let u = -292 - -293. Factor -9/2*b - 6*b**2 - 5/2*b**3 - u.
-(b + 1)**2*(5*b + 2)/2
Let n(p) = -p**2 + 7*p - 4. Let o be n(6). Let d(j) = -j**3 + 2*j**2 + 2. Let g be d(o). Factor 0 + 2/5*x**g + 0*x.
2*x**2/5
Let x(c) be the first derivative of -c**4/10 + 4*c**3/5 - 64*c/5 - 61. Determine b, given that x(b) = 0.
-2, 4
Suppose 0 - 3/7*h**2 + 9/7*h = 0. Calculate h.
0, 3
Let a(b) be the second derivative of -b**5/10 + b**4/3 + 4*b - 3. Factor a(v).
-2*v**2*(v - 2)
Let c(q) be the third derivative of -q**8/12 - 4*q**7/7 - 5*q**6/3 - 8*q**5/3 - 5*q**4/2 - 4*q**3/3 + 5*q**2. Solve c(r) = 0.
-1, -2/7
Let u(m) be the second derivative of -m**5/100 - m**4/40 + 5*m**2/2 + 2*m. Let k(t) be the first derivative of u(t). Determine a so that k(a) = 0.
-1, 0
Let q(l) be the third derivative of l**5/360 - l**4/24 + l**3/4 + 16*l**2. Suppose q(b) = 0. Calculate b.
3
Let k(v) be the first derivative of 3*v**5/50 - v**4/15 - v**3/5 + 2*v**2/5 - 2*v + 3. Let d(i) be the first derivative of k(i). Factor d(q).
2*(q - 1)*(q + 1)*(3*q - 2)/5
Suppose 0 = 2*k - 3 - 1. Solve k*w**2 - w**2 + w**2 = 0.
0
Let d(l) be the first derivative of l**6/165 + l**5/110 - l**4/66 - l**3/33 + 5*l - 3. Let m(u) be the first derivative of d(u). Factor m(r).
2*r*(r - 1)*(r + 1)**2/11
Let w(z) = -2*z + 28. Let l be w(13). Find c such that -2/3 + 8/9*c**l + 2/9*c = 0.
-1, 3/4
Let w(t) = -13*t**3 - 1. Let h be w(-1). What is b in -h*b**3 + 9*b**4 + b**2 + 3*b**4 + 5*b**2 - 4*b**5 - 2*b**2 = 0?
0, 1
Let z(a) be the first derivative of a**9/840 - a**8/1400 - 2*a**7/525 + a**6/225 - a**3 - 3. Let c(n) be the third derivative of z(n). Factor c(u).
2*u**2*(u + 1)*(3*u - 2)**2/5
Let m be 44/8 + 1/2. Suppose h + 20 = m*h. Factor 2*s**h - s**5 + 4*s**2 - 2*s**2 + s - 4*s**4.
-s*(s - 1)*(s + 1)**3
Let i(t) be the third derivative of t**7/1155 + t**6/330 - 2*t**5/165 - 2*t**4/33 + 20*t**2. Find m, given that i(m) = 0.
-2, 0, 2
Let y(c) be the second derivative of c**8/6720 + c**7/3360 - c**6/1440 - c**5/480 + c**3/2 + c. Let u(r) be the second derivative of y(r). Factor u(g).
g*(g - 1)*(g + 1)**2/4
Let x be 28/35 + (2 - (-41)/(-20)). Factor 3 + x*t**2 - 3*t.
3*(t - 2)**2/4
Suppose 5*g = 4*u + 25, -2*g - 2*u - 3 - 5 = 0. Let v = 3 - g. Factor 1/3 - 1/3*b**3 - 1/3*b**v + 1/3*b.
-(b - 1)*(b + 1)**2/3
Suppose -u = 2*l + 4, -4*u + 6*l + 36 = l. Suppose 2*j**3 - 2/3*j**u - 2*j + 4/3 - 2/3*j**2 = 0. What is j?
-1, 1, 2
Let s = 3/11 + -4/55. Let 1/5*a**2 + s + 2/5*a = 0. Calculate a.
-1
What is v in 1/2*v**2 + 1/4*v**3 + 0 + 1/4*v = 0?
-1, 0
Suppose -8*k + 3*k - 30 = 0. Let s(u) = -3*u**2 + 29*u + 5. Let w = 56 - 39. Let r(l) = -l**2 + 10*l + 2. Let x(n) = k*s(n) + w*r(n). Factor x(d).
(d - 2)**2
Let y = 3282/5 - 654. Solve -12/5 - 3/5*w**2 + y*w = 0.
2
Let v(s) = 3*s**2 + 4*s + 1. Let w(l) = 8*l**2 + 11*l + 3. Let d = 9 - 4. Suppose d*f + 2*k = f - 14, 5*f + 16 = -4*k. Let p(g) = f*w(g) + 11*v(g). Factor p(a).
(a - 1)*(a + 1)
Let u(a) be the second derivative of -5*a**4/12 + 10*a**3/3 + 25*a**2/2 + 11*a. Determine v so that u(v) = 0.
-1, 5
Let p be 2/1 + 48/4. Factor 2*r**5 + p*r + 2*r**4 - 14*r.
2*r**4*(r + 1)
Let w = 123 + -2582/21. Let k(d) be the third derivative of d**2 + 1/420*d**6 + 0 + 1/28*d**4 - 1/70*d**5 + 0*d - w*d**3. Factor k(g).
2*(g - 1)**3/7
Suppose 0 - 8/3*u**4 + 0*u - 2/3*u**3 + 0*u**2 - 2*u**5 = 0. What is u?
-1, -1/3, 0
Let b(r) be the second derivative of -r**6/90 + r**5/10 + r**3 - 6*r. Let a(k) be the second derivative of b(k). Factor a(o).
-4*o*(o - 3)
Let w(o) be the first derivative of -o**6/15 + o**4/5 - o**2/5 + 4. Factor w(b).
-2*b*(b - 1)**2*(b + 1)**2/5
Let p(q) be the third derivative of q**8/40320 - q**7/5040 - q**5/60 + 3*q**2. Let c(y) be the third derivative of p(y). Determine z so that c(z) = 0.
0, 2
Factor 0 + 1/6*k**3 - 1/6*k + 0*k**2.
k*(k - 1)*(k + 1)/6
Let f be 6/8 + 30/(-8). Let q(d) = d**2 + 2*d - 1. Let m be q(f). Find l, given that -l**4 + 0*l**4 + l**m - l - 3*l**3 + 4*l**3 = 0.
-1, 0, 1
Let s(f) be the third derivative of 0 + 0*f**3 + 2*f**2 + 1/96*f**4 + 1/240*f**5 + 0*f. Factor s(w).
w*(w + 1)/4
Let u(h) = -h**2 + 6*h + 1. Let b(k) = -2*k**2 + 11*k + 3. Let p be 10*2/(1 - -1). Let y(j) = p*u(j) - 6*b(j). Let y(o) = 0. Calculate o.
-1, 4
What is z in 3/4*z**2 + 0 - 1/2*z = 0?
0, 2/3
Let x(s) = 2*s**2 - 6*s. Let y be x(3). Factor y - 1/4*k**3 - 1/4*k**2 + 0*k.
-k**2*(k + 1)/4
Solve 6*g**2 + 10*g + 13*g**4 + 5*g**4 + 4 - 20*g**4 + 0*g - 2*g**3 = 0.
-1, 2
Suppose 7*j = 3*j + 16. Suppose -j*u - u = 0. Find f, given that -5/2*f**2 + 2*f**3 - 1/2*f**4 + u + f = 0.
0, 1, 2
Let l = 86 + -84. Solve 4/3 + 2*g + 2/3*g**l = 0 for g.
-2, -1
Suppose -21 - 3 = -3*i. Suppose 3*l - 10 = i. Factor 3*z**3 - l*z**2 + 9 - 1 - 5*z**3.
-2*(z - 1)*(z + 2)**2
Let y(j) = 3*j**2 + 12*j + 7. Let g(p) = 10*p**2 + 38*p + 21. Let m(z) = -2*g(z) + 7*y(z). Factor m(l).
(l + 1)*(l + 7)
Factor 2*t**3 - 4*t + t**4 - 2*t**4 - 5 + 1 + 3*t**2.
-(t - 2)**2*(t + 1)**2
Let s(n) be the third derivative of n**8/3360 + n**7/630 + n**6/360 - n**4/8 - 2*n**2. Let c(m) be the second derivative of s(m). Factor c(d).
2*d*(d + 1)**2
Let q(n) = -n**2 - 6*n + 4. Let w be q(-6). Let z = -4 + w. Solve -2/3*b**2 - 2/3*b**4 + 0*b + 4/3*b**3 + z = 0.
0, 1
Factor -1/4*b**3 - 5/4*b + b**2 + 1/2.
-(b - 2)*(b - 1)**2/4
Let h = 97 - 675/7. Factor 0 + 2/7*u + 2/7*u**3 - h*u**2.
2*u*(u - 1)**2/7
Let n(i) = i**3 - 2*i**2 - 6*i + 9. Let k be n(3). Factor 0*q**3 - 3/2*q**5 + 0*q**2 + k*q - 3/2*q**4 + 0.
-3*q**4*(q + 1)/2
Let a = -39 + 23. Let r be (a/28)/((-2)/7). Factor 0*l**3 - l**4 + l**2 + 2*l**3 - r*l**2.
-l**2*(l - 1)**2
Let q(k) = k**2 - 22*k - 167. Let m be q(-6). Factor -6*b**2 + 5/2*b**3 + 9/2*b - m.
(b - 1)**2*(5*b - 2)/2
Let u be ((-9)/141)/(2 - 1). Let x = 173/235 - u. Factor -x*f + 2/5*f**2 + 0.
2*f*(f - 2)/5
Let m = -121/2 - -61. Let -m*c - c**2 + 0 - 1/2*c**3 = 0. Calculate c.
-1, 0
Factor 1/3*s + 1/3*s**2 + 0.
s*(s + 1)/3
Let t(i) be the third derivative of i**6/360 + i**5/120 + 2*i**3/3 - i**2. Let y(u) be the first derivative of t(u). Factor y(b).
b*(b + 1)
Let c(o) = 193*o**5 + 115*o**4 - 183*o**3 - 112*o**2 - 13*o - 3. Let m(d) = d**5 - d**4 + d**3 - d + 1. Let t(l) = -c(l) - 3*m(l). Let t(q) = 0. What is q?
-1, -2/7, 0, 1
Factor 6*q**3 + 4*q + 23*q**2 + q**5 - 7*q**4 - 19 + 3 - 12*q + q**3.
(q - 4)**2*(q - 1)*(q + 1)**2
Let z(d) be the first derivative of -4*d**3 - 8*d**2 - 4*d + 5. Determine n so that z(n) = 0.
-1, -1/3
Suppose 0 = -4*p + 2*b + 16, 5*p + 0*p - 2*b = 18. Let c(k) be the first derivative of 4/7*k - 9/7*k**p + 2/3*k**3 - 4. Determine u so that c(u) = 0.
2/7, 1
Let w(v) be the third derivative of -2/105*v**5 + 0*v**3 + 0 + 1/245*v**7 - 3/392*v**8 + 2/105*v**6 + 4*v**2 + 0*v + 0*v**4. Factor w(x).
-2*x**2*(x + 1)*(3*x - 2)**2/7
Let w(r) = 140*r**2 - 70*r - 420. Let s(y) = 10*y**2 - 5*y - 30. Let a(d) = -55*s(d) + 4*w(d). Let a(i) = 0. What is i?
-3/2, 2
Let c(x) be the third derivative of x**7/105 + x**6/12 + x**5/5 - x**4/3 - 8*x**3/3 + 15*x**2. Factor c(z).
2*(z - 1)*(z + 2)**3
Let r(d) = 3*d**3 + 18*d**2 - 11*d - 4. Let q(w) = 5*w**3 + 37*w**2 - 2