k(6). Suppose u - q = -5*u. Find y such that -1/3*y + 0 + 0*y**u + 1/3*y**3 = 0.
-1, 0, 1
Let v(g) be the second derivative of g**4/6 - 5*g**3/3 + 5*g**2/2 + 39*g. Let r be v(5). Solve 0 - 5*h**4 + 5/4*h**5 - r*h + 15/4*h**3 + 5*h**2 = 0.
-1, 0, 1, 2
Let d(p) = -8*p**3 + 10*p**2 + 10*p - 6. Let s(z) = 9*z**3 - 11*z**2 - 10*z + 7. Let f(t) = -6*d(t) - 4*s(t). Find q, given that f(q) = 0.
-1, 1/3, 2
Suppose 4*y + 4*c = -8, -c + 20 = -6*c. Suppose h - y = -h. Find p, given that 7*p**2 - h + 6 - 4*p**2 - 6*p - 2 = 0.
1
Let k(d) = -2*d**3 - 4*d**2 + 2*d + 3. Let b be k(-3). Suppose -4*s = -b + 3. Factor -2*p**s - 10*p + 8 - 4 + 19*p**2 - 11*p**2.
-2*(p - 2)*(p - 1)**2
Let v(j) be the first derivative of 35 - 10/3*j**3 - 5*j - 5/8*j**4 - 25/4*j**2. What is a in v(a) = 0?
-2, -1
Let p(q) be the first derivative of -5/2*q**2 - 1/3*q**3 - 4*q + 13. Determine r, given that p(r) = 0.
-4, -1
Let p = 12 + -282. Let a = 272 + p. Determine z so that -2/7 + 3/7*z - 1/7*z**a = 0.
1, 2
Let q(r) = -r**2 - 11*r. Let g be q(-11). Factor 0*h**2 + 2*h**2 + 15 - 65*h + g*h**2 + 18*h**2.
5*(h - 3)*(4*h - 1)
Let w be ((-3)/18)/((-3)/12). Let r = -160/3 + 54. Determine a, given that 0 + w*a**4 - 2/9*a**3 + 2/9*a - r*a**2 = 0.
-1, 0, 1/3, 1
Let y(d) = 3*d**2 - d. Suppose -7*j = 2*p - 3*j - 8, 2*j = -3*p - 4. Let x(b) = -3*b**2 + 2*b. Let o(l) = p*y(l) - 5*x(l). Factor o(n).
3*n*(n - 2)
Let d(l) be the third derivative of -l**6/600 + 13*l**5/300 - 2*l**4/5 + 6*l**3/5 - 34*l**2. Factor d(k).
-(k - 6)**2*(k - 1)/5
Let i = 793/360 + -1/360. Suppose -z**5 - 12/5*z**4 + 0*z + i*z**3 + 6/5*z**2 + 0 = 0. Calculate z.
-3, -2/5, 0, 1
Let m(f) = 123*f - 1965. Let s be m(16). Factor -44/3*j**2 + 2*j**s - 4 + 50/3*j.
2*(j - 6)*(j - 1)*(3*j - 1)/3
Let d be (-1 + 3)/(60/90). Let g(k) be the first derivative of -1/4*k**d + 0*k + 3/20*k**5 - 1/8*k**6 - 3 + 3/16*k**4 + 0*k**2. Solve g(j) = 0 for j.
-1, 0, 1
Factor -4*w**3 + 2*w**2 + 14*w + 9 - 8*w**2 - 2*w**2 + w**4 + 5*w**2 - 17.
(w - 4)*(w - 1)**2*(w + 2)
Suppose -10*k = -8*k - 420. Suppose 147*j**5 - 9*j**3 + 60*j**2 + 48 + 12*j - k*j**4 - 48 = 0. What is j?
-2/7, 0, 1
Let v(z) = -5*z + 300. Let c be v(60). Let x(u) be the second derivative of -8*u + c*u**2 + u**3 + 0 - 1/4*u**4. Determine l, given that x(l) = 0.
0, 2
Factor -162/7 - 30/7*a**2 + 18*a + 2/7*a**3.
2*(a - 9)*(a - 3)**2/7
Suppose -23/2*h**4 + 0 + 47/2*h**3 - 37/2*h**2 + 3/2*h**5 + 5*h = 0. Calculate h.
0, 2/3, 1, 5
Let s(h) be the first derivative of 3*h**4/4 + 17*h**3 + 60*h**2 - 900*h - 173. Factor s(m).
3*(m - 3)*(m + 10)**2
Let v(d) be the second derivative of d**6/18 + 3*d**5/4 + 35*d**4/18 - 2*d + 34. Factor v(h).
5*h**2*(h + 2)*(h + 7)/3
Find q, given that 0*q + 0*q**2 + 0 - 3/7*q**3 = 0.
0
Let y = -1190 - -1194. Let n(b) be the third derivative of -1/60*b**5 + 0*b**3 - 4*b**2 - 1/24*b**y + 0 + 0*b. Factor n(v).
-v*(v + 1)
Let n = -51 - -53. Factor 8*v**n - 11*v + 4*v - 18*v**3 + 16*v**3 - 3*v + 4.
-2*(v - 2)*(v - 1)**2
Let n(v) be the first derivative of 2*v**3 - 9*v**2 - 4 - v - 1/6*v**4. Let z(p) be the first derivative of n(p). Solve z(q) = 0.
3
Let g(d) be the first derivative of -d**6/180 + d**5/20 - d**4/6 + 2*d**3/3 - 52*d + 39. Let o(z) be the third derivative of g(z). Let o(i) = 0. What is i?
1, 2
Let c = 91 - 79. Solve c*o**3 - 145*o**4 + 75*o**4 + 10*o**2 + 3*o + o**5 + 76*o**4 = 0 for o.
-3, -1, 0
Let x(t) be the first derivative of -3/4*t**4 + 4*t - 6*t**2 + 11/3*t**3 + 14. Solve x(i) = 0 for i.
2/3, 1, 2
Find m, given that 8/7*m**2 + 4/7*m**3 - 16/7*m - 32/7 = 0.
-2, 2
Suppose 5*p = 4*a - a + 4, -4*p = -5*a + 2. Factor 26*b**2 - 6 - 2*b**3 + 2*b - 9*b**a - 11*b**2.
-2*(b - 3)*(b - 1)*(b + 1)
Let g(v) = 6*v**3 - 8*v**2 + 2*v**3 - 6*v**3 + 9*v**2. Let b(a) = 4*a**3 + a**2 - 2*a. Let n(f) = -2*b(f) + 2*g(f). Find k such that n(k) = 0.
-1, 0, 1
Let u be ((-4)/(-10))/(202/1010). Let d(h) be the first derivative of -6 + 2/3*h**3 + 1/4*h**4 - 1/2*h**2 - u*h. Factor d(z).
(z - 1)*(z + 1)*(z + 2)
Let s(p) be the second derivative of -p**7/5460 - 25*p**3/6 - 4*p. Let j(d) be the second derivative of s(d). Find r, given that j(r) = 0.
0
Let z(w) be the first derivative of -w**6/42 + 2*w**5/35 + 3*w**4/14 - 20*w**3/21 + 19*w**2/14 - 6*w/7 - 215. Factor z(i).
-(i - 2)*(i - 1)**3*(i + 3)/7
Let w(m) = 4*m - 3. Let j be w(2). Suppose j*h - 39 = 2*h. Factor 7*i**2 - 11*i**2 - 3*i**3 - 2*i - 4*i + h*i**2.
-3*i*(i - 2)*(i - 1)
Suppose 4*i - 431 = -3*k - 0*i, -i + 2 = 0. Let y = k + -1265/9. Factor -y*u + 2/9*u**3 + 0 + 2/9*u**2.
2*u*(u - 1)*(u + 2)/9
Find g such that 2*g - 7/3*g**5 - 13*g**3 + 11*g**4 + 7/3*g**2 + 0 = 0.
-2/7, 0, 1, 3
Let i(s) be the first derivative of -s**5/90 - s**4/6 - 5*s**3/9 + 25*s**2/2 + 2. Let f(n) be the second derivative of i(n). Let f(g) = 0. What is g?
-5, -1
Let x(z) be the second derivative of z**5/30 + z**4/36 - z**3/18 + z + 45. Factor x(f).
f*(f + 1)*(2*f - 1)/3
Let n(m) be the first derivative of -5*m**6/6 + 13*m**5 - 85*m**4/2 - 310*m**3/3 + 175*m**2/2 + 245*m - 107. Solve n(v) = 0.
-1, 1, 7
Factor -17/7*a - 1/7*a**2 + 38/7.
-(a - 2)*(a + 19)/7
Suppose -13*n + 5*n = 12*n. Let l(t) be the second derivative of 6*t - 3/20*t**5 + 0 + 3/4*t**4 + n*t**3 - 6*t**2. Factor l(w).
-3*(w - 2)**2*(w + 1)
Let f be (-306)/1120 + 1/((-98)/(-28)). Let z(x) be the second derivative of 1/48*x**4 + 0 - 1/8*x**2 + f*x**5 - 1/24*x**3 - 5*x. Factor z(k).
(k - 1)*(k + 1)**2/4
Let b(v) be the third derivative of -v**2 + 0 + 3/70*v**7 - 1/112*v**8 - 1/10*v**5 - 1/20*v**6 + 3/8*v**4 - 1/2*v**3 + 0*v. Factor b(j).
-3*(j - 1)**4*(j + 1)
Let b(d) be the second derivative of -d**6/480 + 3*d**5/40 - 9*d**4/8 - 7*d**3/6 - 18*d. Let k(c) be the second derivative of b(c). What is h in k(h) = 0?
6
Let z(j) be the second derivative of -1/54*j**4 + 2*j + 0 + 2/27*j**3 - 1/9*j**2. Find r such that z(r) = 0.
1
Suppose 0 = r + 2*r + 33. Let b = r - -13. What is a in -5*a + b*a - 6 - 3*a**2 - 6*a = 0?
-2, -1
Suppose -2*s = -4*p - 8, 6*s + p - 26 = 3*s. Suppose 6*q = s*q. Factor q + 3/7*j**4 + 0*j + 6/7*j**3 + 0*j**2.
3*j**3*(j + 2)/7
Let v = -46 + 49. Determine a so that 0 + 71*a - 91*a + 44*a**v + 21*a**3 - 40 + 70*a**2 + 15*a**4 = 0.
-2, -1, 2/3
Let r = 7 + -5. Suppose 0*a - 4 = -4*c + a, -a = -3*c + r. Factor n**2 - n**5 - c*n**2 + 18*n**3 + 3*n**2 - 15*n**3.
-n**2*(n - 2)*(n + 1)**2
Factor -33/4*s**2 - 3/4*s**4 + 0 - 9/2*s - 9/2*s**3.
-3*s*(s + 1)*(s + 2)*(s + 3)/4
Let s(n) be the third derivative of 0*n - 1/2*n**4 + 1/30*n**6 + 0 - 2/15*n**5 + 0*n**3 + 2*n**2. Determine t so that s(t) = 0.
-1, 0, 3
Solve 524288/21 + 2/21*h**3 + 8192/7*h + 128/7*h**2 = 0 for h.
-64
Let z(f) = 2*f**4 + 32*f**3 + 17*f**2 - 13. Let j(g) = -g**4 - 15*g**3 - 8*g**2 + 6. Let p(a) = 13*j(a) + 6*z(a). Solve p(o) = 0.
-2, -1, 0
Let i = 1421/3565 + 1/713. Let 16/5 + i*f**3 + 24/5*f + 12/5*f**2 = 0. What is f?
-2
Let f(y) be the first derivative of -3*y**4/4 - 10*y**3 - 75*y**2/2 - 280. Factor f(c).
-3*c*(c + 5)**2
Let t(v) = -v**3 + 21*v**2 - v + 24. Let s be t(21). Factor -6*c**s - 2 - 12*c - 22*c**2 + 2.
-2*c*(c + 3)*(3*c + 2)
Let i = 203 - 122. Let z be 2*39 - (5 - 6). Factor -6*a - z*a**2 + 2*a**3 + 2*a + i*a**2.
2*a*(a - 1)*(a + 2)
Factor -3/2*d**2 + 6 - 4*d + d**3.
(d - 2)*(d + 2)*(2*d - 3)/2
Let z(c) be the third derivative of -c**7/1365 - c**6/390 + 9*c**5/130 - 36*c**3/13 - c**2 + 132. Find n, given that z(n) = 0.
-6, -2, 3
Let d = 64 + -56. Let s be 2 + -2 + 2/d. Solve -1/2*y + s*y**4 - y**3 + 5/4*y**2 + 0 = 0.
0, 1, 2
Factor 0 + 2/21*m - 2/21*m**2.
-2*m*(m - 1)/21
Let u = -3/6547 + 3640231/216051. Let m = u - 50/3. Factor 6/11*z + m*z**2 + 4/11.
2*(z + 1)*(z + 2)/11
Let m(f) be the first derivative of 325*f**5 - 85/2*f**2 - 725/2*f**4 + 530/3*f**3 - 625/6*f**6 - 46 + 5*f. Find p such that m(p) = 0.
1/5, 1
Factor 15*k - 12*k**3 + 6*k**2 - 3*k**5 - 12*k**4 + 51 - 17 - 28.
-3*(k - 1)*(k + 1)**3*(k + 2)
Let a(y) = 3 - 11*y - y**3 + 4*y**2 - 4*y**3 + y**3 + 5*y**3. Let l(q) = -4*q**3 - 20*q**2 + 56*q - 16. Let n(b) = 16*a(b) + 3*l(b). What is u in n(u) = 0?
-2, 0, 1
Let x(y) be the second derivative of 0*y**2 + 1/24*y**4 - 1/40*y**5 + 0*y**3 - 32*y + 0. Determine h, given that x(h) = 0.
0, 1
Let q(y) = -4*y**2 + 4*y + 8. Let p(r) = -5*r**2 + 5*r + 10. Let f(k) = 3*p(k) - 4*q(k). Suppose