4*h(x) - 3*z(x). Determine t so that f(t) = 0.
1, 2
Let f(k) = -k**3 - 13*k**2 + 3*k + 18. Let l be f(-13). Let a = l + 23. Let -2/3*w - 2/3*w**a + 4/3 = 0. What is w?
-2, 1
Let s be 2/4*-2*-3. Suppose -2*z - 23 = -5*b - z, 3*b + s*z - 21 = 0. Solve 0*f**2 + 4 + b*f - 7*f - 2*f**2 = 0.
-2, 1
Let g(r) be the second derivative of r**7/63 - r**6/45 - r**5/15 - 4*r. Factor g(z).
2*z**3*(z - 2)*(z + 1)/3
Let t(y) be the second derivative of y**4/4 + 29*y**3/18 + y**2 - 28*y. Factor t(r).
(r + 3)*(9*r + 2)/3
Let k(p) be the first derivative of -6*p**6 - 24*p**5/5 + 8*p**4 + 8*p**3 + 2*p**2 + 9. Let k(y) = 0. What is y?
-1, -1/3, 0, 1
Let c(z) = -4*z**2 + 1. Suppose -3*q + 6 - 3 = 4*r, 5*q + 24 = 3*r. Let s(x) = 5*x**2 - 1. Let d(p) = r*s(p) + 4*c(p). Solve d(t) = 0.
-1, 1
Let b(n) = 1. Let i(z) = -6. Let p(y) = 11*b(y) + 2*i(y). Let v(h) = -h**3 + 2. Let j(w) = -2*p(w) - v(w). Factor j(x).
x**3
Let i = -67/403 - -3/13. Let p = 118/93 + i. Factor -2*f**2 + 0 + 2/3*f**3 + p*f.
2*f*(f - 2)*(f - 1)/3
What is z in -5/4*z**2 - 1 + 1/4*z**3 + 2*z = 0?
1, 2
Let j(d) be the third derivative of -d**8/1344 + d**7/840 + d**6/240 - d**5/120 - d**4/96 + d**3/24 + 10*d**2. Factor j(y).
-(y - 1)**3*(y + 1)**2/4
Determine i, given that 16*i**4 + 8*i**2 + 4*i**3 + 2*i - 24*i**2 - 6*i = 0.
-1, -1/4, 0, 1
Let v(j) be the third derivative of -3*j**2 + 0 + 1/108*j**4 + 0*j + 2/945*j**7 - 1/1512*j**8 - 1/135*j**5 + 0*j**6 + 0*j**3. Factor v(g).
-2*g*(g - 1)**3*(g + 1)/9
Let p(x) be the third derivative of -x**7/126 - x**6/36 - x**5/36 - 2*x**2. Factor p(i).
-5*i**2*(i + 1)**2/3
Let h(q) be the second derivative of -q**6/180 + q**5/20 - q**3/2 - 4*q. Let b(g) be the second derivative of h(g). Factor b(d).
-2*d*(d - 3)
Let v be 76/(-32)*-1 - 2. Let m(f) be the first derivative of 0*f + v*f**2 + 3 + 3/4*f**4 + f**3. Let m(h) = 0. What is h?
-1/2, 0
Let i(n) = -n**3 + 18*n**2 - 15*n - 32. Let u be i(17). Factor -5/2*p**2 + 6*p - u.
-(p - 2)*(5*p - 2)/2
Suppose -2*q + 16 = 4. Suppose -16 = -q*o + 2*o. Factor -2*r**o - 4*r**3 + 2*r**2 + 2*r**3 - r**5 + 3*r**5.
2*r**2*(r - 1)**2*(r + 1)
Let p(i) be the first derivative of 4*i**3/3 - 5*i**2/3 - 2*i/3 + 5. Factor p(b).
2*(b - 1)*(6*b + 1)/3
Let -12/5*x + 24/5*x**2 + 9/5*x**4 + 0 + 33/5*x**3 = 0. Calculate x.
-2, 0, 1/3
Let l(p) be the first derivative of 1 - 1/12*p**4 - 1/6*p**2 - 2/9*p**3 + 0*p. Solve l(u) = 0 for u.
-1, 0
Factor 0*w - 4/5*w**2 + 2/5 + 0*w**3 + 2/5*w**4.
2*(w - 1)**2*(w + 1)**2/5
Let z(o) be the third derivative of o**7/40 + 2*o**6/15 + o**5/10 + o**3/6 + 2*o**2. Let w(d) be the first derivative of z(d). Suppose w(t) = 0. What is t?
-2, -2/7, 0
Factor 0 + 3/2*o - 1/4*o**2.
-o*(o - 6)/4
Factor -98 + 97 + 8*k**2 - 7*k**2.
(k - 1)*(k + 1)
Let r(v) be the first derivative of -1/2*v**2 - 2 + 0*v**4 + 1/120*v**5 + 0*v**3 + 0*v. Let p(o) be the second derivative of r(o). What is g in p(g) = 0?
0
Let g(s) be the first derivative of s**8/1680 + s**7/840 - s**6/360 - s**5/120 - s**3/3 - 1. Let y(i) be the third derivative of g(i). What is q in y(q) = 0?
-1, 0, 1
Let q = -2 + 5. Suppose 0 = 3*a - 4*a + q. Factor 5/3*g + 1/3*g**4 - g**2 - 2/3 - 1/3*g**a.
(g - 1)**3*(g + 2)/3
Let y(o) be the second derivative of o**5/230 - o**4/69 - o**3/69 + 2*o**2/23 + 14*o. Factor y(w).
2*(w - 2)*(w - 1)*(w + 1)/23
Let p(z) be the second derivative of 1/60*z**5 + 0 - 1/12*z**4 - 5*z + 1/6*z**3 - 1/6*z**2. Factor p(b).
(b - 1)**3/3
Let b(q) be the first derivative of 14*q**3/15 + 4*q**2/5 - 6*q/5 + 15. Factor b(i).
2*(i + 1)*(7*i - 3)/5
Determine o so that -10/9*o - 4/3*o**2 - 2/9*o**3 + 0 = 0.
-5, -1, 0
Let b(p) be the third derivative of -p**7/315 + p**6/18 - 13*p**5/90 - 5*p**4/3 - 4*p**3 - 18*p**2. Let b(i) = 0. What is i?
-1, 6
Let v(y) be the third derivative of -3/8*y**3 + 0 + 1/16*y**4 + 3*y**2 + 0*y - 1/240*y**5. Factor v(s).
-(s - 3)**2/4
Let s(b) = -b**4 + 4*b**3 - 16*b**2 + 13*b. Let r(t) = -t**2 + t. Suppose -n = n - 4. Let l(k) = n*s(k) - 22*r(k). Factor l(x).
-2*x*(x - 2)*(x - 1)**2
Let j(d) = -2*d - 5. Suppose -12 = 3*o - 5*u, -3*u = -2*o - 0*o - 8. Let r be j(o). Factor -3 + 2*n**2 - 2 + r.
2*(n - 1)*(n + 1)
Let w be (2/6)/(6/(-6 + 96)). Suppose -8/9*g**3 - 4/9 + 0*g**4 + 2/9*g**w + 4/9*g**2 + 2/3*g = 0. What is g?
-2, -1, 1
Let z be (104/(-18) + 6)*(-3)/(-2). Find s such that -2/3*s**2 + 0 - z*s**3 - 1/3*s = 0.
-1, 0
Let 14/9*k**3 - 10/9*k**5 - 2/3*k**4 + 2/3*k**2 + 0 - 4/9*k = 0. Calculate k.
-1, 0, 2/5, 1
Let z(b) be the third derivative of b**5/15 + b**4/2 + 4*b**3/3 + 3*b**2. Factor z(u).
4*(u + 1)*(u + 2)
Let s(u) = u**3 + 2*u**2 - u + 3. Let m be s(-3). Let i be ((-3)/m + -2)*0. Factor 0*n**2 + 2/5*n**5 - 4/5*n**3 + i*n**4 + 2/5*n + 0.
2*n*(n - 1)**2*(n + 1)**2/5
Let o(l) be the third derivative of 0 + 0*l - 1/35*l**7 + 0*l**3 + 1/16*l**6 + 1/224*l**8 - 1/20*l**5 - l**2 + 0*l**4. Find a such that o(a) = 0.
0, 1, 2
Let h = -186 - -191. Factor -3/2*p**3 - 3/4*p**h - 3/4 + 9/4*p**4 + 9/4*p - 3/2*p**2.
-3*(p - 1)**4*(p + 1)/4
Let z(f) = -2*f + 4*f - 16*f**2 + f + 17*f**2. Let k be z(-4). Factor 0*v - 2/7*v**3 + 2/7*v**5 + 0*v**k + 0 + 0*v**2.
2*v**3*(v - 1)*(v + 1)/7
Let w(a) = a. Let x be w(3). Suppose -k + 0*k + 3*k + 5*k**2 + 2*k**2 + 5*k**x = 0. Calculate k.
-1, -2/5, 0
Factor 0 - 2/17*s**3 + 0*s + 2/17*s**2.
-2*s**2*(s - 1)/17
Let q(y) be the third derivative of -2*y**7/105 - y**6/15 + y**5/15 + y**4/3 - 2*y**2. Factor q(o).
-4*o*(o - 1)*(o + 1)*(o + 2)
Suppose 18*z + 14 = 25*z. Let a(k) be the first derivative of 0*k**2 + 0*k - 1/16*k**4 + z - 1/20*k**5 + 0*k**3. Factor a(y).
-y**3*(y + 1)/4
Let g(j) be the third derivative of -j**8/2352 + 2*j**7/735 - j**6/280 - j**5/105 + j**4/42 + 22*j**2. Find m such that g(m) = 0.
-1, 0, 1, 2
Let y(z) be the first derivative of z**6/75 - z**4/30 - 2*z - 6. Let n(k) be the first derivative of y(k). Suppose n(r) = 0. Calculate r.
-1, 0, 1
Determine k, given that 1331/7*k**3 - 8/7 - 726/7*k**2 + 132/7*k = 0.
2/11
Let d = -1385/4 + 347. Suppose -3/4*c**2 + d*c + 1/4*c**3 - 1/4 = 0. What is c?
1
Let c(g) = -7*g**2 - 11*g - 4. Let m(x) = 35*x**2 + 56*x + 21. Let y be -4 + (4/1 - 2). Let u(f) = y*m(f) - 11*c(f). Factor u(t).
(t + 1)*(7*t + 2)
Let n(w) be the first derivative of 0*w - 4/9*w**3 + 1/6*w**4 - 3 + 1/3*w**2. Factor n(q).
2*q*(q - 1)**2/3
Factor -14/9*h**2 + 0 + 10/9*h**3 - 2/9*h**4 + 2/3*h.
-2*h*(h - 3)*(h - 1)**2/9
Let i(t) be the first derivative of -25*t**2 - 8*t**4 + 112/3*t**3 + 6*t - 11. Factor i(g).
-2*(g - 3)*(4*g - 1)**2
Factor -3/2*n - 7/2*n**2 + 5/2*n**4 + 1 + 3/2*n**3.
(n - 1)*(n + 1)**2*(5*n - 2)/2
Let t(w) be the first derivative of w**5/10 + w**4/6 - w**3/9 - w**2/3 - w/6 + 5. Factor t(o).
(o - 1)*(o + 1)**2*(3*o + 1)/6
Let v(n) be the third derivative of -n**8/12 - 22*n**7/105 - 16*n**6/105 - 4*n**5/105 + 11*n**2. Factor v(h).
-4*h**2*(h + 1)*(7*h + 2)**2/7
Let y(m) be the first derivative of m**3/6 - m**2/2 + m/2 + 1. Factor y(p).
(p - 1)**2/2
Let p(q) be the second derivative of -2/11*q**2 + 5/33*q**3 + 0 + 5*q - 1/22*q**4 - 1/110*q**5 + 1/165*q**6. Factor p(k).
2*(k - 1)**3*(k + 2)/11
Factor -2/11*d**2 + 2/11*d**3 + 10/11*d**4 + 6/11*d**5 + 0*d + 0.
2*d**2*(d + 1)**2*(3*d - 1)/11
Factor 6/11*r + 4/11 - 2/11*r**3 + 0*r**2.
-2*(r - 2)*(r + 1)**2/11
Let u(f) be the second derivative of f**4/48 + f**3/8 + f**2/4 - 11*f. Factor u(r).
(r + 1)*(r + 2)/4
Let v(u) be the first derivative of -u**5 + 5*u**4/16 + 5*u**3 - 55*u**2/8 + 5*u/2 - 18. Find h such that v(h) = 0.
-2, 1/4, 1
Let q(x) be the second derivative of x**7/1260 - x**6/90 + x**5/20 - x**4/3 + 4*x. Let d(g) be the third derivative of q(g). Factor d(r).
2*(r - 3)*(r - 1)
Let g(n) = 3*n**5 + 7*n**4 + 4*n**3 - 4*n**2 + 4. Let u(q) = 6*q**5 + 15*q**4 + 9*q**3 - 9*q**2 + 9. Let x(o) = -9*g(o) + 4*u(o). Factor x(a).
-3*a**4*(a + 1)
Suppose -u - 4*u = 3*x - 10, 0 = 4*x - 4*u + 8. Determine h so that 3/5*h + x + 3/5*h**5 + 0*h**4 + 0*h**2 - 6/5*h**3 = 0.
-1, 0, 1
Let z(t) = 11*t**5 + 19*t**4 + 5*t**3 + 2*t**2 - 5*t - 5. Let g(y) = -5*y**5 - 9*y**4 - 3*y**3 - y**2 + 2*y + 2. Let i(o) = 5*g(o) + 2*z(o). Factor i(f).
-f**2*(f + 1)**2*(3*f + 1)
Let l(u) be the third derivative of 1/210*u**5 + 4*u**2 + 0*u**3 + 0*u + 1/84*u**4 + 0. Factor l(v).
2*v*(v + 1)/7
Factor -64/5 - 64/5*h + 16/5*h**3 + 4/5*h**4 + 0*h