 0 + 0*i**4 - 5/2*i**5 + 0*i**2.
-5*i*(i - 1)**2*(i + 1)**2/2
Let k(v) be the third derivative of v**6/720 - v**5/180 + 10*v**2. Suppose k(t) = 0. Calculate t.
0, 2
Let t(u) be the first derivative of u**7/350 - u**6/200 - u**5/100 + u**4/40 + 3*u**2/2 + 1. Let f(g) be the second derivative of t(g). Let f(c) = 0. What is c?
-1, 0, 1
Let o = 162 + -160. Factor 6/7*w**o + 2/7*w**3 + 6/7*w + 2/7.
2*(w + 1)**3/7
Let p be 0 - 5/((-15)/9). Suppose 0*g = -p*g. Find k, given that -2/3*k**2 + g + 2/3*k = 0.
0, 1
Let c(k) be the second derivative of k**5/10 + k**4/6 - 4*k. Suppose c(g) = 0. Calculate g.
-1, 0
Let a(w) = -7*w**5 - 5*w**4 + 3*w**3 + 9*w**2 - 11*w + 1. Let j(g) = -3*g**5 - 2*g**4 + 2*g**3 + 4*g**2 - 5*g. Let h(q) = 2*a(q) - 5*j(q). Factor h(s).
(s - 2)*(s - 1)*(s + 1)**3
Let i = -6 - -9. Let s(u) = u**3 - 17*u**2 + 43*u - 11. Let a be s(14). Determine z, given that -z**i + 3*z**a - z**3 - z = 0.
-1, 0, 1
Let u(d) be the second derivative of -d**6/180 + d**5/60 - d**3/18 + d**2/12 - 54*d. Determine f so that u(f) = 0.
-1, 1
Let b(l) be the third derivative of l**7/70 - l**6/10 - l**5/4 + 2*l**2 - 43*l. Determine q, given that b(q) = 0.
-1, 0, 5
Let i = -23 + 32. Let p(w) = 13*w**2 + 5*w. Let a(o) = 3*o**2 + o. Let f(n) = i*a(n) - 2*p(n). Let f(m) = 0. What is m?
0, 1
Let w = -2/11313 - -1086058/56565. Find q such that -256/5*q - 1/5*q**4 - w*q**2 - 16/5*q**3 - 256/5 = 0.
-4
Let f(g) be the first derivative of 1/16*g**4 + 1/8*g**2 + 0*g - 1/6*g**3 + 3. What is w in f(w) = 0?
0, 1
Let p(u) be the third derivative of u**4/24 - 5*u**3/6 + 5*u**2. Let f be p(5). Factor f - 2/7*h**2 + 2/7*h.
-2*h*(h - 1)/7
Let k(w) = 10*w**2 - 8*w - 10. Suppose -4*c + 2 = -2*c. Let g(o) = 3*o + o**2 - c + 2*o - 6*o. Let j(h) = -8*g(h) + k(h). Determine v, given that j(v) = 0.
-1, 1
Let k(d) be the first derivative of d**4/6 + d**3 + 2*d**2 + 8*d - 8. Let z(f) be the first derivative of k(f). Solve z(x) = 0 for x.
-2, -1
Factor 0 - 1/4*w - 1/4*w**3 - 1/2*w**2.
-w*(w + 1)**2/4
Let j = -54/35 + 22/7. Let k be 7/(35/2) + 6/5. Factor -j*l**3 - 2/5 - 2/5*l**4 - 12/5*l**2 - k*l.
-2*(l + 1)**4/5
Suppose -3*h + 6 + 3 = 0. Let o = h - 1. Factor f**4 + o*f**3 - f**4 + 6*f**4 - 4*f**4.
2*f**3*(f + 1)
Let r = 14 - 8. Suppose -v + r*v - 25 = 0. Let -v*t**3 + 3*t**3 - 4*t**2 + 0*t**3 = 0. Calculate t.
-2, 0
Suppose -2*w + 0*w = -4. Suppose 5 + 1 = w*i. Determine t, given that -2*t - 2 + 6 + 2*t**3 - t**4 + i*t**4 - 6*t**2 = 0.
-2, -1, 1
Let m = -8/21 - -23/42. Let w(i) be the second derivative of 0 + 1/20*i**5 + 0*i**4 + 2*i + 0*i**2 - m*i**3. Factor w(g).
g*(g - 1)*(g + 1)
Suppose -6*f = -2*f. Let j(x) be the third derivative of f*x**4 + 0*x + 2*x**2 + 0*x**3 + 0 - 1/240*x**6 + 1/120*x**5. Determine b, given that j(b) = 0.
0, 1
Suppose -5*k - 17 + 2 = 5*p, 0 = -2*k - 6. Suppose 0*x**3 + 9/4*x**4 + 0 + 3/2*x**5 - 3/4*x**2 + p*x = 0. What is x?
-1, 0, 1/2
Factor -7/2*k**2 - 3/2 - 23/4*k + 3/4*k**3.
(k - 6)*(k + 1)*(3*k + 1)/4
Suppose -6*i = -i - g - 7, 2*i - g - 1 = 0. Determine k, given that 1/3*k**4 + 1/3*k**3 + 0*k + 0*k**i + 0 = 0.
-1, 0
Let v(s) be the first derivative of s**9/3024 - s**7/280 - s**6/180 - s**3/3 + 2. Let f(p) be the third derivative of v(p). Find j such that f(j) = 0.
-1, 0, 2
Factor -37*v**2 + 36*v - 56*v**2 + 33*v**2 - 4*v**4 + 28*v**3.
-4*v*(v - 3)**2*(v - 1)
Let m(x) be the third derivative of 0 - 10*x**2 - 1/300*x**5 + 0*x - 3/10*x**3 - 1/20*x**4. Factor m(k).
-(k + 3)**2/5
Let v(f) be the third derivative of -21*f**6/200 + f**5/100 + f**4/20 - 10*f**2. Determine d so that v(d) = 0.
-2/7, 0, 1/3
Let v(h) be the first derivative of -3*h**5/35 - 3*h**4 - 42*h**3 - 294*h**2 - 1029*h + 24. Factor v(a).
-3*(a + 7)**4/7
Factor -18 + k**2 - 25 + 68 + 10*k.
(k + 5)**2
Solve 1/8*x**3 - 1/8*x**2 + 0 + 0*x = 0 for x.
0, 1
Factor 35*f**2 + 5*f**3 + 105*f - 24 - 65*f - 56.
5*(f - 1)*(f + 4)**2
Solve 1/6*s**2 + 6 + 2*s = 0.
-6
Let u be (15 - 9 - 4) + (2 - 1). Let s(n) be the first derivative of 4 - 3/2*n**2 + 1/2*n**u + 3/2*n. Suppose s(x) = 0. What is x?
1
Factor 3*d**2 + 0*d + 3/4*d**4 + 3*d**3 + 0.
3*d**2*(d + 2)**2/4
Let w(o) be the first derivative of 2/3*o - 1/6*o**2 - 1 - 2/9*o**3 + 1/12*o**4. Suppose w(s) = 0. Calculate s.
-1, 1, 2
Factor -114/7*c - 10/7*c**3 - 36/7 - 64/7*c**2.
-2*(c + 3)**2*(5*c + 2)/7
Factor 2/3 + x**4 - 5/3*x**2 + 1/3*x**3 - 1/3*x.
(x - 1)*(x + 1)**2*(3*x - 2)/3
Let l be (-8)/36 + 4/18. Suppose l = f - 5*f + 72. What is y in 13 + f*y + 11 + 3 + 3*y**2 = 0?
-3
Let l(r) be the second derivative of -3*r**4/4 - r**3 + 5*r. Factor l(k).
-3*k*(3*k + 2)
Determine g so that -15*g - 21*g**4 + 5*g**2 + 15*g**3 + 37*g**4 - 21*g**4 = 0.
-1, 0, 1, 3
Let w be (-4)/((-4)/(-7)) + 3. Let i be -1*w/(-40)*-4. Factor -4/5 + i*y**2 - 2/5*y.
2*(y - 2)*(y + 1)/5
What is w in 3*w**2 + 2 - 3*w**4 - 3*w + 3*w**3 - 2 = 0?
-1, 0, 1
Suppose 3*z = -p + 16, -2 = 5*z - 3*z. Factor -4*i**3 + p*i**4 - 12*i**4 - 2*i**2 - 9*i**4.
-2*i**2*(i + 1)**2
Let t be 7/(8 - (-4)/(-1)). Let 1/2 - t*b - 9/4*b**2 = 0. Calculate b.
-1, 2/9
Let s be (-76)/(-18) - (-3 - 116/(-36)). Let 2/9*z**3 - 2/9*z**s + 0 + 2/9*z**2 - 2/9*z = 0. Calculate z.
-1, 0, 1
Let c(p) = -2*p**3 + 6*p**2 - 4*p. Let y(o) = 4*o**3 - 13*o**2 + 9*o. Let j = 20 - 7. Suppose 0 = 8*s - 4*s - 24. Let w(x) = j*c(x) + s*y(x). Solve w(a) = 0.
-1, 0, 1
Suppose 0 = -0*y - 4*y - 4*n + 32, -3*n = 2*y - 19. Factor -2*d**3 + 3*d**3 + 0*d**3 - d**y.
-d**3*(d - 1)*(d + 1)
Suppose 3 + 7 = 5*d. Let s be ((-15)/d)/5 + 2. Suppose 0*u - s*u**3 + 0 + 0*u**2 = 0. Calculate u.
0
Let m(a) be the first derivative of 21*a**4/4 + 2*a**3 + 6. Let m(k) = 0. What is k?
-2/7, 0
Let p(y) be the third derivative of 0 + 0*y - 1/6*y**3 + 1/30*y**5 - y**2 + 0*y**6 + 0*y**4 - 1/210*y**7. Find o such that p(o) = 0.
-1, 1
Let h(t) be the first derivative of -t**6/36 + t**5/10 - t**4/12 - t**3/9 + t**2/4 - t/6 - 19. Factor h(p).
-(p - 1)**4*(p + 1)/6
Factor 2/3 + 7/3*m + m**2.
(m + 2)*(3*m + 1)/3
Let l be 0/8 - (-1 + -2). Determine y, given that 3*y**2 + 0*y**l + 0*y + y + y**3 + y**4 + 2*y**3 = 0.
-1, 0
Find r, given that 0 + 2/7*r**3 - 24/7*r**2 + 72/7*r = 0.
0, 6
Let n(u) be the third derivative of 1/12*u**4 + 0*u + 0 - 1/60*u**6 + 3*u**2 + 1/3*u**3 - 1/30*u**5. Suppose n(x) = 0. Calculate x.
-1, 1
Let d(o) be the third derivative of -o**6/60 - o**5/6 + o**4/12 + 5*o**3/3 - 11*o**2. Factor d(v).
-2*(v - 1)*(v + 1)*(v + 5)
Let w be -1*(0 - (1 + -2)). Let g = w - -3. Let 23*l**g + 9*l**3 + 30*l + 49*l**2 + 4 + 45*l**3 = 0. What is l?
-2/3, -1/3
Let -2*p**4 + 12 + 2*p**2 + 10 - 2*p**5 + 2*p**3 - 22 = 0. Calculate p.
-1, 0, 1
Suppose -52 = 11*p - 52. Factor -2/9*f + p - 2/9*f**2.
-2*f*(f + 1)/9
Let x = 0 - 0. Let c be (2 + -2 + x)/2. What is g in 0*g**4 - 2/5*g**3 + 0 + 1/5*g + 1/5*g**5 + c*g**2 = 0?
-1, 0, 1
Let d(h) be the first derivative of -h**6/2 + 6*h**5/5 - 18. Solve d(i) = 0 for i.
0, 2
Factor -2/3*p**3 - 4/3 - 10/3*p - 8/3*p**2.
-2*(p + 1)**2*(p + 2)/3
Let c(i) = 0 + 3 - i**2 + 3 - 10*i - 1. Let n be c(-10). Solve -3/2*t**3 - 3/2*t**4 - 1/2*t**n + 0 + 0*t - 1/2*t**2 = 0.
-1, 0
Let h(w) = -3*w**4 - 12*w**3 - 2*w**2 + 5*w + 19. Let k(q) = -q**4 - 4*q**3 - q**2 + 2*q + 6. Let x(a) = 6*h(a) - 21*k(a). Factor x(d).
3*(d - 1)*(d + 1)*(d + 2)**2
Let s be 1/(-3) - (-133)/21. Let p(x) be the third derivative of 0*x**3 + 1/120*x**5 + 2*x**2 + 0*x + 0 + 1/480*x**s + 1/96*x**4. Factor p(o).
o*(o + 1)**2/4
Let n(t) = t**2 - 3*t + 3. Let p be n(3). Let u be (4/(-14))/(p/(-7)). Solve 16/3*q**3 + 0*q**4 - 3*q**5 + u*q**2 - 2/3 - 7/3*q = 0.
-1, -2/3, -1/3, 1
Factor 48*n**2 + 256 + 34*n - n**3 - 226*n - 3*n**3.
-4*(n - 4)**3
Let t(r) be the third derivative of r**6/360 - r**5/180 + 29*r**2 - r. Factor t(h).
h**2*(h - 1)/3
Let b(x) be the first derivative of -x**5/210 - x**4/28 - 2*x**3/21 + x**2 - 2. Let g(i) be the second derivative of b(i). Find t such that g(t) = 0.
-2, -1
Let b(r) = 16*r**3 + 8*r**2 - 16*r - 8. Let l(q) = 31*q**3 + 16*q**2 - 31*q - 16. Let z(f) = 7*b(f) - 4*l(f). Suppose z(h) = 0. Calculate h.
-1, -2/3, 1
Let p be 3 + ((-3)/1)/(-3). Suppose 3*z - 5*z = -8. Factor z*s**2 + p*s - 5*s**2 + 2*s**2 + 2 + s**2.
2*(s + 1)**2
Let b(f) be the first derivative of -14*f**3/39 + 16*f**2/13 - 8*f/13 + 5. Factor b(h).
-2*(h - 2)*(7*h - 2)/13
Let m(j) 