*4 = 0.
-2, -1
Let v(h) = h + 12. Let u be v(-9). Let q = 8 + -6. Suppose 2*p + 0*p + u*p**q + p**3 + 1 + p = 0. What is p?
-1
Let v(q) be the third derivative of -q**8/20160 + q**7/840 - q**6/80 + q**5/20 + 4*q**2. Let l(m) be the third derivative of v(m). Factor l(f).
-(f - 3)**2
Let b(t) be the second derivative of 1/3*t**6 - t**5 + 0 + t**2 - 1/21*t**7 - 5/3*t**3 + 3*t + 5/3*t**4. Factor b(j).
-2*(j - 1)**5
What is v in 4*v + 2/5*v**2 + 10 = 0?
-5
Let h be 3/(-15)*(-6 + -2). Let n = 21/10 - h. Find q such that -n + 1/2*q**2 + 0*q = 0.
-1, 1
Suppose -4*f = 5 - 1. Let i be (-4 - -3)*(-2 - f). Determine s, given that 5*s**2 - 2*s**3 + 0*s**3 + i + 4*s + 4*s**3 = 0.
-1, -1/2
Factor 24*n + 4 - 24*n - 24 + 45*n + 5*n**3 - 30*n**2.
5*(n - 4)*(n - 1)**2
Let i(k) be the second derivative of 2/9*k**2 - k + 1/54*k**4 + 0 - 1/45*k**5 + 5/27*k**3. Factor i(z).
-2*(z - 2)*(z + 1)*(2*z + 1)/9
Let j(t) = -t**3. Let c(n) = -3*n**4 + 22*n**3 - 36*n**2 + 30*n - 9. Let v(b) = -c(b) - 4*j(b). Factor v(y).
3*(y - 3)*(y - 1)**3
Let i be 0 + -2 - (-20 - (-376)/28). Solve -2/7*s**3 - 2*s**2 + i - 16/7*s = 0.
-4, 1
Let 0*x + 0 + 0*x**2 - 2/3*x**3 + 1/3*x**4 = 0. What is x?
0, 2
Factor 25*y + 55/2 - 5/2*y**2.
-5*(y - 11)*(y + 1)/2
Let g(a) be the third derivative of -a**10/151200 - a**9/30240 - a**8/20160 - a**5/60 - 3*a**2. Let t(l) be the third derivative of g(l). Factor t(s).
-s**2*(s + 1)**2
Let c be ((-1)/(-10))/(-4 - (-69)/15). Let r(x) be the second derivative of 0 + 2*x - c*x**4 + 1/6*x**3 - 1/20*x**5 + x**2. Determine l so that r(l) = 0.
-2, -1, 1
Suppose -s = 4*p + 2, s - 4*p = -p + 26. Suppose -k + 8 = -5*f - s, 2*f = -8. Factor 8*v + v**2 - 4*v + 0*v**k + 4.
(v + 2)**2
Let z be 4/(-1) - 0/(-10). Let n(r) = r**3 + 5*r**2 - 6*r - 4. Let a(o) = -o**3 + o**2 + 1. Let k(v) = z*a(v) - n(v). Factor k(c).
3*c*(c - 2)*(c - 1)
Let o be 1/(-2*(-4)/8). Let b(j) be the first derivative of -1/15*j**3 + 1/5*j + 0*j**2 + o. Solve b(t) = 0.
-1, 1
Let m(n) be the third derivative of -7*n**6/40 - n**5/10 - 2*n**2. Let m(x) = 0. Calculate x.
-2/7, 0
Factor -33*c**2 - 212 + 5*c**3 - 12*c**2 + 135*c + 77.
5*(c - 3)**3
Suppose -3*u + j + 17 = 0, -5*j - 30 = -3*u - u. Suppose -2*b + 20 = u*c, -3*c - 8 = 3*b - 5*c. Factor -3/2*z**4 + 0 + b*z + 0*z**2 - 3/2*z**3.
-3*z**3*(z + 1)/2
Suppose 0 = -70*u + 66*u + 12. Suppose 3/2*n**2 - 3/2*n - 3/2 + 3/2*n**u = 0. What is n?
-1, 1
Let c(q) be the first derivative of -q**3 - 9*q**2/2 - 6*q + 3. Let m(z) = -6*z**2 - 19*z - 13. Let y(d) = -13*c(d) + 6*m(d). Factor y(u).
3*u*(u + 1)
Let v(c) = -4*c - 3. Let p(l) = -5*l - 4. Let t(g) = 3*p(g) - 4*v(g). Let f(i) = 8*i**2 + 8*i + 1. Let y(b) = -f(b) + 2*t(b). Factor y(o).
-(2*o + 1)*(4*o + 1)
Let o(y) be the second derivative of y**4/12 - y**3/6 - y**2 + 7*y. Find x such that o(x) = 0.
-1, 2
Let z(p) be the third derivative of 1/240*p**5 - 1/1344*p**8 + 0*p**3 + 0*p + 0*p**4 + 1/480*p**6 + 3*p**2 - 1/840*p**7 + 0. Factor z(s).
-s**2*(s - 1)*(s + 1)**2/4
Let b(r) = 6*r**4 + 31*r**3 + 77*r**2 + 65*r + 13. Let i = -1 - -6. Let d(c) = -3*c**4 - 16*c**3 - 38*c**2 - 32*c - 7. Let s(p) = i*d(p) + 2*b(p). Factor s(o).
-3*(o + 1)**3*(o + 3)
Factor 16/7 + 0*c - 4/7*c**2.
-4*(c - 2)*(c + 2)/7
Let y = 374/3 - 124. What is k in -2/3*k**4 + 0*k**2 - 4/3*k**3 + 4/3*k + y = 0?
-1, 1
What is n in -85*n**2 + 2*n + 2*n + 87*n**2 = 0?
-2, 0
Let 17*r**4 + 5*r**5 - 8*r**4 - 12 - 3*r**3 - 33*r**2 - 2*r**5 - 4*r - 32*r = 0. Calculate r.
-2, -1, 2
Factor -4*i + 3*i**5 + 4*i**2 - 3*i**4 + 0*i**4 + 11*i**2 - 9*i**3 - 2*i.
3*i*(i - 1)**3*(i + 2)
Let a(x) be the third derivative of 1/180*x**6 + 0*x + 4*x**2 + 0*x**5 + 0*x**4 + 0*x**3 + 0. Factor a(f).
2*f**3/3
Solve 0*i + 0 + 1/2*i**3 + i**2 = 0.
-2, 0
Suppose 4*x - 21 = -13. Let b(h) be the third derivative of -x*h**2 + 0*h**5 + 0*h**3 + 0*h + 0 + 1/120*h**4 - 1/300*h**6 + 0*h**7 + 1/1680*h**8. Factor b(w).
w*(w - 1)**2*(w + 1)**2/5
Factor 10*n**2 - 18*n**2 - 13*n**2 - 3*n**3 + 24*n.
-3*n*(n - 1)*(n + 8)
Let a(p) be the second derivative of 0 + p + 1/70*p**5 - 2/21*p**3 + 0*p**2 - 1/42*p**4. Solve a(l) = 0 for l.
-1, 0, 2
Let c(d) be the second derivative of 8*d**7/105 + 4*d**6/15 + 3*d**5/10 + d**4/6 - 4*d**3/3 + 9*d. Let j(b) be the second derivative of c(b). Factor j(s).
4*(s + 1)*(4*s + 1)**2
Let k(y) be the third derivative of -y**5/15 - y**4/2 - 17*y**2. Factor k(g).
-4*g*(g + 3)
Let p be 2/(-5)*(-35)/7. Let q(m) be the third derivative of 1/525*m**7 - 1/50*m**5 + 1/300*m**6 + 0*m + 2/15*m**3 - 2*m**p - 1/60*m**4 + 0. Factor q(j).
2*(j - 1)**2*(j + 1)*(j + 2)/5
Let u = 1153/3 + -383. Determine g, given that 2*g**2 - 14/3*g**3 + 0 + u*g - 2*g**4 + 10/3*g**5 = 0.
-1, -2/5, 0, 1
Let f(q) = q. Let s(i) = -2*i**4 + 24*i**3 - 108*i**2 + 222*i - 162. Let g = 0 - -6. Let t(p) = g*f(p) - s(p). Let t(v) = 0. Calculate v.
3
Solve 0*b + 0*b**2 + 2*b**2 + b**3 + 3*b - 2*b = 0 for b.
-1, 0
Find c, given that -2 - 20*c**3 - 27*c**5 + 8*c - 3*c**4 + 2*c**4 + 9*c**4 - 2*c**2 + 43*c**5 = 0.
-1, 1/2
Factor -9*w**2 + 0*w**2 + 2*w + 3*w + w**4 + 3*w**3.
w*(w - 1)**2*(w + 5)
Determine n so that 147*n**4 + 29*n**4 + 250*n**3 - 141*n**2 - 79*n**2 + 40*n - 315*n**5 + 19*n**4 = 0.
-1, 0, 2/7, 2/3
Let m(y) be the first derivative of -5*y**4/16 + 5*y**3/6 + 18. Solve m(t) = 0.
0, 2
Let f = -51168 - -4656335/91. Let q = -3/13 + f. Determine o so that -2/7*o**2 + q*o + 0 = 0.
0, 1
Let s = -235/4 - -59. Find q, given that 0 - s*q**3 + 1/4*q**5 + 0*q**4 + 0*q**2 + 0*q = 0.
-1, 0, 1
Let r = 20 - 18. Let g(x) be the third derivative of -1/24*x**3 + 2*x**r + 0 - 1/120*x**6 - 1/40*x**5 + 0*x - 1/840*x**7 - 1/24*x**4. Factor g(p).
-(p + 1)**4/4
Factor 11*u**3 + 0*u + 9*u + 5*u**2 - 16*u**3 - 4*u - 5*u**4.
-5*u*(u - 1)*(u + 1)**2
Factor 1/9*w**3 + 0*w**2 - 4/9*w + 0.
w*(w - 2)*(w + 2)/9
Let c be -2 - (-48)/(-5)*(-1)/4. Factor -12/5*u**2 + 8/5*u + 8/5*u**3 - 2/5 - c*u**4.
-2*(u - 1)**4/5
Let x be (-3935)/(-25) + 2/(-5). Let j = x + -467/3. Factor -j*g**2 - 2/3*g**5 + 2/3 - 2/3*g + 2/3*g**4 + 4/3*g**3.
-2*(g - 1)**3*(g + 1)**2/3
Suppose 1 = 2*r - 3*r. Let c = r + 6. Let f(w) = 10*w**3 - 12*w**2 + 7*w. Let g(k) = -k**3 + k**2 - k. Let y(n) = c*g(n) + f(n). Let y(a) = 0. Calculate a.
0, 2/5, 1
Suppose 21*v - 18*v = -60. Let b be 4/6*(-12)/v. Factor -2/5 + 2/5*j + b*j**2 - 2/5*j**3.
-2*(j - 1)**2*(j + 1)/5
Suppose 0 - 6 = -2*r. Find o such that -3*o**5 - 14*o + r*o**3 - 6*o**2 + 6 + 5*o + 9*o**3 = 0.
-2, -1, 1
Let a(d) = -d**5 - 3*d**4 - 4*d**3 + 4*d - 4. Let b(f) = -f**5 - 4*f**4 - 5*f**3 + 5*f - 5. Let x(s) = 5*a(s) - 4*b(s). Suppose x(r) = 0. What is r?
0, 1
Let v(j) be the second derivative of 1/8*j**2 + 4*j + 1/24*j**3 - 1/80*j**5 - 1/48*j**4 + 0. Factor v(r).
-(r - 1)*(r + 1)**2/4
Let g(v) be the third derivative of -1/70*v**7 - 1/25*v**6 + 0 - 1/560*v**8 + 0*v + 2*v**2 + 0*v**3 - 1/25*v**5 + 0*v**4. Factor g(x).
-3*x**2*(x + 1)*(x + 2)**2/5
Let f be 4*((55/(-14) - -3) + 1). Let r = -75 + 527/7. Factor -r*v**3 + f*v**2 + 0 + 0*v.
-2*v**2*(v - 1)/7
Suppose 4*u - 5 + 25 = -4*n, 2*n - 5*u = 25. Let j(y) be the second derivative of 0*y**2 + y + 1/6*y**4 + n + 2/3*y**3. Find b, given that j(b) = 0.
-2, 0
Let q(f) be the first derivative of 1/2*f**2 + 0*f + 3 - 1/2*f**4 + 1/6*f**6 + 0*f**3 + 0*f**5. Factor q(n).
n*(n - 1)**2*(n + 1)**2
Let 1/7 + 2/7*w + 0*w**2 - 1/7*w**4 - 2/7*w**3 = 0. What is w?
-1, 1
Factor 1/5*q**2 - 4/5 + 3/5*q.
(q - 1)*(q + 4)/5
Let s(b) be the first derivative of b**4/2 + 2*b**3 - 4*b**2 - 24*b - 63. Find k, given that s(k) = 0.
-3, -2, 2
What is h in -27/4 + 9/2*h - 3/4*h**2 = 0?
3
Let q(v) = v**3 - v**2 + v - 1. Suppose 8 = -0*t - 4*t. Let k(f) = 6*f**3 - 5*f**2 + 4*f - 5. Let a(w) = t*k(w) + 10*q(w). What is l in a(l) = 0?
-1, 0, 1
Factor 0*t**2 - 2/9*t**4 + 0 - 2/3*t**3 + 0*t.
-2*t**3*(t + 3)/9
Let h(c) be the first derivative of 0*c**2 + 3/4*c**4 + 3 - 3/5*c**5 + 0*c**3 + 0*c. Determine f, given that h(f) = 0.
0, 1
Suppose 0 = -3*b - l + 4 - 24, 5*b - 4*l + 22 = 0. Let z be b/(-4)*4/3. Determine i so that z*i**2 - 4*i**2 + 4*i + 0*i**2 - 2 = 0.
1
Factor 1/2*c**2 - 1 - 1/2*c.
(c - 2)*(c + 1)/2
Let j(o) be the second derivative of -o**9/15120 + o**8/6720 + o**7/2520 - o**6/720 - 5*o**4/12 - 4*o. Let b(v) be the third derivative of j(v). Factor b(t).
-t*(t - 1)**2*(t + 1)
Fact