(w + 1)/3
Determine f, given that -1/3*f**5 + 0*f + 0 + 5/3*f**3 - 1/3*f**4 - f**2 = 0.
-3, 0, 1
Let v = 982/5 - 196. Determine x, given that 0*x**3 + v*x**4 - 2/5*x**2 + 0*x + 0 = 0.
-1, 0, 1
Suppose -3*v = v + 48. Let p(f) = f**2 + 12*f + 2. Let j be p(v). Factor -2*x - 1/2*x**j - 2.
-(x + 2)**2/2
Suppose 0*t + 3*t + 2*t = 0. Let m(j) be the third derivative of 2*j**2 - 1/840*j**7 - 1/80*j**5 + 0 - 1/96*j**4 + t*j**3 - 1/160*j**6 + 0*j. Solve m(d) = 0.
-1, 0
Suppose -4*u**4 + 16*u + 23*u**3 + 16*u**2 - 12*u**3 - 15*u**3 = 0. What is u?
-2, -1, 0, 2
Let a(i) be the second derivative of -i**4/3 + 4*i**3/3 + 3*i. Suppose a(z) = 0. What is z?
0, 2
Let h = 6595/7 + -941. Factor 0 - h*b**2 + 8/7*b**4 - 4/7*b**5 + 0*b**3 + 4/7*b.
-4*b*(b - 1)**3*(b + 1)/7
Let z(m) = -12*m**3 + 90*m**2 - 119*m + 31. Let f(i) = 18*i**3 - 135*i**2 + 178*i - 47. Let p(k) = -5*f(k) - 7*z(k). Determine v, given that p(v) = 0.
1/2, 1, 6
Let l(j) be the second derivative of j**6/45 + j**5/15 - j**4/18 - 2*j**3/9 - j. Determine p, given that l(p) = 0.
-2, -1, 0, 1
Let h(w) = 90*w**2 + 110*w + 20. Let b(y) = -45*y**2 - 55*y - 10. Let p(l) = 11*b(l) + 6*h(l). Factor p(d).
5*(d + 1)*(9*d + 2)
Let p(h) = h**2 + 1. Let b(y) = -6*y**2 - 4. Let z = -5 - -1. Let l(n) = z*p(n) - b(n). Solve l(k) = 0 for k.
0
Let i(y) be the second derivative of y**8/840 + y**7/210 + y**6/180 - y**3/6 - 4*y. Let c(r) be the second derivative of i(r). Factor c(q).
2*q**2*(q + 1)**2
Let o = 262 - 1832/7. Suppose -o*k**2 + 6/7*k - 4/7 = 0. What is k?
1, 2
Let b(c) be the first derivative of 0*c**3 - 1/36*c**4 + 2*c + 1 + 1/6*c**2. Let u(t) be the first derivative of b(t). Solve u(w) = 0.
-1, 1
Let j = 5 + -6. Let y be 42/15 + j/(-5). Find i such that -5*i**3 + 4*i**5 + i + 3*i**3 - y*i**5 = 0.
-1, 0, 1
Let p(a) = a**2 + 8*a + 7. Let z be p(-1). Let s(q) be the third derivative of 1/120*q**5 + 0*q**4 - 1/12*q**3 + z*q + q**2 + 0. Factor s(t).
(t - 1)*(t + 1)/2
Let f(p) be the third derivative of -p**8/1848 + 8*p**7/1155 - 3*p**6/110 + 8*p**5/165 - 5*p**4/132 + 2*p**2. Factor f(t).
-2*t*(t - 5)*(t - 1)**3/11
Find b such that -32/7 + 244/7*b**3 + 120/7*b**4 - 144/7*b - 100/7*b**5 - 88/7*b**2 = 0.
-1, -2/5, 1, 2
Let t(b) be the first derivative of -2/21*b**3 + 4 + 0*b + 2/7*b**2. Factor t(s).
-2*s*(s - 2)/7
Let r(w) = -w**5 + w**4 + w**3 - w - 1. Let v(p) = 3*p**5 + 2*p**4 - 13*p**3 + 2*p**2 + 6*p + 6. Let f(t) = -6*r(t) - v(t). Determine c so that f(c) = 0.
0, 2/3, 1
Let t(g) be the first derivative of -352/25*g**5 - 64/15*g**6 - 2/5*g - 14/5*g**2 - 86/5*g**4 - 146/15*g**3 - 4. Factor t(a).
-2*(a + 1)**2*(4*a + 1)**3/5
Determine k so that 3/8*k**2 - 1/8*k + 0 = 0.
0, 1/3
Factor 8*f**2 - 4*f**4 - 1 + 0*f**4 - 3.
-4*(f - 1)**2*(f + 1)**2
Let f be -1 - ((-2920)/(-385))/4. Let u = 35/11 + f. Find p, given that 2/7*p**2 + u*p - 4/7 = 0.
-2, 1
Factor 2/3*c**2 + 1/9 + 4/9*c**3 + 1/9*c**4 + 4/9*c.
(c + 1)**4/9
Find d, given that -146*d + 2*d**2 - d**2 + 80*d + 74*d = 0.
-8, 0
Let j(z) = -14*z**2 - 4*z - 5. Let u(l) = -4 - 5*l - 18*l**2 + l + 4*l**2. Suppose 2 + 3 = -k. Let s(y) = k*u(y) + 4*j(y). Determine w, given that s(w) = 0.
-2/7, 0
Let w(x) = 15*x**3 + 3*x**2 - 18*x + 12. Let b(h) = -6*h**3 - h**2 + 7*h - 5. Let m(s) = -12*b(s) - 5*w(s). Factor m(f).
-3*f*(f - 1)*(f + 2)
Suppose 0*n = -3*n. Factor 0 + 6 + 3*r - 3*r**3 + n - 6*r**2.
-3*(r - 1)*(r + 1)*(r + 2)
Let u be (22/(-154))/(15/(-7)). Let o(i) be the first derivative of -1/3*i**3 + 1/3*i**2 - 1 + 0*i**4 + u*i**5 + 0*i. Let o(q) = 0. Calculate q.
-2, 0, 1
Let l = 221/10 + -108/5. Find d, given that 1/2*d**4 - d**3 + l*d**2 + 0 + 0*d = 0.
0, 1
Let i(t) be the second derivative of -3*t + 0 - 1/30*t**3 + 1/60*t**4 - 1/5*t**2. Factor i(h).
(h - 2)*(h + 1)/5
Suppose -2*n = 4*q + 2, 3*q - 9 = -9*n + 4*n. Factor 0 - 3/2*z**2 - 1/2*z - z**n.
-z*(z + 1)*(2*z + 1)/2
Let f(h) be the second derivative of -h**9/504 - h**8/84 - h**7/35 - h**6/30 - h**5/60 - h**3/3 + 2*h. Let m(w) be the second derivative of f(w). Factor m(y).
-2*y*(y + 1)**3*(3*y + 1)
Find d, given that 0*d + 0*d - d**2 + 10*d - 4 + 2*d**3 - 7*d**2 = 0.
1, 2
Let s(l) = l + 7. Let k be s(-3). What is g in 3*g**3 - g**3 - 2*g**k - 2*g**2 + 2*g**2 = 0?
0, 1
Let r = 27 - 241/9. Factor -r*a**2 - 8/9*a**3 - 8/9*a**4 + 0 + 0*a.
-2*a**2*(2*a + 1)**2/9
Let c(y) = y + 13. Let s be c(-6). Let b = -7 + s. Factor 2/3*j**5 + 0*j**3 + 2/3*j**4 + 0*j**2 + 0 + b*j.
2*j**4*(j + 1)/3
Let r(g) be the second derivative of -g**5/110 + g**4/33 - g**3/33 - 19*g. Factor r(l).
-2*l*(l - 1)**2/11
Let l(s) be the third derivative of -s**8/336 - s**7/70 - s**6/40 - s**5/60 + 10*s**2. What is a in l(a) = 0?
-1, 0
Let t(z) = -4 + 0*z**2 + z**2 + 2. Let p be t(-2). Factor 8/7*y + 8/7 + 2/7*y**p.
2*(y + 2)**2/7
Let v(y) = y**2 + y. Let p(i) = -6*i**2 + 8*i - 18. Let d(l) = p(l) + 4*v(l). Solve d(z) = 0 for z.
3
Let o = 16 + -16. Let f(j) be the third derivative of 0 + o*j**4 + 2*j**2 + 0*j + 1/120*j**5 + 0*j**3. Factor f(u).
u**2/2
Factor 2/3*q**3 - 14/3*q**2 - 6 + 10*q.
2*(q - 3)**2*(q - 1)/3
Let x be 0/(-1 + 3/(-3)). Let m = 2 - x. Factor 3*h**m - h**4 + h - 2*h**2 - 2*h**3 + h**3.
-h*(h - 1)*(h + 1)**2
Let r(g) = -6*g + 2 - 9*g + 2*g. Let w be r(-2). Let w*s**5 - 20*s**2 - s**5 + 32*s - 53*s**2 - 4 + 81*s**4 + 9*s**3 = 0. Calculate s.
-2, 1/3
Let j(z) be the third derivative of -z**7/420 + z**6/240 + z**5/30 - z**4/12 - 8*z**2. Factor j(m).
-m*(m - 2)*(m - 1)*(m + 2)/2
Let i(g) = -3*g - 3. Let p(y) = y + 1. Let k(o) = 2*i(o) + 7*p(o). Let j(h) = -h**4 + 6*h**3 - 13*h**2 + 16*h. Let s(d) = -j(d) + 4*k(d). Factor s(z).
(z - 2)**2*(z - 1)**2
Suppose 0*v**4 + 3*v - 2*v**3 - v**5 - 21*v**2 - 1 + 19*v**2 + 3*v**4 = 0. What is v?
-1, 1
Suppose 11 = 4*z - 3*w, 3 = -0*w - 3*w. Let v = 6 + -2. Factor -v*m - 15*m**2 + m**z + 0*m.
-2*m*(7*m + 2)
Let b(d) be the third derivative of 0 + 1/8*d**4 - 1/120*d**6 + 2*d**2 + 0*d + 1/3*d**3 + 0*d**5. Factor b(h).
-(h - 2)*(h + 1)**2
Suppose -2*y + 23 = 3*g, -4*g + 28 = 8. Let m(a) be the third derivative of 1/60*a**6 + 0*a + a**2 + 0 - 1/60*a**5 + 0*a**y + 0*a**3 - 1/210*a**7. Factor m(u).
-u**2*(u - 1)**2
Suppose 936*d - 3*d**4 - 36 + 2*d**4 - 13*d**2 - 996*d + 10*d**3 = 0. Calculate d.
-1, 6
Let f = -28 + 30. Factor 0 + 8/3*d**3 - f*d**2 - 2/3*d.
2*d*(d - 1)*(4*d + 1)/3
Let c = 15 + -11. Solve -q**5 - 8*q + 4*q**3 + 5*q**5 + 12*q**c - 12*q**2 - 3*q**3 + 3*q**3 = 0.
-2, -1, 0, 1
Let t(j) be the first derivative of 2*j**3/21 + 3*j**2/7 + 5. Suppose t(k) = 0. What is k?
-3, 0
Let u(a) be the second derivative of 2/3*a**3 - 1/42*a**7 - 2/15*a**6 + 0 + 1/3*a**4 + 0*a**2 - 3/20*a**5 + 4*a. Suppose u(f) = 0. Calculate f.
-2, -1, 0, 1
Let k(f) be the third derivative of 0 + 0*f + 1/84*f**4 - 1/420*f**6 + 1/735*f**7 - 1/70*f**5 - 6*f**2 + 2/21*f**3. Factor k(m).
2*(m - 2)*(m - 1)*(m + 1)**2/7
Let m(d) = d**3 - 4*d**2 + d - 4. Let n be m(4). Let w(f) be the second derivative of n + 4/21*f**3 - 2*f + 1/42*f**4 + 4/7*f**2. Factor w(c).
2*(c + 2)**2/7
Factor 0 - 12*d**2 + 16*d**3 - 20/3*d**4 + 8/3*d.
-4*d*(d - 1)**2*(5*d - 2)/3
Let n(j) be the first derivative of 2 + 2/9*j**3 + 0*j - 1/3*j**2. Determine l, given that n(l) = 0.
0, 1
Suppose 0 = 5*u - z - 27, -3*u = z + z - 11. Let i(d) = d**2 - 7*d. Let p(b) = -2*b**2 + 11*b. Let g(j) = u*p(j) + 7*i(j). Let g(q) = 0. What is q?
0, 2
Let l = -255 - -257. Factor -10/9*o**l - 16/9*o - 2/9*o**3 - 8/9.
-2*(o + 1)*(o + 2)**2/9
Let p(m) = m**3 + 3*m - 4. Let a(j) = -j**3 - 2*j + 3. Let q be 0 + (-4 - -2) - 2. Let n(u) = q*a(u) - 3*p(u). Factor n(s).
s*(s - 1)*(s + 1)
Let j = 8 + 3. Let c(f) = -17*f**4 - f**3 + 5*f**2 + 11*f + 11. Let t(g) = 9*g**4 - 3*g**2 - 6*g - 6. Let b(n) = j*t(n) + 6*c(n). Let b(v) = 0. What is v?
-1, 0
Factor -20*k - 30*k - 68*k**2 + 63*k**2 - 125.
-5*(k + 5)**2
Let p(w) be the third derivative of w**6/240 - 26*w**2. Factor p(o).
o**3/2
Let c(f) = -3*f**3 + 7*f**2 + 2*f - 2. Let o(u) = -20*u**3 + 50*u**2 + 15*u - 15. Let w(i) = 15*c(i) - 2*o(i). Determine l, given that w(l) = 0.
0, 1
Factor 1/4*x**2 - 1 + 1/4*x**3 - x.
(x - 2)*(x + 1)*(x + 2)/4
Let o = -396/35 - -58/5. Let p(m) be the second derivative of 2/7*m**4 + 1/14*m**5 + o*m**2 + 3/7*m**3 - 3*m + 0. Factor p(l).
2*(l + 1)**2*(5*l + 2)/7
Let k(r) = -r**5 - r**4 + r**3 - r**2 + r. Let p(