
Let b(s) be the first derivative of 8/7*s**2 + 3 - 104/21*s**3 + 5*s**4 + 0*s + 14/5*s**5. Factor b(z).
2*z*(z + 2)*(7*z - 2)**2/7
Determine u so that 4/3*u - 2*u**2 - 2/3*u**3 + 2*u**4 + 0 - 2/3*u**5 = 0.
-1, 0, 1, 2
Suppose 2*b - b = 2*h + 13, 2*b - h = 14. Find y, given that -b*y + 2*y + 16*y**2 - 3 + 52*y**2 - 8*y**2 = 0.
-1/5, 1/4
Let j = 16 - 13. Suppose -j*g + 10 - 1 = 0. Factor 0*a**2 + 0 + 0*a + 2/5*a**4 + 0*a**g.
2*a**4/5
Suppose 3*t + 4 = 2*p - 11, 6 = -2*t. Let b(z) be the second derivative of 1/4*z**2 + p*z - 1/6*z**3 + 0 + 1/24*z**4. Solve b(k) = 0.
1
Let c be -1 + (4 - 2 - 23). Let q be 6/(-33) - 48/c. Factor -2/7*b**4 + 0*b**q + 0*b + 4/7*b**3 + 0.
-2*b**3*(b - 2)/7
Determine i so that -11 + 5 + 3 + 3*i**2 = 0.
-1, 1
Let b(k) be the first derivative of 3/35*k**5 + 5 - 3/14*k**4 - 1/7*k**3 + 3/7*k**2 + 0*k. Determine m, given that b(m) = 0.
-1, 0, 1, 2
Let p(s) be the first derivative of -s**5/100 + s**4/60 + s**3/15 + 4*s - 3. Let f(j) be the first derivative of p(j). Let f(v) = 0. What is v?
-1, 0, 2
Let w(q) be the third derivative of q**5/150 - 11*q**4/30 + 121*q**3/15 - 34*q**2. Determine o, given that w(o) = 0.
11
Let t(n) be the second derivative of n**7/14 + 3*n**6/10 + 3*n**5/20 - 3*n**4/4 - n**3 + 21*n. Suppose t(j) = 0. Calculate j.
-2, -1, 0, 1
Let s(b) be the first derivative of b**3/12 - b**2/4 + b/4 + 6. Factor s(r).
(r - 1)**2/4
Let t be (4/5)/1*70/42. Solve -2/3*q**2 + 0 - 2/3*q**3 + t*q = 0 for q.
-2, 0, 1
Let q(c) be the first derivative of -1/36*c**4 + 0*c**2 + 1 - 1/9*c**3 - 2*c. Let a(f) be the first derivative of q(f). Factor a(k).
-k*(k + 2)/3
Factor -3*h**3 - 2*h**3 + 0*h**5 + 6*h**4 + 2*h**2 - h**3 - 2*h**5.
-2*h**2*(h - 1)**3
Let l = 117 - 350/3. Factor -4/3*b + l + b**2.
(b - 1)*(3*b - 1)/3
Let c = 3007/5 - 601. Factor 2/15*q**3 - c*q**4 + 0 + 0*q + 0*q**2.
-2*q**3*(3*q - 1)/15
Suppose -n - 5 = -2*n. Determine z, given that -4/3*z - 4/3*z**2 + 2/3*z**4 - 4/3*z**n + 8/3*z**3 + 2/3 = 0.
-1, 1/2, 1
Solve 6/5*c**4 - 4/5*c**3 - 4/5*c**2 - 2/5*c**5 - 2/5 + 6/5*c = 0.
-1, 1
Let f(n) be the second derivative of -n**7/189 + n**5/45 - n**3/27 + 16*n. Factor f(w).
-2*w*(w - 1)**2*(w + 1)**2/9
Suppose 0 = 3*u + u + 4. Let s be 4/2 - (2 + u). Factor s - 1 - 2*p**2.
-2*p**2
Let b be (27/2)/3 - 15/10. Let 1/4*h**4 - 1/2*h + 1/2*h**b + 0*h**2 - 1/4 = 0. Calculate h.
-1, 1
Let o(f) be the second derivative of -f - 1/6*f**3 + 0 - 1/24*f**4 + 0*f**2. Determine i so that o(i) = 0.
-2, 0
Let r(s) be the second derivative of -s**4/24 - s**3/12 + s**2/2 - 5*s. Factor r(v).
-(v - 1)*(v + 2)/2
Let l(h) be the third derivative of -h**6/270 + h**5/30 + 2*h**4/9 + 7*h**3/6 - 5*h**2. Let x(p) be the first derivative of l(p). Let x(k) = 0. What is k?
-1, 4
Let n(j) be the first derivative of j**7/420 - j**6/45 + 13*j**5/240 - j**4/16 - j**3 + 4. Let f(h) be the third derivative of n(h). Let f(l) = 0. Calculate l.
1/2, 3
Let u(b) be the third derivative of 0*b + 0 + 0*b**3 - 2*b**2 + 1/630*b**7 - 1/360*b**6 + 0*b**4 + 1/1008*b**8 - 1/180*b**5. Factor u(m).
m**2*(m - 1)*(m + 1)**2/3
Let d(b) be the first derivative of -2*b**3/3 - 8*b**2 - 32*b - 12. What is r in d(r) = 0?
-4
Suppose -5*i = -31 - 29. Let p = i - 9. Suppose -p*w**2 - 4*w - w + 2*w**2 + 3*w = 0. What is w?
-2, 0
Let t be 2 + 2 + -3 + -31. Let b be (20/t)/(2/(-6)). Solve 2/3*u**3 + 2/3*u + 0 + 4/3*u**b = 0 for u.
-1, 0
Let c(q) be the second derivative of -q**7/735 - q**6/420 - 2*q**2 - 2*q. Let v(k) be the first derivative of c(k). What is p in v(p) = 0?
-1, 0
Let i = -2/15 - -19/30. Let b(s) be the first derivative of 1 + 2*s + i*s**4 - s**2 - 2/3*s**3. Factor b(y).
2*(y - 1)**2*(y + 1)
Let d(o) be the first derivative of 0*o**2 + 1/18*o**6 + 1/15*o**5 - 1/9*o**3 + 2 + 0*o - 1/12*o**4. Find z, given that d(z) = 0.
-1, 0, 1
Let t(s) be the second derivative of -1/84*s**7 - 1/30*s**6 + 0*s**3 + 0*s**4 + 0 + 3*s - 1/40*s**5 + 0*s**2. Factor t(j).
-j**3*(j + 1)**2/2
Factor 7*a + 6*a**2 + a - 3*a - 3*a - 4.
2*(a + 1)*(3*a - 2)
Let x(v) be the first derivative of -v**5/5 + 2*v**4/3 + v**3/3 - 2*v**2 - 4*v/3 - 4. Solve x(p) = 0 for p.
-1, -1/3, 2
Let z(y) be the second derivative of 0 - y**2 + 1/36*y**4 - 1/90*y**5 + y + 1/9*y**3 - 1/180*y**6. Let i(g) be the first derivative of z(g). Factor i(p).
-2*(p - 1)*(p + 1)**2/3
Let n be 68*2/36 - 2. Let m(z) be the first derivative of -1/2*z**4 - 28/9*z**2 + 20/9*z**3 + n*z - 1. Determine f so that m(f) = 0.
2/3, 2
Let i(g) = -g**3 + 12*g**2 - 10*g - 14. Let s be i(11). Let v be (4/10)/(s/(-6)). Factor 6/5*x**2 + 1/5*x**4 + 1/5 - 4/5*x - v*x**3.
(x - 1)**4/5
Let r(u) = -7*u**3 + 6*u**2 - 2*u - 3. Let g(o) = o**3 + o**2 + 1. Let i(c) = -c**2 - 5*c + 5. Let p be i(-6). Let q(l) = p*r(l) - 3*g(l). Factor q(s).
s*(s - 2)*(4*s - 1)
Let g(u) = -u**3 + 5*u**2 + 6*u + 2. Let f be g(6). Factor 4*l**4 - 2 - 2*l**4 - l + 4*l**3 - f*l - l.
2*(l - 1)*(l + 1)**3
Suppose -4*y - 1 = -2*g + 7, -5*y = 5. Let k(b) be the first derivative of b**3/3 + b**2/2 - 3. Let d(o) = -2*o**2 - o. Let p(j) = g*d(j) + 3*k(j). Factor p(h).
-h*(h - 1)
Let a(v) be the second derivative of 0 - 7/50*v**5 + 3*v + 0*v**2 + 2/15*v**3 - 1/6*v**4. Determine t, given that a(t) = 0.
-1, 0, 2/7
Let k(s) = -5*s**5 + 2*s**4 - 2*s**3 - 4*s**2 + 3*s - 2. Let q(l) = 6*l**5 - 2*l**4 + 3*l**3 + 4*l**2 - 4*l + 3. Let y(x) = 5*k(x) + 4*q(x). Factor y(d).
-(d - 2)*(d - 1)**2*(d + 1)**2
Suppose 4*p = -3*q + 10, 8*q - 5*p - 5 = 3*q. Let w(j) = -j**3 - 2*j**2 + j - 4. Let x be w(-3). Determine r so that 0*r**x + 0*r**2 - r - r**q = 0.
-1, 0
Let b(f) = -f**5 + f**4 - f**2 + 1. Let o(y) = 3*y**5 + 3*y - 6. Let w(d) = -6*b(d) - o(d). Factor w(u).
3*u*(u - 1)**3*(u + 1)
Let h(y) be the first derivative of -2401*y**3/3 + 98*y**2 - 4*y + 18. Factor h(s).
-(49*s - 2)**2
Let p(y) be the third derivative of 1/210*y**7 + 0*y**3 + 0*y + 0 + 0*y**4 + 2*y**2 + 0*y**6 + 0*y**5. Find l such that p(l) = 0.
0
Suppose 5*w - 5*f + 10 = 0, -5*w + 4*f - 3 = 3. Determine g so that 14/3*g**3 + 4/3 + 32/3*g**w + 22/3*g = 0.
-1, -2/7
Let i(d) = -10*d**2 - 5*d + 6. Let v(c) = 9*c**2 + 4*c - 5. Let w be (1 - 2)/(2/(-14)). Let z = 13 - w. Let s(u) = z*v(u) + 5*i(u). What is a in s(a) = 0?
0, 1/4
Let v(t) be the first derivative of t**4/14 - 2*t**3/7 + 8*t/7 - 32. Determine w, given that v(w) = 0.
-1, 2
Determine j, given that -2/7*j**4 + 2/7*j**2 + 2/7*j**5 + 0 + 0*j - 2/7*j**3 = 0.
-1, 0, 1
Let s(o) be the third derivative of o**6/120 + 2*o**5/15 - o**4/3 + 3*o**3/2 - 2*o**2. Let u be s(-9). Factor 1/4*w**2 + 0*w + 1/4*w**3 + u.
w**2*(w + 1)/4
Suppose 4*v + 2 = 5*v. Let a be -2*(2/4 - v). Determine l so that 2/5*l**a - 2/5 + 2/5*l**2 - 2/5*l = 0.
-1, 1
Suppose -5*y + 0*y = 0. Let r = -35/2 + 21. Factor -r*j**2 + 5/2*j**3 + y + j.
j*(j - 1)*(5*j - 2)/2
Suppose 2*p - 9*p = -14. Factor 0 - 4/7*q**p - 2/7*q - 2/7*q**3.
-2*q*(q + 1)**2/7
Let a(q) = -3*q**2 + 2*q + 4. Let o(n) be the second derivative of -5*n**4/12 + n**3/2 + 7*n**2/2 + 3*n. Let r(g) = -7*a(g) + 4*o(g). Factor r(d).
d*(d - 2)
Let i be (20/25)/((-1)/(-10)). Find q such that 20/3*q**4 + 4*q**2 + 2*q**5 + 0 + i*q**3 + 2/3*q = 0.
-1, -1/3, 0
Determine k, given that 14*k**2 - 4*k + 13*k**2 - 30*k**2 - 2*k = 0.
-2, 0
Let z(y) be the first derivative of -y**4/16 - y**3/4 - y**2/4 + 3. Factor z(u).
-u*(u + 1)*(u + 2)/4
Let o(u) = -10*u**4 + 17*u**3 - 11*u**2 + u + 3. Let t(i) = -i**2 + 1. Let w(k) = o(k) - 3*t(k). Solve w(x) = 0.
0, 1/5, 1/2, 1
Let w = -4 + 7. Let t = -10 - -14. Determine p so that 2*p**w - 1/2*p**t - 3*p**2 - 1/2 + 2*p = 0.
1
Suppose -5*i + 4*m + 20 = -i, 2*i + 20 = -4*m. Suppose -z + 3 + 1 = i. Find d such that 1 + 6*d**2 - 5*d**2 - 3*d**4 - 3*d**2 + 4*d**z = 0.
-1, 1
Let y = 2 + -2/3. Let -y*q**2 + 5/3*q - 1/3 = 0. Calculate q.
1/4, 1
Suppose 3*h - 12 + 3 = 0. Suppose -3*i + 4 = w + h*w, -4 = i + 4*w. Find f such that 3*f**2 - 6*f**3 + f**3 + 4*f**3 - i = 0.
-1, 2
Let x(n) be the third derivative of -1/12*n**4 + 0*n**3 - 1/30*n**6 + n**2 + 0 + 1/10*n**5 + 0*n. Solve x(k) = 0 for k.
0, 1/2, 1
Let h be 5 + 3/(-1) + -16. Let g = 21 + h. Factor 1 + g*u + 49/4*u**2.
(7*u + 2)**2/4
Let -4/9 + 4/9*k**2 + 2/9*k**3 - 2/9*k = 0. Calculate k.
-2, -1, 1
Let x be (-1 + -5)*(-5)/(-10). Let n be (-34)/51*x/7. Solve -n*z**2 - 2/7 - 4/7*z = 0 for z.
-1
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