Suppose 7 + 3 = 5*j. Let q be j - (0 - (0 - 0)). Factor -3*m - 2*m**2 + m - m**q - 1 + 2*m**2.
-(m + 1)**2
Let r(d) be the first derivative of -d**4/18 - 2*d**3/27 - 7. What is a in r(a) = 0?
-1, 0
Suppose -2*u + 2*y + 0*y - 20 = 0, 26 = -5*u - y. Let i be ((-2)/u)/(55/33). Factor -1/5*d + 1/5*d**3 - i*d**2 + 1/5.
(d - 1)**2*(d + 1)/5
Let l(p) = p**2 + 2*p. Let n(k) = 2*k**2 + 7*k. Let b(h) = -11*l(h) + 4*n(h). Factor b(f).
-3*f*(f - 2)
Find w, given that -2/7 + 2/7*w**2 + 0*w = 0.
-1, 1
Let 3/2*n**4 + 3/2 + 3/4*n**5 - 3*n**2 - 3/2*n**3 + 3/4*n = 0. What is n?
-2, -1, 1
Find x, given that 1/4*x**3 + 0*x**4 + 0*x**2 + 0 - 1/8*x**5 - 1/8*x = 0.
-1, 0, 1
Let n be ((-66)/(-15) - 4)*5. Suppose 4*c - 23 = 5*a + 2, 4*a + 20 = 0. Find t such that -1/2*t**n - 1/2*t**3 + c + 0*t = 0.
-1, 0
Suppose 0 = -k - 5*h + 13, -3*h - h = -5*k + 7. Factor 0*f**2 - f**k + f + 1/2*f**4 - 1/2.
(f - 1)**3*(f + 1)/2
Determine h so that 6/5*h**2 - 2/5 + 4/5*h = 0.
-1, 1/3
Let h(u) be the third derivative of -u**7/315 - u**6/90 - u**5/90 + 7*u**2. Factor h(p).
-2*p**2*(p + 1)**2/3
Solve 0*n + 4/3*n**2 - 2/3*n**3 + 0 = 0 for n.
0, 2
Let h = 34 + -28. Suppose 6*p = 9*p - h. What is w in 6/5*w**5 + 6/5*w**3 + 3*w**4 - 3/5 - 12/5*w**p - 12/5*w = 0?
-1, -1/2, 1
Factor 0 - 1/4*g**4 + 1/4*g**2 - 1/2*g**3 + 1/2*g.
-g*(g - 1)*(g + 1)*(g + 2)/4
Let v = 15 + -2. Let t = 15 - v. Factor 0 + 0*s - 3/4*s**t.
-3*s**2/4
Factor -16/5*q**3 + 16/5*q + 4/5*q**2 - 4/5.
-4*(q - 1)*(q + 1)*(4*q - 1)/5
Suppose m - 9 = -7. Factor -2/7*w**3 - 30/7*w - 18/7 - 2*w**m.
-2*(w + 1)*(w + 3)**2/7
Let 4*u**3 + 3*u + 2*u**2 - 8*u**2 - u**3 + 0*u**2 = 0. What is u?
0, 1
Let m be (0/3)/(-34 + 39). Factor 1/2*a**2 + 0*a + m - 1/2*a**3.
-a**2*(a - 1)/2
Let l = -14 + 28. Suppose 5*c = l - 4. Factor 0 + 0*j - 2/11*j**c - 2/11*j**3.
-2*j**2*(j + 1)/11
Let c(q) be the second derivative of -27*q**5/20 + 6*q**4 - 13*q**3/2 + 3*q**2 - 16*q. Factor c(i).
-3*(i - 2)*(3*i - 1)**2
Let q(c) = -2*c**3 - 7*c**2 - 3*c - 5. Suppose 0*w + 2*w = 14. Let h(f) = -w*f**2 + 4 - 5 - 6 - f**3 - 2*f + 3. Let a(y) = 5*h(y) - 4*q(y). Factor a(o).
o*(o - 2)*(3*o - 1)
Let t(x) be the second derivative of 0*x**2 + 0*x**4 + 0 - 1/60*x**5 - 5*x + 0*x**3. Factor t(k).
-k**3/3
Let t(h) = -39*h**3 - 42*h**2 - 18*h - 18. Let r(j) = 11*j**3 + 12*j**2 + 5*j + 5. Let v be 30/(-9)*6/(-4). Let k(s) = v*t(s) + 18*r(s). Factor k(d).
3*d**2*(d + 2)
Let l = 2/95 + 17/95. Suppose -z + 3*z = 0. Factor l*w**2 + z*w - 1/5.
(w - 1)*(w + 1)/5
Let q = -1 - -1. Let m(k) be the third derivative of q*k**3 - 2*k**2 + 0 + 1/96*k**4 + 0*k - 1/60*k**5. Suppose m(a) = 0. Calculate a.
0, 1/4
Suppose 4*t + d + 0*d = -4, 14 = -3*t + 2*d. Let n be -1 - -6 - (4 + t). Let 3*h**n + 0*h**3 - 5*h**3 - 2*h**2 = 0. What is h?
-1, 0
Find t such that -t**2 + 8*t + 4 + 8*t**2 - 3*t**2 = 0.
-1
Let x = -8 - -8. Let h(f) = 3 - 3*f**2 + x - 1 + f. Let l(k) = -k**2 - k + 1. Let g(m) = -h(m) + 2*l(m). Factor g(j).
j*(j - 3)
Let m(s) = -4*s + 2. Let z(w) = w**2. Let o(a) = -m(a) - 2*z(a). What is l in o(l) = 0?
1
Let k(b) be the second derivative of -b**6/15 + 9*b**5/10 - 14*b**4/3 + 12*b**3 - 16*b**2 - 29*b. Find m such that k(m) = 0.
1, 2, 4
Factor -3 + 1/2*s**3 - 2*s**2 - 11/2*s.
(s - 6)*(s + 1)**2/2
Let j(d) be the first derivative of -d**4/4 - d**3 + d**2/2 + 3*d + 12. Factor j(m).
-(m - 1)*(m + 1)*(m + 3)
Let y(w) be the second derivative of 25*w**4/48 + 5*w**3/6 + w**2/2 + 22*w. Factor y(a).
(5*a + 2)**2/4
Solve 1/5*h**4 - 1/5*h**2 + 0 - 1/5*h**3 + 1/5*h = 0 for h.
-1, 0, 1
Let y(i) be the third derivative of 0 - i**2 + 1/1155*i**7 + 1/330*i**6 + 0*i**4 + 0*i**3 + 0*i + 1/330*i**5. Factor y(o).
2*o**2*(o + 1)**2/11
Let p(v) be the first derivative of -3*v**4/4 - 4*v**3 - 6*v**2 - 3. Let p(y) = 0. Calculate y.
-2, 0
Let d be 9/(1*9/(-6)). Let p be d/(-5)*(-70)/(-21). Factor -1/2*v**3 - 1/4*v**2 + 0 - 1/4*v**p + 0*v.
-v**2*(v + 1)**2/4
Let s(u) = u**4 + u**3 - u**2 - 1. Let k(n) = -25*n**4 + 9*n**3 + 15*n**2 + 4*n - 3. Let i(c) = k(c) - 3*s(c). Solve i(l) = 0.
-1/2, -2/7, 0, 1
Let v(m) be the second derivative of -m**7/7 - 4*m**6/9 - 13*m**5/30 - m**4/9 - 5*m. Let v(s) = 0. What is s?
-1, -2/9, 0
Let m(d) be the third derivative of d**5/22 + d**4/44 + 15*d**2. Find z, given that m(z) = 0.
-1/5, 0
Let q(g) = g**3 + 4*g**2 - g - 12. Let o be q(-3). Factor -3/4 + 3/4*c**2 + o*c.
3*(c - 1)*(c + 1)/4
Let w(l) be the third derivative of -l**8/672 + l**7/140 - l**6/120 - l**5/60 + l**4/16 - l**3/12 + 11*l**2. Solve w(a) = 0 for a.
-1, 1
Let y(h) be the second derivative of -h**8/504 - h**7/315 + h**6/180 + h**5/90 - h**2 + h. Let i(a) be the first derivative of y(a). Factor i(o).
-2*o**2*(o - 1)*(o + 1)**2/3
Let n(v) be the first derivative of -4*v**3/9 - 4*v**2 - 12*v - 34. Let n(i) = 0. Calculate i.
-3
Let a = 1357 - 6771/5. Solve -14/5*q**3 - 4/5*q**2 + 4/5 + a*q = 0.
-1, -2/7, 1
Let v = 0 - 0. Let s(h) be the first derivative of v*h**3 - 1 + 1/8*h**6 - 5/8*h**2 - 1/2*h + 1/2*h**5 + 5/8*h**4. Factor s(p).
(p + 1)**4*(3*p - 2)/4
Let b(p) = 4*p. Let t be b(0). Let a(s) = s - 3. Let o be a(4). Factor -o - k**2 + t + 0 - 2*k.
-(k + 1)**2
Let q = -14 - -17. What is f in -48*f + 0*f**4 - 44*f**2 + 4*f**3 - f**4 - f**4 - 18 - 20*f**q = 0?
-3, -1
Let j(k) = -k**2 - 6*k + 2. Let y be j(-6). Let p(f) = -f**2 + 5. Let r be p(0). Suppose -5/2*l**4 - 5*l**3 - 5/2*l - 5*l**y - 1/2 - 1/2*l**r = 0. Calculate l.
-1
Let b(p) = -2*p**2 + 15*p - 18. Let m(a) = 6*a**2 - 44*a + 54. Suppose -2*u - 3 = -u. Let k(l) = u*m(l) - 8*b(l). Factor k(s).
-2*(s - 3)**2
Let a = 39 + -27. Suppose 0 = -5*h + 8 + a. Factor -5*z**2 - z**h + z + 6*z**2 - z**3 + 0*z.
-z*(z - 1)*(z + 1)**2
Let n(d) = d**4 + d**2 + d - 1. Let b = -2 + 1. Let r(j) = 2*j**4 + 6*j**2 + 4*j - 4. Let i(s) = b*r(s) + 4*n(s). Factor i(z).
2*z**2*(z - 1)*(z + 1)
Let d(h) be the third derivative of h**11/1164240 - h**9/105840 + h**7/17640 - h**5/12 - 5*h**2. Let f(p) be the third derivative of d(p). Factor f(c).
2*c*(c - 1)**2*(c + 1)**2/7
Let x(j) = -j**3 - 13*j**2 + j - 3. Let a be x(-13). Let r = a + 19. Factor 2/7*f**5 + 0 + 0*f**2 + 2/7*f**r + 0*f - 4/7*f**4.
2*f**3*(f - 1)**2/7
Let y be (18 + -19)/(1/(-4)). Factor -2/7*l**2 + 0*l + 0*l**3 + 0 + 2/7*l**y.
2*l**2*(l - 1)*(l + 1)/7
Let n be (12/(-270))/(1/(-5)). What is x in -2/9*x**2 + n*x + 0 = 0?
0, 1
Let u(r) be the second derivative of 1/900*r**6 + 2*r + 0*r**2 + 1/6*r**3 + 0 - 1/100*r**5 + 1/30*r**4. Let b(c) be the second derivative of u(c). Factor b(i).
2*(i - 2)*(i - 1)/5
Solve 0 + 2/3*c**2 - 1/3*c = 0.
0, 1/2
Factor 24/5*b + 2*b**2 + 8/5.
2*(b + 2)*(5*b + 2)/5
Factor 3*s**5 + 5*s**4 + 0*s**4 + 0*s**4 + 2*s**3.
s**3*(s + 1)*(3*s + 2)
Let n = 15 - 13. Let c(s) be the first derivative of 4 - 1/10*s**4 + 0*s**n + 0*s + 2/15*s**3. Factor c(b).
-2*b**2*(b - 1)/5
Let t(z) be the second derivative of z**7/735 + z**6/210 - z**5/210 - z**4/42 - 5*z**2 + 4*z. Let g(b) be the first derivative of t(b). Factor g(h).
2*h*(h - 1)*(h + 1)*(h + 2)/7
Factor -1/5*j**2 + 1/5*j**3 + 0*j + 0.
j**2*(j - 1)/5
Let t(m) = m**4 - m + 1. Let j(c) = c**5 - 4*c**4 + 2*c - 3 + 2*c + 0*c - 1 - c**3. Let r(z) = j(z) + 4*t(z). Factor r(s).
s**3*(s - 1)*(s + 1)
Let i(f) = 3*f**3 - 9*f**2 + 4*f + 7. Let j(g) = 4*g**3 - 10*g**2 + 5*g + 8. Let t(d) = 5*i(d) - 4*j(d). Let w be t(-5). Factor a**w - 2*a + 2*a**2 + 0*a + 3*a.
a*(a + 1)**2
Factor 2*w**3 - 3*w - w + 2*w**3 - 4*w**5 + 4*w**3.
-4*w*(w - 1)**2*(w + 1)**2
Let w(i) be the first derivative of 0*i**2 + 1/16*i**4 + 1/12*i**3 - 3 + 0*i. Factor w(h).
h**2*(h + 1)/4
Let k be ((-2)/25)/(4/40)*-1. Suppose -2/5*x**2 + k*x + 0 = 0. What is x?
0, 2
Let q(s) be the first derivative of -3*s**5/25 - 3*s**4/10 + 3*s**2/5 + 3*s/5 - 4. Solve q(f) = 0.
-1, 1
Let l = -11 + 6. Let c = 8 + l. Factor 0*g**2 - 7 - g**2 + c - 4*g.
-(g + 2)**2
Let k(o) be the first derivative of o**4 + 0*o + 7 + 4/3*o**3 - 4*o**2. Factor k(c).
4*c*(c - 1)*(c + 2)
Suppose a = -2, -3*c = -6*c - 2*a + 11. Factor -d**2 + 2*d**3 - 1 + 2*d**2 - d - 4*d**2 + c*d**2 - d**4 - d**5.
-(d - 1)**2*(d + 1)**3
Let a(u) be the third derivative of u**10/37800 + u**9/8400 + u**8/5600 + u**7/12600 + u**4/12 + 2*u**2. Let h(y) be the second derivative of a(y). Factor h(q).
q**2*(q + 1)**2*(4*q + 1)/5
Let o(f) = -f**2 - f. Let d(h) 