 0.
-1, -1/4, 1
Suppose -3*o = 4*k - 30, 50 = -0*o + 5*o - 2*k. Let p = o - 6. Determine j so that j**2 + p*j**3 - 5*j**3 + j**2 = 0.
0, 2
Let v(l) be the first derivative of -1/5*l**5 - 13/3*l**3 + 6*l**2 + 3/2*l**4 + 2 - 4*l. Factor v(u).
-(u - 2)**2*(u - 1)**2
Factor -22 - 3*r**3 - 42 + 11*r - 9*r**2 + 16*r + 49.
-3*(r - 1)**2*(r + 5)
Let z(k) = -k**2 + 16*k + 62. Let s be z(19). Factor 0 + 0*a**4 + 1/3*a**3 + 0*a**2 - 1/3*a**s + 0*a.
-a**3*(a - 1)*(a + 1)/3
Suppose c = -9 + 8. Let v = 5/4 + c. What is p in 0 - v*p**4 - 1/4*p**3 + 1/4*p**2 + 1/4*p = 0?
-1, 0, 1
Suppose 3*w = -2*k + 32, -5*k + w + 96 + 1 = 0. Factor 2*o**3 + 10*o**2 + 0 + 6*o + 1 - k.
2*(o - 1)*(o + 3)**2
Let c(i) be the third derivative of 0*i**6 - 2*i**2 + 0*i + 0 - 1/350*i**7 + 1/140*i**8 + 0*i**5 + 0*i**3 + 0*i**4. Factor c(f).
3*f**4*(4*f - 1)/5
Suppose -5 - 1 = -3*h. Solve -g**h + 4*g**3 - 4*g**3 - g**5 + g**4 - g**3 + 2*g**3 = 0.
-1, 0, 1
Determine g so that 4 - 8*g - 36*g**3 - 4 - 54*g**2 + 10*g**2 = 0.
-1, -2/9, 0
Let m(k) be the second derivative of k**6/240 + k**5/120 - 2*k**2 - 5*k. Let t(p) be the first derivative of m(p). Factor t(y).
y**2*(y + 1)/2
Let b be (-8)/(-3) - 1/(-3). Suppose -b*u + 6 = -0*u. Factor -2/7*f**u + 0 - 2/7*f.
-2*f*(f + 1)/7
Find j, given that -2/9*j**3 + 0 + 0*j - 2/9*j**2 = 0.
-1, 0
Let c = -15 + 30. Let t = -13 + c. Find w, given that 1/3*w**5 + 1/3*w - 4/3*w**4 + 2*w**3 - 4/3*w**t + 0 = 0.
0, 1
Let v(s) = -2*s**2 - s + 5. Let p(z) = z**2 + z - 1. Let q(b) = -p(b) - v(b). Factor q(o).
(o - 2)*(o + 2)
Let s(x) be the third derivative of -x**6/540 + x**4/36 - 2*x**3/27 - 5*x**2. Suppose s(u) = 0. What is u?
-2, 1
Let o = 29 - 29. Determine t so that 0*t + 2/7*t**2 + o = 0.
0
Let u(h) = -9*h**3 + 27*h**2 - 39*h + 21. Let n(f) = -f**3 + f**2 + f - 1. Let k(t) = -6*n(t) + u(t). Let k(q) = 0. What is q?
1, 3
Let 0*y**2 + 6/11*y**3 + 0 - 8/11*y - 2/11*y**4 = 0. Calculate y.
-1, 0, 2
Let x(h) be the third derivative of 0*h**3 + 0 + 1/90*h**5 + 1/360*h**6 + 1/72*h**4 + 0*h - 3*h**2. Find m, given that x(m) = 0.
-1, 0
Let y be 123/18*-2*180. Let w = 22196/9 + y. Suppose 16/9*x**5 + 2/9 + w*x**4 + 16/9*x + 76/9*x**3 + 50/9*x**2 = 0. Calculate x.
-1, -1/2
Let d(m) be the second derivative of m**5/5 - 7*m**4/15 + 4*m**3/15 + 13*m. Solve d(l) = 0.
0, 2/5, 1
Suppose 0 = -5*d - 4*a + 36, -2*d - 4*a + 13 + 11 = 0. Let j = 124 - 247/2. Suppose -j*t**d + t + 0*t**2 - t**3 + 1/2 = 0. What is t?
-1, 1
Let u(l) = -15*l**5 - 6*l**4 + 15*l**3 - 3*l**2 - 9*l. Let z(j) = 7*j**5 + 3*j**4 - 7*j**3 + j**2 + 4*j. Let i(n) = -4*u(n) - 9*z(n). Factor i(b).
-3*b**2*(b - 1)*(b + 1)**2
Let o(v) = -2560*v**3 + 2880*v**2 - 1083*v + 135. Let a(k) = -7680*k**3 + 8640*k**2 - 3248*k + 405. Let z(d) = -3*a(d) + 8*o(d). Factor z(j).
5*(8*j - 3)**3
Let f = -61 + 245/4. Let p(k) be the first derivative of 0*k**2 + 0*k - f*k**4 - 1/3*k**3 - 3. What is o in p(o) = 0?
-1, 0
Let a be 2 + -7 + 8 - (-2 + 2). Let s(q) be the second derivative of 1/9*q**2 + 1/54*q**4 - a*q + 0 - 2/27*q**3. Factor s(k).
2*(k - 1)**2/9
Let m(n) = -n**4 - n**3 + n**2. Let o = -9 - -8. Let t(y) = -6*y**4 - 3*y**3 + 6*y**2 - 2*y. Let j(f) = o*t(f) + 5*m(f). Factor j(x).
x*(x - 2)*(x - 1)*(x + 1)
Let a = 468/1195 + 2/239. Factor 2/5 - 8/5*f + a*f**4 + 12/5*f**2 - 8/5*f**3.
2*(f - 1)**4/5
Let z(j) be the first derivative of j**4/6 - 3*j - 2. Let d(s) be the first derivative of z(s). Solve d(w) = 0.
0
Let j(k) = -k**3 + 4*k**2 + 2*k - 4. Let g be j(4). Factor -16*t**3 + 3*t**2 + 16 - 15*t**2 + 7*t + 9*t + t**4 - 5*t**g.
-4*(t - 1)*(t + 1)*(t + 2)**2
Suppose -5*q + 1 = -9. Factor 2*r - r + r**4 - q*r**3 + r + 0*r - 1.
(r - 1)**3*(r + 1)
Let f be (2 - (-6)/(-2)) + 4. Let p(v) be the first derivative of -1/16*v**4 + 1 - 1/8*v**2 - 1/6*v**f + 0*v. Factor p(h).
-h*(h + 1)**2/4
Let j(h) be the third derivative of 0*h**3 + 1/180*h**5 + 0 - 2*h**2 + 1/72*h**4 + 0*h. Factor j(q).
q*(q + 1)/3
Let r(b) be the first derivative of 3 - 1/7*b**2 + 2*b - 1/42*b**4 + 2/21*b**3. Let u(m) be the first derivative of r(m). Factor u(y).
-2*(y - 1)**2/7
Let k be 3 - -4 - 3 - 1. Suppose -h + 3*o + 3 = 0, 2*o - k*o - 12 = -4*h. Factor g + 2*g**2 + 4 - 2*g**2 - g**h - 3 - g**2.
-(g - 1)*(g + 1)**2
Let n(i) be the second derivative of i**4/36 - i**3/18 - 10*i. Factor n(h).
h*(h - 1)/3
Suppose -2*a = -3*a + 2. Suppose 0 - 2/3*b**a - 1/3*b = 0. What is b?
-1/2, 0
Let s(r) be the third derivative of -9*r**8/2240 - 2*r**7/105 - r**6/48 + r**5/20 - r**4/8 + 7*r**2. Let m(t) be the second derivative of s(t). Factor m(p).
-3*(p + 1)**2*(9*p - 2)
Let a(h) = h**5 + 2*h**4 - h**3 - 2*h**2 - 2*h. Let k(j) = -j**5 - j**4 + j**3 + j**2 + j. Let n(o) = -a(o) - 2*k(o). Factor n(s).
s**3*(s - 1)*(s + 1)
Let h(w) be the first derivative of -2/3*w**3 - 1/2*w**4 + 1 + 0*w + 2*w**2. Find v such that h(v) = 0.
-2, 0, 1
Let g(h) be the first derivative of h**7/2940 + h**6/1260 - h**5/420 - h**4/84 + 5*h**3/3 - 1. Let r(x) be the third derivative of g(x). Solve r(b) = 0 for b.
-1, 1
Let z be (3 + 3)*(-3)/(-6). Factor 4/5*j + 6/5*j**2 + 14/5*j**4 - 24/5*j**z + 0.
2*j*(j - 1)**2*(7*j + 2)/5
Suppose 0*n = -n + 1. Factor -x**2 - 2 + 3 - x + n.
-(x - 1)*(x + 2)
Let c(f) be the first derivative of f**7/147 + f**6/105 + f - 8. Let w(x) be the first derivative of c(x). Suppose w(o) = 0. Calculate o.
-1, 0
Let m(j) = 3*j**3 + 21*j**2 - 12*j - 21. Let n(h) = h**3 + 5*h**2 - 3*h - 5. Let g(u) = 2*m(u) - 9*n(u). Let g(a) = 0. What is a?
-1, 1
Factor 2/5*i**2 + 2*i + 8/5.
2*(i + 1)*(i + 4)/5
Let f(k) be the second derivative of k**4/24 - k**3/12 - k**2/2 + 4*k. Factor f(r).
(r - 2)*(r + 1)/2
Solve 4/13 - 10/13*a - 6/13*a**2 = 0 for a.
-2, 1/3
Let w be (-3)/(-4)*(-2 + 6). Suppose -5*h + w*l = 15 - 41, -5*h + 30 = -5*l. Factor 0 + 2/3*v**h + 1/3*v**5 + 1/3*v**3 + 0*v + 0*v**2.
v**3*(v + 1)**2/3
Let p(b) be the first derivative of -b**3/6 - b**2/2 - b/2 - 5. Factor p(m).
-(m + 1)**2/2
Determine b, given that 1/4*b**2 - 5/4*b + 1 = 0.
1, 4
Find k such that -450*k**4 + 8 + 79*k**3 + 41*k**3 - 66*k + 442*k**2 - 54*k = 0.
-1, 2/15, 1
Suppose 1 = -4*z + 2*p + 29, 0 = -4*z + 3*p + 32. Let c = 5 - z. Factor -3*d**3 - d**2 - d - d**2 + c*d**3 + 2*d**3.
-d*(d + 1)**2
Let h(b) be the first derivative of b**8/504 + 2*b**7/315 + b**6/180 + 7*b**2/2 + 7. Let j(t) be the second derivative of h(t). Factor j(a).
2*a**3*(a + 1)**2/3
Let f(k) = -15*k**2 - 645*k - 165. Let p(w) = w**2 + 46*w + 12. Let y(q) = 4*f(q) + 55*p(q). Suppose y(v) = 0. What is v?
-10, 0
Suppose -4*q - 28 = -2*y, -3*y + 4*q = y - 40. Let 5*l**3 - 3*l**2 - y*l**3 + 4*l**2 = 0. Calculate l.
0, 1
Let q = -39 + 185. Suppose -5*x = -4*b + 164, -q = -3*b + x - 3*x. Factor 0 - 54*j**2 + 19*j - 4 - 14*j**4 + b*j**3 + 7*j.
-2*(j - 1)**3*(7*j - 2)
Let p(w) be the third derivative of 0*w - 4*w**2 + 0*w**3 - 1/21*w**7 + 0*w**4 - 1/20*w**6 + 0 + 1/15*w**5. Determine h, given that p(h) = 0.
-1, 0, 2/5
Let s(v) = v**3 - v**2 - 8*v + 10. Let d be s(3). Find j such that -4/7*j + 18/7*j**d - 40/7*j**3 + 26/7*j**2 + 0 = 0.
0, 2/9, 1
Suppose -22*i**3 - 25*i**2 - 4 - 4*i - 7*i**4 - 7*i**3 - 12*i - i**5 + 10*i**3 = 0. What is i?
-2, -1
Let r(c) be the first derivative of -c**4/12 + c**2/2 - 2*c/3 + 9. Factor r(l).
-(l - 1)**2*(l + 2)/3
Suppose 0*m**4 + 21*m**3 - 21*m**5 + 6*m**2 + 22*m - 6*m**4 - 22*m = 0. Calculate m.
-1, -2/7, 0, 1
Let f(w) be the second derivative of 1/3*w**4 + 1/15*w**6 + 0*w**3 + 0 - 3/10*w**5 + 2*w + 0*w**2. What is t in f(t) = 0?
0, 1, 2
Solve 0*b - 2/7*b**2 + 8/7 = 0.
-2, 2
Factor 0 + 0*w + 5/4*w**4 + 1/2*w**2 + 11/4*w**3.
w**2*(w + 2)*(5*w + 1)/4
Let u(s) = -2*s + 17. Let n be u(7). Suppose -4*r - n*y = -17, -r - 1 = 3*r - 3*y. Factor -1/2*k**5 - 3/2*k**3 + 0*k + 3/2*k**4 + 0 + 1/2*k**r.
-k**2*(k - 1)**3/2
Let f(y) be the first derivative of -1/6*y**4 - 1/6*y**3 + 0*y**2 + y - 1 - 1/20*y**5. Let c(a) be the first derivative of f(a). Find z, given that c(z) = 0.
-1, 0
Let q(r) be the second derivative of -3*r + 0*r**2 - 1/6*r**4 + 0 + 2/3*r**3. Factor q(i).
-2*i*(i - 2)
Let o(f) be the first derivative of f**6/18 - 5*f**5/3 + 125*f**4/6 - 1250*f**3/9 + 3125*f**2/6 - 3125*f/3 - 7. Find k, given that o(k) = 0.
5
Factor -8/7*i + 2/7*i**2 + 6/7.
2*(i - 3)*(i - 1)/7
Let y(o) be the first derivative of 0*o**2 + 0*o**4 + 