- 1)/3
Determine k, given that 2/5*k**2 + 6/5*k + 4/5 = 0.
-2, -1
Let h(p) be the third derivative of -p**6/720 - p**3/6 + 2*p**2. Let d(k) be the first derivative of h(k). Factor d(j).
-j**2/2
Let i(m) = -m**3 + m**2 + m - 1. Let w(o) = 9*o**3 + 3*o**2 - 6*o - 6. Let k(l) = 6*i(l) + w(l). Suppose k(t) = 0. Calculate t.
-2, 1
Let a(t) be the third derivative of -t**7/42 + 7*t**6/24 - 5*t**5/4 + 65*t**4/24 - 10*t**3/3 + 39*t**2. Solve a(j) = 0 for j.
1, 4
Let h(c) = -2*c**3 + 0 - 5 + 3*c + 2*c - 6*c**3. Let a(l) = -l**3 + l - 1. Let g(o) = 5*a(o) - h(o). What is n in g(n) = 0?
0
Factor 0*v + 2/15*v**3 + 0 + 4/15*v**2.
2*v**2*(v + 2)/15
Let s(z) be the third derivative of 0 + 1/180*z**6 + 1/9*z**3 + 0*z + 1/30*z**5 + 5*z**2 + 1/12*z**4. Factor s(o).
2*(o + 1)**3/3
Factor 3*o**2 - 3*o + 4*o**2 - o**2 - 4*o**2 + 1.
(o - 1)*(2*o - 1)
Let h(y) be the first derivative of -4*y**3/3 + 8*y**2 - 16*y + 9. Determine w so that h(w) = 0.
2
Let b(i) be the first derivative of -2*i**3/21 + 2*i**2/7 - 2*i/7 + 1. Let b(p) = 0. What is p?
1
Let s(u) be the first derivative of -u**8/112 - 3*u**7/70 - 3*u**6/40 - u**5/20 - u**2/2 - 2. Let v(b) be the second derivative of s(b). Factor v(g).
-3*g**2*(g + 1)**3
Let q = -74 - -122. Let o be q/20 - (-2)/(-5). Solve 2/3 - 2/3*r**o + 0*r = 0.
-1, 1
Let s(m) = -m**2 + m + 1. Let v(r) = -20*r**2 + 16*r + 28. Let u(z) = 24*s(z) - v(z). Let u(a) = 0. Calculate a.
1
Let t(v) be the second derivative of -v**4/30 - 2*v**3/15 + 3*v**2/5 - 6*v. Factor t(b).
-2*(b - 1)*(b + 3)/5
Factor 0*c + 0*c**2 + 4/3*c**3 + 0 + 4/3*c**4.
4*c**3*(c + 1)/3
Let t be (1 - 19)*3/(-2). Suppose 7 = s - 0*s + b, 0 = s + 5*b - t. Determine h so that -4*h**s - 2*h**5 + h**2 + 2*h + h**4 + 3*h**4 - h**2 = 0.
-1, 0, 1
Let z(x) be the third derivative of -x**5/210 + 4*x**4/21 - 64*x**3/21 - 9*x**2. Solve z(s) = 0 for s.
8
Solve 0 - 2/9*k**4 + 14/9*k**2 + 8/9*k + 4/9*k**3 = 0 for k.
-1, 0, 4
Let x(r) = -3*r - 1. Let a be x(-1). Factor -8*q + 3*q**3 - 6*q**2 - 2*q**4 - 11*q**3 + 7*q**a - 13*q**2 - 2.
-2*(q + 1)**4
Let n be 3 + 3*(2 + -3). Suppose n + 4/5*v - 2/5*v**2 - 2/5*v**3 = 0. What is v?
-2, 0, 1
Factor 31/2*q**2 - 9 + 7/2*q**4 - 37/2*q**3 + 57/2*q.
(q - 3)**2*(q + 1)*(7*q - 2)/2
Suppose -u = -3*u + 4. Find y such that 2*y**u + 3*y + 4*y + 2 + 0*y**2 - 3*y = 0.
-1
Let o be ((-3)/2)/(9/60). Let a = o - -12. What is t in 8/5 + 0*t - 6/5*t**a + 2/5*t**3 = 0?
-1, 2
Let q(y) = -y**3 + 6*y**2 - 5*y - 2. Let l be q(5). Let i be (1/3)/((-1)/l). Factor -i*n**2 + 0*n + 0.
-2*n**2/3
Let u(w) = 9*w**3 - 49*w**2 + 49*w - 20. Let l(a) = 2*a**3 - 10*a**2 + 10*a - 4. Let o(i) = -11*l(i) + 2*u(i). Let o(p) = 0. Calculate p.
1
Let w be ((-4)/(-6) - 1)*(11 - 12). Factor 0*p - 2/3*p**2 + 0 - w*p**3.
-p**2*(p + 2)/3
Let y(w) = 6*w**4 - 18*w**3 - 6*w**2 + 3*w. Let t(m) = 12*m**4 - 35*m**3 - 13*m**2 + 5*m. Let i(p) = 3*t(p) - 5*y(p). Suppose i(o) = 0. What is o?
-1/2, 0, 3
Suppose 4*m + 13 = -3*v, -2*m = 2*v - 4*v + 10. Let l = 0 - m. Factor 0 + 2/7*n**l - 4/7*n**3 + 0*n + 2/7*n**2.
2*n**2*(n - 1)**2/7
Let s = 24 + -25. Let g(q) = -q + q + q**3 + q**2. Let j(b) = -b**5 + 2*b**4 + 8*b**3 + 2*b**2 - b + 2. Let n(c) = s*j(c) + 6*g(c). Factor n(o).
(o - 2)*(o - 1)**2*(o + 1)**2
Let a(u) be the second derivative of -3/20*u**5 + 0*u**4 - 1/14*u**7 + 0*u**3 + 0 - 1/5*u**6 + 8*u + 0*u**2. Factor a(y).
-3*y**3*(y + 1)**2
Let b = -104/3 - -35. Find t, given that b*t**2 - 2/3*t + 1/3 = 0.
1
Let k(c) be the second derivative of c**7/945 - c**6/540 - 3*c**2/2 + 4*c. Let l(j) be the first derivative of k(j). Factor l(q).
2*q**3*(q - 1)/9
Let u(f) be the first derivative of f**6/540 + f**5/45 + f**4/9 - f**3/3 + 3. Let k(n) be the third derivative of u(n). Find g such that k(g) = 0.
-2
Let u = -693/5 + 139. Determine n, given that 2*n**2 + u*n - 6/5*n**4 - 2/5*n**3 - 4/5 = 0.
-1, 2/3, 1
Let m(t) = -2*t - 4. Let i(l) = -l - 2. Let u(a) = -11*i(a) + 6*m(a). Let n be u(-4). Solve -y**3 - 2*y**2 + 2*y**n = 0.
0
Solve 2/3*m + 0*m**3 - 2/3*m**5 + 4/3*m**2 + 0 - 4/3*m**4 = 0 for m.
-1, 0, 1
Suppose 0 = 2*d - 0*d. Let b(v) be the third derivative of -1/28*v**4 - v**2 - 1/60*v**6 + 2/21*v**3 - 2/35*v**5 + 0 + d*v. Factor b(n).
-2*(n + 1)**2*(7*n - 2)/7
Factor -5*q - 10*q + 4*q**2 - q**2.
3*q*(q - 5)
Let n = -1/246 + 1481/1230. Let a be 112/180 - (-5)/(-90)*4. What is u in 4/5*u - n*u**2 + 0 + a*u**3 = 0?
0, 1, 2
Let m(y) be the third derivative of -y**5/90 + y**4/36 - 28*y**2. Factor m(i).
-2*i*(i - 1)/3
Suppose -12 = -3*v - v. Factor 3*p**5 - p**5 + p**v - 3*p**5.
-p**3*(p - 1)*(p + 1)
Let u(t) be the first derivative of 0*t - 1/20*t**6 + 1/42*t**4 - t**2 + 3 + 0*t**3 - 1/210*t**5. Let w(a) be the second derivative of u(a). Factor w(z).
-2*z*(3*z + 1)*(7*z - 2)/7
Factor -1/5*j**2 + 2/5*j + 3/5.
-(j - 3)*(j + 1)/5
Let r(t) = 4*t**2 + 2*t - 3. Let i(g) = 9*g**2 + 4*g - 7. Let k = 11 - 18. Let b(o) = k*r(o) + 3*i(o). Let b(p) = 0. What is p?
-2, 0
Let v(l) be the first derivative of -3*l**2 - 3/2*l**3 - 2*l - 1. Suppose v(o) = 0. Calculate o.
-2/3
Factor 4 + 7*w - 45/2*w**2 + 7/2*w**4 + 8*w**3.
(w - 1)**2*(w + 4)*(7*w + 2)/2
Let q be -1 - (-3 + 2 - 1). Let d be 3/q + 48/(-18). Solve -1/3 - 2/3*y - d*y**2 = 0 for y.
-1
Let n(t) be the third derivative of t**5/20 - t**3/2 + 11*t**2. Suppose n(u) = 0. What is u?
-1, 1
Let 4 - 12*x - 4*x**3 + 11*x**2 + x**2 + 0*x**2 = 0. Calculate x.
1
Let a(j) be the third derivative of 9*j**2 - 1/54*j**6 - 1/1512*j**8 + 0 - 1/27*j**5 - 1/189*j**7 + 0*j - 5/108*j**4 - 1/27*j**3. Factor a(i).
-2*(i + 1)**5/9
Factor 6/7*h - 6/7*h**3 - 4/7 + 2/7*h**2 + 2/7*h**4.
2*(h - 2)*(h - 1)**2*(h + 1)/7
Determine n so that 1/3*n**2 - 1/3 - 1/3*n + 1/3*n**3 = 0.
-1, 1
Suppose -15 = -4*o - o. Suppose 9 = -f + o. Let s(m) = m**3 - m - 1. Let n(h) = 8*h**3 - 18*h**2 + 48*h - 60. Let p(v) = f*s(v) + n(v). Factor p(t).
2*(t - 3)**3
Let k(m) be the first derivative of m**3/24 + 3*m**2/8 + 9*m/8 + 8. Factor k(z).
(z + 3)**2/8
Suppose 0 = i - 2, i + 1 = -2*m + 3*m. Suppose 3*w = 5*d + 20, -2*w - 3*d + m = -4. What is o in 4 + o**w - 4 - o**3 = 0?
-1, 0, 1
Factor 32/11 + 2/11*v**2 + 16/11*v.
2*(v + 4)**2/11
Factor 0 - 1/6*u**4 + 1/6*u**3 + 1/3*u**2 + 0*u.
-u**2*(u - 2)*(u + 1)/6
Let c(n) be the third derivative of -n**5/420 + n**4/56 - n**3/21 - 3*n**2 + n. Let c(w) = 0. What is w?
1, 2
Let z = 17 - -5. Let v = z - 21. Determine h so that 5/2*h - 2*h**2 - v + 1/2*h**3 = 0.
1, 2
Let d(l) = -4*l**4 + l**3 + l**2 + 2*l. Let q(p) = 5*p**4 - p**3 - p**2 - 3*p. Let r(m) = -4*d(m) - 3*q(m). Find a, given that r(a) = 0.
-1, 0, 1
Let a(z) be the first derivative of z**6/15 - 6*z**5/25 + 3*z**4/10 - 2*z**3/15 + 3. Find k, given that a(k) = 0.
0, 1
Suppose 0 = 5*f - 15, -3*i - 3*f + 18 - 3 = 0. Let a be ((-30)/75)/((-2)/10). Factor l + i*l - l**a - 5*l.
-l*(l + 2)
Let s(r) be the third derivative of 75*r**8/112 - 2*r**7 - 6*r**6/5 + 12*r**5/5 + 2*r**4 + 4*r**2. Find t such that s(t) = 0.
-2/5, 0, 2/3, 2
Let a(u) = u**2 - 5*u + 2. Let n be a(3). Let m be 1*n*(-7)/98. Factor 0*i - 2/7*i**2 + m.
-2*(i - 1)*(i + 1)/7
Let x(i) be the third derivative of i**5/300 + 3*i**4/40 - i**3/3 - 10*i**2. Suppose x(c) = 0. What is c?
-10, 1
Let k(j) be the first derivative of 0*j - 1/2*j**4 + 0*j**5 + 0*j**3 + 1/6*j**6 - 2 + 1/2*j**2. Determine a, given that k(a) = 0.
-1, 0, 1
Let y = 94 - 92. Let o(j) be the third derivative of -2*j**y + 0 - 1/24*j**3 - 1/96*j**4 + 1/240*j**5 + 1/480*j**6 + 0*j. Find w such that o(w) = 0.
-1, 1
Let h(w) be the first derivative of w**6/15 - 12*w**5/25 + w**4/2 + 49. Find j such that h(j) = 0.
0, 1, 5
Let s(w) be the first derivative of -w**6/120 + w**4/8 + w**3/3 - w**2/2 - 2. Let z(n) be the second derivative of s(n). Factor z(p).
-(p - 2)*(p + 1)**2
Find x such that -2*x - 5*x - 33*x**5 + 8*x**2 + 34*x**5 - 2*x**4 + 2 - 2*x**3 = 0.
-2, 1
Let o(h) be the first derivative of 4/33*h**3 - 2/55*h**5 + 1 + 0*h**2 - 2/11*h + 0*h**4. Suppose o(l) = 0. Calculate l.
-1, 1
Let v(h) be the first derivative of 2/5*h**5 + 2/3*h**3 + 0*h**2 + 0*h + h**4 - 2. Factor v(z).
2*z**2*(z + 1)**2
Let p = -3 + 5. Let z(j) be the third derivative of -1/30*j**5 + 0*j + 0*j**4 - 2*j**p + 0 + 1/3*j**3. Solve z(k) = 0 for k.
-1, 1
Let c = 207 - 3725/18. Let x(n) be the second derivative of -c*n**4 - 1/30*n**5