- 7*t. Solve r(a) = 0.
0, 1/2, 1
Determine r so that 0*r**2 + 3/4*r - 3/4*r**3 + 0 = 0.
-1, 0, 1
Suppose -4*g + 4*g = 6*g. Let i(r) be the first derivative of g*r**2 + 1 + 0*r + 2/33*r**3. Solve i(s) = 0 for s.
0
Let r(t) be the second derivative of 3*t**5/20 + 3*t**4/4 - 5*t**3 + 6*t. Factor r(n).
3*n*(n - 2)*(n + 5)
Let h(t) be the second derivative of -t**7/7560 + t**5/360 + t**4/4 + 4*t. Let b(v) be the third derivative of h(v). Factor b(w).
-(w - 1)*(w + 1)/3
Let p(f) be the second derivative of f**6/360 + f**5/180 - f**4/72 - f**3/18 + f**2/2 - 2*f. Let v(l) be the first derivative of p(l). Solve v(k) = 0 for k.
-1, 1
Factor 2 - 4/3*q - 2/3*q**2.
-2*(q - 1)*(q + 3)/3
Let t = 302/3 + -100. Factor -2/3*b**4 - 4/3*b**3 + t*b**2 + 4/3*b + 0.
-2*b*(b - 1)*(b + 1)*(b + 2)/3
Suppose 2*d - 3*d = -0*d. Find i such that -1/3 + i**2 + 2/3*i**3 + d*i = 0.
-1, 1/2
Let k(m) = -7*m**3 + 3*m**2 - 3*m - 7. Let l(g) = -15*g**3 + 7*g**2 - 6*g - 15. Let b(a) = -13*k(a) + 6*l(a). Find c such that b(c) = 0.
-1
Determine a, given that -24/7*a**2 - 24/7*a**5 - 36/7*a**3 - 6/7 + 4*a + 62/7*a**4 = 0.
-3/4, 1/3, 1
Let s(o) be the second derivative of o**7/21 + o**6/15 - 7*o**5/10 - 13*o**4/6 - 2*o**3 + 26*o. Find q, given that s(q) = 0.
-2, -1, 0, 3
Let j(n) be the second derivative of -7*n**5/100 - n**4/20 + 5*n**2/2 + 6*n. Let i(c) be the first derivative of j(c). Suppose i(y) = 0. What is y?
-2/7, 0
Let q(g) be the third derivative of -g**8/9240 + g**6/990 - g**4/132 - g**3 - g**2. Let m(r) be the first derivative of q(r). Find y, given that m(y) = 0.
-1, 1
Let h(v) = 3*v**3 - 5*v**2 - 3*v - 3. Let z(g) = -g**3 + g**2 + g + 1. Let j(w) = -h(w) - 4*z(w). Factor j(b).
(b - 1)*(b + 1)**2
Factor -4 + 9*q**2 - 13*q**2 - 5 - 12*q + 1.
-4*(q + 1)*(q + 2)
Determine m, given that 2*m**3 + 6*m - m**2 - 4*m**3 - 5*m**2 + 10*m**2 = 0.
-1, 0, 3
Let q(h) = h**2 - 4 + h - 5*h - 1 + 5*h. Let c(y) = 2*y - 4. Let j(p) = -3*c(p) + 2*q(p). Factor j(k).
2*(k - 1)**2
Let f = 32 - 30. Let y(i) be the third derivative of -i**f + 0*i**5 + 0*i + 1/120*i**6 - 1/8*i**4 + 0 + 1/3*i**3. Factor y(s).
(s - 1)**2*(s + 2)
Let m(z) be the first derivative of z**5/5 - z**4/4 - z**3/4 + z**2/2 - z/4 - 8. Suppose m(n) = 0. Calculate n.
-1, 1/2, 1
Let z be (-33)/(-9)*4/22. Find u, given that -6*u**2 - z + 10/3*u + 14/3*u**3 - 4/3*u**4 = 0.
1/2, 1
Find b, given that -5*b**2 - 6*b**2 + 15*b**2 - 4 + 2*b**3 - 2*b = 0.
-2, -1, 1
Let o(r) be the first derivative of -5 - 3/7*r**2 - 4/7*r - 1/21*r**6 + 2/7*r**4 + 0*r**5 + 4/21*r**3. Find k, given that o(k) = 0.
-1, 1, 2
Let k(t) be the first derivative of 2*t**6 - 68*t**5/5 + 34*t**4 - 112*t**3/3 + 16*t**2 - 9. Determine a so that k(a) = 0.
0, 2/3, 1, 2
Let n(d) be the second derivative of -4*d + 0 + 0*d**2 + 1/20*d**5 + 0*d**3 + 1/12*d**4. Factor n(w).
w**2*(w + 1)
Let m(c) = 7*c**4 - 2 - 2*c**3 + 0*c**4 + 9*c**3 - 3*c**4 + c. Let o(j) = -8*j**4 - 13*j**3 + j**2 - j + 3. Let u(w) = -10*m(w) - 6*o(w). Factor u(y).
2*(y + 1)**2*(2*y - 1)**2
Find q such that -28 + 14*q**2 - 36*q**3 + 32 - 28*q + 46*q**2 = 0.
1/3, 1
Let f = -1096 + 14255/13. Let l = f - 23/91. Solve 8/7*h**3 + 8/7*h + 2/7 + 12/7*h**2 + l*h**4 = 0.
-1
Let v(t) = 5*t**5 + 2*t**4 - t**3 - 4*t**2 - t + 5. Let b(w) = -24*w**5 - 10*w**4 + 6*w**3 + 20*w**2 + 4*w - 24. Let s(i) = 6*b(i) + 28*v(i). Factor s(m).
-4*(m - 1)**2*(m + 1)**3
Let q(b) be the second derivative of b**4/84 - b**3/14 - 2*b**2/7 + 20*b. Factor q(d).
(d - 4)*(d + 1)/7
Let o(z) = 2*z - 3. Let m be o(-6). Let c = m - -49. Factor -10*x**4 + 4*x**4 + 24*x**2 - 8 - c*x**3 + 10*x**5 + 14*x**2.
2*(x - 1)**3*(x + 2)*(5*x + 2)
Suppose n + 7*n = n. Solve 1/2*m**3 + 1/2*m**2 + n - 1/2*m - 1/2*m**4 = 0.
-1, 0, 1
Let n(y) be the second derivative of -y**7/21 - 2*y**6/15 + y**4/3 + y**3/3 + y. Find k, given that n(k) = 0.
-1, 0, 1
Let u be 0/((-12)/(-4)*-1). Let r(c) be the third derivative of -1/60*c**4 + 0*c + u - c**2 - 1/150*c**5 + 0*c**3. Factor r(b).
-2*b*(b + 1)/5
Factor -8/23*k + 2/23*k**3 + 4/23*k**2 - 16/23.
2*(k - 2)*(k + 2)**2/23
Suppose 3*w + 2*m - 11 = 3*m, 0 = -5*m - 10. Let v be (0 + 4/7)/2. Factor v*l**w + 0*l + 2/7*l**2 + 0.
2*l**2*(l + 1)/7
Let h(i) = -i + 2. Let w be h(-3). Suppose 3*y = -d + 8, 0 = 2*d - 0*d + w*y - 14. Solve -d*r - 2*r + 12*r**2 + 2*r**2 = 0 for r.
0, 2/7
Let x(i) be the first derivative of 0*i**3 - 1/24*i**4 - 1/240*i**6 + 0*i - 3/2*i**2 - 2 - 1/40*i**5. Let y(d) be the second derivative of x(d). Factor y(k).
-k*(k + 1)*(k + 2)/2
Suppose 5*m = 5*p + 5, 5*m - p + 19 = -2*p. Let j = m + 4. Factor -8*t**3 - 8*t + 12*t**2 + j + 2*t**4 + 0*t + 1.
2*(t - 1)**4
Let s be 70/(-175) - (0 + -1). Factor -9/5*p**4 - s*p**3 + 0 + 8/5*p**2 + 4/5*p.
-p*(p - 1)*(3*p + 2)**2/5
Let i(j) = -4*j**2 - 40*j - 4. Let q(f) = f**2 + 8*f + 1. Let y(k) = 3*i(k) + 16*q(k). Factor y(s).
4*(s + 1)**2
Factor 4/7*x + 6/7 - 2/7*x**2.
-2*(x - 3)*(x + 1)/7
Let r = -41 + 124/3. Factor 1/3 - 1/3*a - r*a**2 + 1/3*a**3.
(a - 1)**2*(a + 1)/3
Let c = -6 + 8. Let -3*n + 0*n + 9*n**c - 10*n**3 + 7*n**2 - 5*n + 2*n**4 = 0. What is n?
0, 1, 2
Suppose -10 = -4*n - 2. Suppose 0 = -5*l + 6 - 1. Solve m - l + 1 - m**n = 0.
0, 1
Let q(c) be the second derivative of -c**7/630 - c**6/120 - c**5/60 - c**4/72 + 3*c**2/2 + 6*c. Let n(d) be the first derivative of q(d). Factor n(b).
-b*(b + 1)**3/3
Factor -2/3*j - 10/3*j**3 - 16/3*j**2 + 4/3.
-2*(j + 1)**2*(5*j - 2)/3
Suppose -j + 6*j + b - 40 = 0, 0 = -3*j - 5*b + 2. Let w be 2/(-3) + 42/j. Let 0*h**2 + 1/3*h + 1/3*h**5 + 0*h**w - 2/3*h**3 + 0 = 0. Calculate h.
-1, 0, 1
Let b(r) = -12*r**3 + 15*r**2 - 7*r - 2. Let c(v) = -v**3 - 1. Let z(d) = -b(d) + 3*c(d). Suppose z(p) = 0. What is p?
1/3, 1
Suppose 2*t + 10 = -5*a + 4*t, 3*a + 3*t - 15 = 0. What is x in 1/2*x**2 + 0*x + 0 - 1/2*x**4 + a*x**3 = 0?
-1, 0, 1
Let m(z) be the second derivative of -3*z**5/10 + 11*z**4/18 - 2*z**3/9 - 53*z. Factor m(u).
-2*u*(u - 1)*(9*u - 2)/3
Let z(n) be the third derivative of -n**7/210 - 7*n**6/360 - n**5/90 + 20*n**2. Solve z(x) = 0.
-2, -1/3, 0
Factor 24 + 45/2*n - 3/2*n**2.
-3*(n - 16)*(n + 1)/2
Let g(n) be the first derivative of 5 + 1/7*n**3 + 0*n - 3/14*n**2 + 3/28*n**4 - 3/35*n**5. Factor g(i).
-3*i*(i - 1)**2*(i + 1)/7
Factor 0 + 3/10*c**4 + 1/10*c**3 + 0*c - 1/5*c**2.
c**2*(c + 1)*(3*c - 2)/10
Let -1/3*r**2 - 2/3*r + 0 = 0. What is r?
-2, 0
Let f(n) = -3*n**2 - 27*n - 24. Let m(l) = -3*l**2 - 28*l - 25. Let s(h) = -4*f(h) + 3*m(h). Solve s(p) = 0 for p.
-7, -1
Suppose 2*n + 20 = 4*n. Suppose n*s = 3*s. Factor -3/4*k + 3/4*k**3 + 0*k**2 + s.
3*k*(k - 1)*(k + 1)/4
Let g be ((-30)/(-4))/(6/8). Suppose 5*z + g = 0, z + 0*z + 12 = 5*w. Let -2*k**2 + 5*k**3 - 2*k**4 + k**3 - 8*k**2 + 4*k**w + 2*k = 0. Calculate k.
0, 1
Let i(n) = -31*n**5 - 47*n**4 - 36*n**3 + n**2. Let p(f) = 21*f**5 + 31*f**4 + 24*f**3 - f**2. Let m(u) = -5*i(u) - 7*p(u). Factor m(l).
2*l**2*(l + 1)**2*(4*l + 1)
Let o(j) = -2*j**4 + j**3 + j**2. Let q(s) = -s**5 + s**4 + s**3 + s**2 - s - 1. Let v = -1 + -1. Let f(i) = v*o(i) - 2*q(i). Factor f(y).
2*(y - 1)**2*(y + 1)**3
Let x be (-26)/273*(-6)/8. Let k(u) be the second derivative of x*u**4 - 1/70*u**5 + u + 0 + 1/7*u**2 - 1/7*u**3. Factor k(m).
-2*(m - 1)**3/7
Let l(c) be the first derivative of c**6/2 - 3*c**4/4 - 17. Factor l(x).
3*x**3*(x - 1)*(x + 1)
Let q(p) be the second derivative of 7*p**4/36 - p**3/9 + 22*p. Solve q(z) = 0 for z.
0, 2/7
Let t(j) = 4*j**4 - 4*j**3 - j**2 + 3*j. Let d(p) = p**4 + p. Let b(n) = -3*d(n) + 3*t(n). Let b(k) = 0. Calculate k.
-2/3, 0, 1
Factor -11 + 5 + 14*u**3 - 4*u**2 - 21*u + 7*u**3 + 10*u**2.
3*(u - 1)*(u + 1)*(7*u + 2)
Let z(y) be the third derivative of y**5/120 + 5*y**4/24 + 25*y**3/12 - 12*y**2. Let z(j) = 0. Calculate j.
-5
Let g(n) be the first derivative of 0*n**3 + 0*n + 0*n**4 - 1/240*n**5 + 1/2*n**2 + 1/480*n**6 + 1. Let y(t) be the second derivative of g(t). Factor y(o).
o**2*(o - 1)/4
Let q(o) be the third derivative of 1/24*o**6 - 2/15*o**3 - 3/20*o**5 - 6*o**2 + 1/5*o**4 + 0*o + 0. Factor q(l).
(l - 1)*(5*l - 2)**2/5
Let l(z) = z**3 - 5*z**2 - 6*z. Suppose -v + 5 = 0, n + 3*n + 1 = 5*v. Let g be l(n). Solve -1/2*t + g + 1/4*t**2 = 0 for t.
0, 2
Let t(c) be the third derivative of -2*c**7/315 + c**6/45 + 2*c**2. Solve t(r) = 0 for r.
0, 2
Let d(v