of 1/18*t**4 + 0 - 3*t**2 + 1/45*t**5 + 0*t + 0*t**3. Let l(j) = 0. What is j?
-1, 0
Let u(a) = 7*a**2 - 3*a - 3. Let z(s) = s**2 - s + 1. Let p(r) = -2*u(r) - 6*z(r). Factor p(c).
-4*c*(5*c - 3)
Let r(g) be the second derivative of g**4/54 - g**3/27 + 18*g. Determine n, given that r(n) = 0.
0, 1
Let j(b) be the third derivative of b**8/16 + 3*b**7/70 - 73*b**6/280 - 17*b**5/140 + 3*b**4/7 - 2*b**3/7 - 2*b**2 - 10. Suppose j(n) = 0. What is n?
-1, 2/7, 1
Let l(t) = -t**3 - t**2. Let v(f) = -6*f**3 - 2*f. Suppose -24 = -o + 5*q, 0 = -5*o - 4*q - 3 - 22. Let z(k) = o*v(k) + 4*l(k). Find m, given that z(m) = 0.
0, 1
Let q be (-6)/(-4)*(-12)/(-9). Solve -2*t**3 + 2 + 2*t + 2*t + t**4 + 3*t**4 - 6*t**2 - q*t = 0 for t.
-1, -1/2, 1
Let l = -28 - -30. Let o(m) be the first derivative of -1/3*m**3 + 0*m - l + m**2. Factor o(u).
-u*(u - 2)
Let n(p) be the second derivative of p**8/1680 - p**7/420 + p**6/360 - p**3/6 - 10*p. Let f(a) be the second derivative of n(a). Determine w so that f(w) = 0.
0, 1
Let c be (-5)/(-2)*(48/(-20))/(-3). Let -2/3*n + 2/9*n**c + 4/9 = 0. What is n?
1, 2
Suppose i - 16 = -7*i. Suppose 6/5*x**5 - 14/5*x**4 + 6/5*x**3 + 6/5*x**i + 0 - 4/5*x = 0. What is x?
-2/3, 0, 1
Let y(n) = -4*n**4 - 7*n**3 + 7*n**2 + 7*n. Let h(o) = 3*o**4 + 6*o**3 - 6*o**2 - 6*o. Let m(j) = -7*h(j) - 6*y(j). Find z such that m(z) = 0.
0
Suppose -4*i + 0 - 4 = 0. Let u(y) = y**3 - 3*y**2 + 2*y + 2. Let d(a) = a**3 - a**2 + a + 1. Let t(n) = i*u(n) + 2*d(n). Factor t(s).
s**2*(s + 1)
Let o = -362 - -7610/21. Let i(a) be the first derivative of -3 + 4/35*a**5 - 1/7*a**4 - o*a**3 + 4/7*a + 1/21*a**6 + 1/7*a**2. Find p such that i(p) = 0.
-2, -1, 1
Let h(g) = 2 - 5 - 7*g + 5 - g**2. Let s be h(-7). Factor -3*m**2 + 7*m**2 - 5*m**s.
-m**2
Let f(q) be the second derivative of -3*q**5/160 - q**4/16 + 24*q - 2. Factor f(t).
-3*t**2*(t + 2)/8
Let i(y) be the first derivative of -y**5/10 - y**4/6 + 2*y + 2. Let k(q) be the first derivative of i(q). Factor k(h).
-2*h**2*(h + 1)
Let w(o) be the first derivative of -o**5/30 + o**3/9 - 2*o + 1. Let i(m) be the first derivative of w(m). Let i(v) = 0. What is v?
-1, 0, 1
Let h(p) = -5*p**2 + 4*p - 1. Let d(w) = w**2 + w - 1. Let v = -19 - -21. Let s(c) = v*d(c) + h(c). Factor s(n).
-3*(n - 1)**2
Factor 10*l - 4 - l**3 + l**3 + 6*l**2 - 10*l**3 - 2*l**2.
-2*(l - 1)*(l + 1)*(5*l - 2)
Let u = -227/33 - -105/11. Let 1/3 - u*s**4 + 23/6*s**2 + 4*s**3 - 5/2*s = 0. What is s?
-1, 1/4, 2
Let w(l) be the first derivative of l**4/10 - l**2/5 - 26. Factor w(u).
2*u*(u - 1)*(u + 1)/5
Factor -7/4*w**2 + 9/4*w**3 + 1/2*w - 5/4*w**4 + 1/4*w**5 + 0.
w*(w - 2)*(w - 1)**3/4
Suppose -28 = -3*t + 2. Suppose 13*o = t*o. Find a such that 1/3*a**2 + o*a + 0 = 0.
0
Suppose -3*g - 5*j + 0*j = -11, 0 = -g - 4*j + 6. Solve -3/2*d**4 + 3/2*d**g - 3/4*d + 0 + 0*d**3 + 3/4*d**5 = 0.
-1, 0, 1
Let k(g) be the second derivative of 5*g**4/24 - 5*g**3/2 + 25*g**2/4 + 3*g + 4. Factor k(q).
5*(q - 5)*(q - 1)/2
What is g in 8/3 - 2/3*g**4 + 2/3*g**5 - 10/3*g**3 + 16/3*g + 2/3*g**2 = 0?
-1, 2
Let n(z) = -z**3 - 5*z**2 - 4. Let f be n(-5). Let g be (-15)/f - 3/(-12). What is r in g*r + 14*r**4 - 10*r**5 + 3*r**2 - 11*r**2 - 6*r**2 + 6*r**3 = 0?
-1, 0, 2/5, 1
Let q(w) = -3*w**2 + 2*w**2 + 2 + 3 + 9*w**2 - w. Let t(b) = 7*b**2 - b + 4. Let s(p) = -6*q(p) + 7*t(p). Solve s(o) = 0.
-1, 2
Let 4*o - 21*o**4 + 9*o**4 + 4*o**2 + 11*o**4 - o**3 = 0. Calculate o.
-2, -1, 0, 2
Factor 2*c + 3 + 5 - 9*c**3 - 2 + 7*c - 6*c**2.
-3*(c - 1)*(c + 1)*(3*c + 2)
Let y(k) = -k**2 + 6. Let l be y(2). Suppose -1/3*s**5 + 1/3*s**l + 0 + 0*s + s**4 - s**3 = 0. Calculate s.
0, 1
Let u = -50 + 55. Solve 0*m**2 + 0 + 0*m + 1/3*m**3 + 1/3*m**u - 2/3*m**4 = 0 for m.
0, 1
Let m(d) be the third derivative of -d**9/7560 + d**8/3360 - d**4/8 + 5*d**2. Let a(p) be the second derivative of m(p). Let a(v) = 0. What is v?
0, 1
Let u(n) be the first derivative of -n**8/7560 + n**7/1260 - n**6/540 + n**5/540 + n**3 + 3. Let t(b) be the third derivative of u(b). Let t(x) = 0. What is x?
0, 1
Let v(y) be the second derivative of y**7/42 - 3*y**6/40 - 13*y**5/40 - 3*y**4/16 + y**3/6 + 14*y. Let v(c) = 0. What is c?
-1, 0, 1/4, 4
Let g(m) be the first derivative of -m**6/420 + m**5/210 + m**4/42 - 3*m**2 - 5. Let u(r) be the second derivative of g(r). Factor u(s).
-2*s*(s - 2)*(s + 1)/7
Let d(k) be the first derivative of k**6/27 + 2*k**5/15 + k**4/6 + 2*k**3/27 + 3. Suppose d(x) = 0. What is x?
-1, 0
Let i(f) be the first derivative of -4*f**3/3 - 2*f**2 + 8*f + 5. Let i(m) = 0. What is m?
-2, 1
Let p = -19 + 19. Let c = -658/5 + 132. Suppose -2/5*r + 4/5*r**4 + c*r**5 - 4/5*r**2 + 0 + p*r**3 = 0. Calculate r.
-1, 0, 1
Suppose 2*j + 3*b + 60 = 0, 2*j + b = j - 29. Let d be (-9)/j*3/2. Factor -1/4*l**5 - 1/4*l**4 - 1/4*l + 1/2*l**2 + d*l**3 - 1/4.
-(l - 1)**2*(l + 1)**3/4
Let b(x) be the first derivative of -x**6/3 - 2*x**5 - x**4 + 40*x**3/3 + 24*x**2 + 32. What is j in b(j) = 0?
-3, -2, 0, 2
Let x(v) be the third derivative of -v**7/42 + 7*v**6/60 + 2*v**5/15 - 7*v**4/12 - v**3/2 - 26*v**2. Let x(t) = 0. Calculate t.
-1, -1/5, 1, 3
Let t(q) be the first derivative of 0*q**3 + 2/45*q**5 + 0*q**2 - 3 + 0*q + 1/18*q**4. Factor t(i).
2*i**3*(i + 1)/9
Let r(o) be the second derivative of -o**5/240 + o**4/48 - o**3/24 - o**2/2 - 2*o. Let v(f) be the first derivative of r(f). Factor v(g).
-(g - 1)**2/4
Let l be ((-12)/(-9))/(2/(-9)). Let f(a) = 9*a**3 + 12*a**2 + 6*a + 6. Let w(u) = -8*u**3 - 11*u**2 - 5*u - 5. Let c(z) = l*w(z) - 5*f(z). Factor c(y).
3*y**2*(y + 2)
Factor 3*z**2 - 3/4*z**3 + 3/2 - 15/4*z.
-3*(z - 2)*(z - 1)**2/4
Solve -4*y**2 + 2*y**4 - 6*y**3 + 4*y**3 + 0*y**4 = 0.
-1, 0, 2
Let v(i) be the second derivative of i**5/130 + i**4/39 + i**3/39 + i. Determine a so that v(a) = 0.
-1, 0
Let z(b) be the first derivative of -3*b**5/5 - 3*b**4/4 + b**3 + 3*b**2/2 + 6. Determine h, given that z(h) = 0.
-1, 0, 1
Let k = -3 - -6. Suppose -f = -k*f. Solve -3/2*b**2 + f - 3/2*b = 0 for b.
-1, 0
Let l(k) be the first derivative of 3*k**5 - 35*k**4/4 - 35*k**3/3 + 15*k**2/2 - 3. Find b, given that l(b) = 0.
-1, 0, 1/3, 3
Let m be 7 + ((-1)/1)/1. Let q(w) be the first derivative of 1/2*w**2 - 1/2*w**4 - 1/5*w**5 + 1/6*w**m + 2/3*w**3 - w - 1. Find k, given that q(k) = 0.
-1, 1
Let g(n) be the third derivative of 1/840*n**7 + 0 + 0*n**3 + 1/480*n**6 + 0*n - 1/120*n**5 + 7*n**2 + 0*n**4. Let g(q) = 0. What is q?
-2, 0, 1
Let h(l) = 6*l**3 - 8*l - 5*l - 12*l**3 - 11*l**3 - 9*l**2. Let k(i) = -4*i**3 - 2*i**2 - 3*i. Let m(x) = -6*h(x) + 26*k(x). Factor m(p).
-2*p**2*(p - 1)
Let h(p) be the first derivative of -2*p - 1/9*p**3 + 1/6*p**2 + 1/36*p**4 + 2. Let d(n) be the first derivative of h(n). Factor d(b).
(b - 1)**2/3
Let u(y) be the third derivative of 0*y**3 + 0 + 0*y**7 + 0*y**5 + 0*y + 3*y**2 - 1/300*y**6 + 1/120*y**4 + 1/1680*y**8. What is k in u(k) = 0?
-1, 0, 1
Let a(m) = -m**2 + 4*m + 1. Let f(u) = 1. Let g(p) = a(p) - f(p). Let w be 15/(-5)*(0 - 1). Let b(v) = 2*v**2 - 12*v. Let k(d) = w*b(d) + 8*g(d). Factor k(h).
-2*h*(h + 2)
Let z = 9 + -6. Determine i, given that 3*i**5 - 3*i**z + 2*i**4 - 4*i**3 + 4*i**3 - 5*i**4 + 3*i**2 = 0.
-1, 0, 1
Let p(y) be the second derivative of y**6/20 + 3*y**5/20 - 3*y**4/8 - y**3 + 3*y**2 - 2*y. Factor p(f).
3*(f - 1)**2*(f + 2)**2/2
Let m(r) = -r**2 + r - 1. Let l(f) = 2*f**3 + 8*f**2 - 8*f + 12. Let a(p) = 2*l(p) + 28*m(p). Factor a(c).
4*(c - 1)**3
Let u be 0*((-18)/4)/(-9). Let g(x) be the third derivative of u*x**3 + 1/12*x**4 + 1/120*x**6 - 1/20*x**5 + 0 + 0*x - x**2. Factor g(q).
q*(q - 2)*(q - 1)
Let c = 2 + 3. Factor 8*r + c*r**2 + 2*r**2 - 3*r**2.
4*r*(r + 2)
Let j = -251/20 + 51/4. Find g, given that -1/5*g**2 + 2/5 + j*g = 0.
-1, 2
Suppose 5*r + 11 = -2*b - 3, r - 11 = -5*b. Suppose -b - 1 = -j. Factor 0*t - 50/11*t**j + 0 - 2/11*t**2 + 20/11*t**3.
-2*t**2*(5*t - 1)**2/11
Determine s so that 0 - 2/3*s**2 - 2/9*s - 2/9*s**4 - 2/3*s**3 = 0.
-1, 0
Let v be (1 + 4 + -6)*(0 - 0). Let t(q) be the third derivative of v*q**4 + 0*q + 0*q**3 + q**2 + 1/45*q**5 + 1/180*q**6 + 0. Factor t(u).
2*u**2*(u + 2)/3
Let s(j) = -3*j**2 + j - 4*j**3 + 3*j**2 + 3*j**3 + 2*j**2. Let c be s(2). Solve 0*q + 2/3 - 2/3*q**c = 0.
-1, 1
Let t be ((-36)/21)/(9/(-6)). Suppose 0 + 