r + 1/5*r**4 - 2/5*r**3 + 0 - 1/5*r**2 = 0.
-1, 0, 1, 2
Factor 76*s**2 - 70*s**2 - 2*s**3 - 2*s - 2*s.
-2*s*(s - 2)*(s - 1)
Solve 4 + 0*r**5 + 2*r**3 - 116*r**2 + 16*r + 17*r**3 + 141*r**2 + r**5 + 7*r**4 = 0.
-2, -1
Suppose -25 - 10 = -5*s. Let z(i) be the second derivative of 1/63*i**s + 1/10*i**5 + 1/15*i**6 + 0*i**2 + 0*i**3 + 1/18*i**4 + 0 + 2*i. Solve z(k) = 0 for k.
-1, 0
Let h(r) be the first derivative of -r**6/90 - r**5/30 - r**4/24 - 2*r**3/3 + 2. Let z(w) be the third derivative of h(w). Suppose z(l) = 0. What is l?
-1/2
Let n(h) = 4*h - 6. Let c be n(5). Let d(i) = -10*i**2 + 2. Let j(t) = 31*t**2 + t - 7. Let k(g) = c*d(g) + 4*j(g). Factor k(o).
-4*o*(4*o - 1)
Let q(i) be the second derivative of i**4/3 + 4*i**3 + 10*i**2 - 13*i. Factor q(k).
4*(k + 1)*(k + 5)
Let w be (-22)/(-6) + (-4)/(-12). Let z**5 - 15*z**w - z**2 + 0*z**5 + 3*z**3 + 5*z**5 + 7*z**2 = 0. Calculate z.
-1/2, 0, 1, 2
Let b(v) = 9*v**2 + 2*v - 5. Let c(k) be the second derivative of -13*k**4/6 - 5*k**3/6 + 7*k**2 + 3*k. Let g(q) = -17*b(q) - 6*c(q). Factor g(i).
(i - 1)*(3*i - 1)
Let o(a) be the first derivative of 1 - 2/3*a**3 + 0*a - 2*a**2. Solve o(d) = 0.
-2, 0
Let w(v) be the second derivative of -v**9/6480 - v**8/1260 - v**7/1890 + v**4/12 - 5*v. Let a(i) be the third derivative of w(i). Let a(y) = 0. What is y?
-2, -2/7, 0
Let y(w) be the third derivative of -w**6/540 - w**5/135 - 6*w**2. Solve y(p) = 0 for p.
-2, 0
Let a = 6 - 3. Let p(r) be the first derivative of -2 + 1/5*r**2 - 2/25*r**5 + 0*r - 1/10*r**4 + 2/15*r**a. Factor p(l).
-2*l*(l - 1)*(l + 1)**2/5
Let x(z) be the second derivative of -z**4/8 - 3*z**3/2 - 15*z**2/4 + 22*z. Suppose x(a) = 0. Calculate a.
-5, -1
Determine a, given that 0*a**2 + 1/5*a + 0 - 1/5*a**3 = 0.
-1, 0, 1
Let y(s) be the first derivative of 2*s**3/45 - 2*s**2/5 + 2*s/3 - 21. Factor y(x).
2*(x - 5)*(x - 1)/15
Suppose 0 - 2/3*a**5 + 2/3*a - 4/3*a**4 + 4/3*a**2 + 0*a**3 = 0. What is a?
-1, 0, 1
Determine q so that 1/2*q**2 - 1/2*q**3 + 5/2*q + 3/2 = 0.
-1, 3
Let w = -1385/7 - -198. Suppose -w*o**4 - 2/7*o**3 - 1/7*o**2 + 0 + 0*o = 0. What is o?
-1, 0
Let y(l) be the third derivative of l**6/60 - l**5/6 + 2*l**4/3 - 4*l**3/3 - 18*l**2. Factor y(q).
2*(q - 2)**2*(q - 1)
Determine q, given that 6*q**3 + 0*q**4 - 3/2*q**5 - 9/2*q - 3*q**2 + 3 = 0.
-2, -1, 1
Let n be (16/56)/((-9)/(-21)). Factor 0 - n*d**3 + 1/3*d**5 + 0*d - 1/3*d**4 + 0*d**2.
d**3*(d - 2)*(d + 1)/3
Let y(d) = 11*d**4 - 24*d**3 + 34*d**2 + 36*d - 51. Let k(g) = 23*g**4 - 47*g**3 + 67*g**2 + 73*g - 103. Let h(i) = 6*k(i) - 13*y(i). Factor h(t).
-5*(t - 3)**2*(t - 1)*(t + 1)
Let i(u) be the second derivative of 7*u**6/15 - u**5/2 - u**4/3 + 5*u. Determine f, given that i(f) = 0.
-2/7, 0, 1
Let n be -3 - -3 - 10/(-15). Let -n*b - 1/3*b**2 + 0 = 0. What is b?
-2, 0
Let k(i) be the third derivative of 5*i**8/336 + 2*i**7/21 + i**6/4 + i**5/3 + 5*i**4/24 - 31*i**2. Factor k(j).
5*j*(j + 1)**4
Let s(w) be the second derivative of -w**4/12 - w**3/6 + 3*w**2 + 23*w. Factor s(c).
-(c - 2)*(c + 3)
Let s be 2*20/8*3/45. Factor 0 + 0*i + 1/3*i**3 - s*i**4 + 2/3*i**2.
-i**2*(i - 2)*(i + 1)/3
Let q be 4 - 1/(-2)*0. Suppose q*c + 8 = 6*c. Let -h**2 + 0*h**c + h**4 - 4*h**3 + 5*h**3 - h**5 = 0. What is h?
-1, 0, 1
Let u be 6/24 - 114/8. Let z be (u/(-49))/(3/28). Find f, given that 0 - z*f**3 + 2/3*f - 2*f**2 = 0.
-1, 0, 1/4
Let w = -109/3 + 37. Find t such that -8/3*t + 7/6*t**2 + w = 0.
2/7, 2
Let k = 1 + 1. Suppose n - 5 = 5*h - 3*h, h - 10 = -2*n. Factor h*z + 1/4*z**k + 0.
z**2/4
Suppose 20*v - 25*v = 0. Let c(l) be the third derivative of 0*l**3 + 0 + 0*l**5 - 1/120*l**6 + 1/48*l**4 + 1/672*l**8 + 0*l**7 + v*l + 2*l**2. Solve c(s) = 0.
-1, 0, 1
Let u(g) be the first derivative of 2*g**5/85 + 5*g**4/34 + 4*g**3/17 - 4*g**2/17 - 16*g/17 + 10. Suppose u(k) = 0. Calculate k.
-2, 1
Let y be 2/(-1)*(-102)/6. Let v(g) = -11*g**4 - g**3 - 11*g**2 + 35*g - 12. Let o(l) = 2*l**4 + 2*l**2 - 6*l + 2. Let n(k) = y*o(k) + 6*v(k). Factor n(s).
2*(s - 2)*(s - 1)**2*(s + 1)
Let u = -359/9 - -40. Let l(a) be the first derivative of -u*a**3 - 1/2*a**2 - 2/3*a + 3. Factor l(n).
-(n + 1)*(n + 2)/3
Suppose -9/8*l + 3/4 + 3/8*l**2 = 0. What is l?
1, 2
Determine u so that 2/9*u**3 - 2/9*u + 2/9*u**4 - 2/9*u**2 + 0 = 0.
-1, 0, 1
Let f(s) be the first derivative of -s**6/120 - s**5/60 + s**4/24 + s**3/6 + s**2 - 2. Let k(n) be the second derivative of f(n). Solve k(o) = 0 for o.
-1, 1
Let i(j) be the second derivative of j**4/60 - j**3/30 + 9*j. Find y, given that i(y) = 0.
0, 1
Determine w, given that 0 + 1/6*w + 1/2*w**2 = 0.
-1/3, 0
Let k(y) be the third derivative of -y**8/448 + 3*y**6/160 + y**5/40 + 3*y**2 - 2. Let k(h) = 0. What is h?
-1, 0, 2
Let i(u) = 5 + 4 - 6*u + 2*u**3 - 3 + 2*u**3. Let b(m) = -17*m**3 + 24*m - 25. Let a(l) = -2*b(l) - 9*i(l). Factor a(g).
-2*(g - 1)**2*(g + 2)
Let c = 1/54 + 17/54. Let m(j) be the first derivative of -2*j**2 + 1 - 4*j - c*j**3. Factor m(o).
-(o + 2)**2
Let u(y) be the third derivative of y**9/10800 - 3*y**8/11200 + y**7/6300 - y**4/3 - y**2. Let b(l) be the second derivative of u(l). Solve b(n) = 0 for n.
0, 2/7, 1
Factor 48*d + 605 + 5*d**2 - 97*d - 61*d.
5*(d - 11)**2
Let n(u) = -u + 8. Let o be n(5). Let x(f) be the third derivative of o*f**2 + 1/48*f**4 + 0 + 1/240*f**5 + 0*f + 1/24*f**3. Determine y, given that x(y) = 0.
-1
Let l(g) be the second derivative of g**6/165 - g**5/55 - g**4/66 + 2*g**3/33 + 26*g. Find b, given that l(b) = 0.
-1, 0, 1, 2
Let f(w) = w**2 - 5*w - 1. Let c be f(5). Let h(q) = q**3. Let m(x) = 6*x**3 - 2*x**2. Let y be 1 + -1 + -1 + 4. Let u(j) = c*m(j) + y*h(j). Factor u(n).
-n**2*(3*n - 2)
Suppose 2*b - 3*t - 3 = 5*b, b + 13 = -5*t. Factor -1/4*c - 1/2*c**b + 0 - 1/4*c**3.
-c*(c + 1)**2/4
Factor -2/11*c + 4/11 - 2/11*c**2.
-2*(c - 1)*(c + 2)/11
Let r(f) be the first derivative of -f**8/2184 + 2*f**7/1365 - f**6/780 - 3*f**2/2 - 5. Let t(n) be the second derivative of r(n). Find x such that t(x) = 0.
0, 1
Suppose -4*q + 3*a = -51, 2*q = -0*a + 4*a + 28. Suppose 0*t = -3*t + q. Find j such that -2*j**2 + 2*j**4 + 0*j**t + 0*j**4 = 0.
-1, 0, 1
What is s in 0 + 6/5*s**2 - 3*s**3 + 0*s + 12/5*s**4 - 3/5*s**5 = 0?
0, 1, 2
Let l(w) = 17*w**3 + w**2 - 2*w. Let p(k) be the second derivative of 4*k**5/5 + k**4/6 - k**3/3 + k. Let f(t) = 6*l(t) - 7*p(t). Factor f(c).
-2*c*(c + 1)*(5*c - 1)
Let b be (-2 - (-10)/4)*2. Suppose -b = -d - 3*w + 2, 0 = -4*d - 5*w + 12. Factor d*l**3 + l**4 + 15 + 3*l**2 - 15 + l.
l*(l + 1)**3
Let p(q) = -6*q**3 - 9*q**2 - 27*q + 3. Let w(m) = 3*m**3 + 5*m**2 + 13*m - 1. Let t(h) = 4*p(h) + 9*w(h). Factor t(b).
3*(b + 1)**3
Let l = 30 + -28. Suppose -2*y = 3*q - 12, -2*y - y - 8 = -l*q. Suppose 9/2*n**q + 42*n + 51*n**2 + 51/2*n**3 + 12 = 0. What is n?
-2, -1, -2/3
Let p(r) be the first derivative of -1 + 1/10*r**5 + 1/2*r**3 - 1/4*r**2 - 3/8*r**4 + 0*r. What is j in p(j) = 0?
0, 1
Suppose -1 = -3*c - 2*q - 2, 0 = 3*c + q - 4. Suppose -39 + 27 = -c*x. Factor 0*r + 0 - 2/3*r**3 + 2/3*r**x + 2/3*r**5 - 2/3*r**2.
2*r**2*(r - 1)*(r + 1)**2/3
Let r(o) be the second derivative of -o**7/840 - o**6/360 + o**3/6 - 3*o. Let a(n) be the second derivative of r(n). Factor a(y).
-y**2*(y + 1)
Let g be 135/(-18)*(-4)/6. Let m be (-1)/g - (-8)/20. Factor 0 + m*o**5 - 1/5*o**4 + 0*o - 1/5*o**3 + 1/5*o**2.
o**2*(o - 1)**2*(o + 1)/5
Let b(r) be the third derivative of -3*r**8/560 + r**7/350 + 3*r**6/50 - r**5/25 + 20*r**2. Let b(d) = 0. Calculate d.
-2, 0, 1/3, 2
Let w be (-3)/1 + -1 + 4. Let x(j) be the second derivative of -1/36*j**4 - 2*j + w - 1/60*j**5 + 0*j**2 + 1/18*j**3 + 1/90*j**6. Factor x(z).
z*(z - 1)**2*(z + 1)/3
Factor -6/7*t - 2/7 - 6/7*t**2 - 2/7*t**3.
-2*(t + 1)**3/7
Let t be -3 + (2 - 1 - -2). Suppose t*u**2 + 0 + 2/7*u**3 - 2/7*u = 0. What is u?
-1, 0, 1
Let t(s) be the second derivative of -3*s**5/80 + s**3/8 + 6*s. What is h in t(h) = 0?
-1, 0, 1
Suppose -2*q + 0*b + 3*b + 4 = 0, -2*q - 2*b = -4. Let v(n) be the first derivative of 0*n**q - 4/33*n**3 - 1/22*n**4 - 2 + 0*n. Factor v(t).
-2*t**2*(t + 2)/11
Let m(u) = u**2 - u - 1. Suppose 2*w = -0*w - 24. Let y(k) = -3*k**2 + 15*k + 12. Let d(i) = w*m(i) - y(i). Let d(l) = 0. What is l?
-1/3, 0
Let -3/5*p**3 + 1/5*p**5 + 0 - 1/5*p**4 - 2/5*p + p**2 = 