) = -27*q**3 + 27*q**2 + 3*q - 15. Let f(m) = 5*g(m) - 12*o(m). Find t, given that f(t) = 0.
-1, 1
Let d(w) be the third derivative of w**8/784 + 3*w**7/490 + 3*w**6/280 + w**5/140 - 3*w**2. Solve d(x) = 0.
-1, 0
Let -2/9*m**3 + 4/9 + 8/9*m**2 - 10/9*m = 0. What is m?
1, 2
Let c(o) be the first derivative of -2/5*o**5 - 7 + o**4 - 2/3*o**3 + 0*o + 0*o**2. Factor c(m).
-2*m**2*(m - 1)**2
Suppose -8*q = -7*q - 3. Let h(i) be the first derivative of 2/3*i**q + 0*i - 1/2*i**4 + 0*i**2 + 4. Factor h(n).
-2*n**2*(n - 1)
Let b(t) be the third derivative of -t**5/150 - t**4/10 - 3*t**3/5 + 7*t**2. Factor b(c).
-2*(c + 3)**2/5
Find y such that -2/7*y**2 + 6/7*y - 4/7 = 0.
1, 2
Determine s, given that 100/7*s**2 - 40/7*s + 4/7 = 0.
1/5
Let x(y) be the first derivative of 4/5*y - 1/10*y**4 - 4/15*y**3 + 1/5*y**2 + 4. What is a in x(a) = 0?
-2, -1, 1
Let y(q) be the first derivative of -q**8/960 + q**7/280 - q**6/480 - q**5/240 + 5*q**3/3 - 6. Let z(a) be the third derivative of y(a). Factor z(t).
-t*(t - 1)**2*(7*t + 2)/4
Factor -4*t**4 + 13*t**2 - 8 - 28*t - 21*t**2 + 0*t**4 - 28*t**2 - 20*t**3.
-4*(t + 1)**3*(t + 2)
Let o(m) be the third derivative of m**6/160 + m**5/240 - 7*m**2. Find b such that o(b) = 0.
-1/3, 0
Let p(o) = -9*o**2 - 90*o - 762. Let j(a) = 8*a**2 + 91*a + 763. Let n(c) = -6*j(c) - 5*p(c). Factor n(r).
-3*(r + 16)**2
Let m = 11 - 3. Let q be (4/(-24))/((-2)/m). Factor -q*t**3 - 4/3*t**2 + 2/3*t + 4/3.
-2*(t - 1)*(t + 1)*(t + 2)/3
Let c(g) = -g**2 - g + 1. Let x(s) = 4*s**2 + 8*s - 4. Let k(i) = -8*c(i) - x(i). Factor k(q).
4*(q - 1)*(q + 1)
Let s(p) be the third derivative of 0 + 0*p - 1/240*p**6 - 1/240*p**5 - 1/840*p**7 + 0*p**4 + 0*p**3 - 3*p**2. What is r in s(r) = 0?
-1, 0
Let o(n) = -4*n**3 + 6*n**2 - 10*n + 2. Let s(a) = -5*a**3 + 5*a**2 - 10*a + 1. Let k(m) = 3*o(m) - 2*s(m). Factor k(i).
-2*(i - 2)*(i - 1)**2
Let i(w) be the second derivative of 3*w - 32/33*w**3 + 4/11*w**4 + 16/11*w**2 - 4/55*w**5 + 0 + 1/165*w**6. Factor i(o).
2*(o - 2)**4/11
Let l(j) be the first derivative of -j**8/168 + j**6/60 - 3*j**2/2 - 1. Let h(s) be the second derivative of l(s). Suppose h(k) = 0. Calculate k.
-1, 0, 1
Let c be (-6)/14 + 120/35. What is x in 0*x**4 + 4*x**3 - 3*x**4 + 6*x**2 - 3*x**5 - c*x + 2*x**3 - 3 = 0?
-1, 1
Let t = 17/12 + -1/12. Suppose 0*w**3 + t*w**2 - 2/3 - 2/3*w**4 + 0*w = 0. What is w?
-1, 1
Let w be (8/(-18))/((-30)/135). Suppose 3*y - 2*y = -5*v + 20, 3*y = 2*v - 8. Suppose -1/2*h**4 + y*h**3 + 0 + 0*h + 1/2*h**w = 0. What is h?
-1, 0, 1
Let u be 0*((-6)/2)/(-3). Let n be u/(4 + -3 - 0). Solve n + 2/9*i + 0*i**3 - 4/9*i**2 + 4/9*i**4 - 2/9*i**5 = 0 for i.
-1, 0, 1
Find p such that -3*p**2 - 1099 + 1099 + 3*p**3 = 0.
0, 1
Let p(v) be the third derivative of v**5/120 - 3*v**4/16 + 2*v**3/3 + 15*v**2. Factor p(y).
(y - 8)*(y - 1)/2
Suppose 7 + 8 = 5*c. Suppose 0 = c*n + n - 12. Solve -2*u**n - 2 + 1 - 4*u + u**4 + 6*u = 0 for u.
-1, 1
Factor 2/3*q**4 + 0*q - 4/3*q**2 + 0*q**3 + 2/3.
2*(q - 1)**2*(q + 1)**2/3
Let n(u) be the second derivative of 0 - 3/2*u**2 - 1/30*u**6 - u**4 - 5/3*u**3 - 3/10*u**5 - 9*u. Factor n(b).
-(b + 1)**3*(b + 3)
Let m(z) be the third derivative of 0*z - 1/150*z**6 - 1/525*z**7 + z**2 + 1/30*z**4 + 0 + 1/15*z**3 + 0*z**5. Factor m(k).
-2*(k - 1)*(k + 1)**3/5
Let j = -190 - -193. Factor 0 - 6*a - 30*a**2 - 75/2*a**j.
-3*a*(5*a + 2)**2/2
Let i(w) be the first derivative of w**9/12096 - w**8/3360 - w**7/3360 + w**6/720 + w**3 - 4. Let j(y) be the third derivative of i(y). Solve j(x) = 0 for x.
-1, 0, 1, 2
Let u be 6/(-4) + 5/(-10). Let n be (-12)/(-9) - u/(-3). Factor -4/3 + n*b**2 - 2/3*b.
2*(b - 2)*(b + 1)/3
Let x(l) = 9*l**5 - 9*l**4 - 12*l**3 + 25*l**2 - 3*l - 5. Let k(u) = 10*u**5 - 10*u**4 - 12*u**3 + 26*u**2 - 2*u - 6. Let b(r) = -5*k(r) + 6*x(r). Factor b(h).
4*h*(h - 1)**3*(h + 2)
Let d(k) be the second derivative of -k**5/35 + 4*k**4/21 - 2*k**3/7 - 10*k. Factor d(t).
-4*t*(t - 3)*(t - 1)/7
Let c(m) be the third derivative of -m**10/181440 + m**9/45360 - m**8/40320 + m**4/12 - m**2. Let q(a) be the second derivative of c(a). Factor q(f).
-f**3*(f - 1)**2/6
Let y(g) be the second derivative of g**4/120 - g**3/20 - g**2/5 - 4*g. Suppose y(a) = 0. Calculate a.
-1, 4
Factor -2/5 + 2/5*c**2 + 0*c.
2*(c - 1)*(c + 1)/5
Determine z, given that -1/7*z**3 - 4/7*z**2 + 0 - 4/7*z = 0.
-2, 0
Let z(a) be the third derivative of a**6/120 + a**5/40 - a**3/2 - 3*a**2. Let w(l) be the first derivative of z(l). Factor w(b).
3*b*(b + 1)
Let m(b) be the third derivative of b**6/180 + b**5/30 + b**4/18 - b**2. What is z in m(z) = 0?
-2, -1, 0
Let l = -6 + 6. Let d be 3/6*(l + 0). Solve 0*w - 2/3*w**3 + d + 4/3*w**2 = 0.
0, 2
Let c(v) = -3*v + 22. Let a be c(6). Suppose -a*d = 5*j - 4*j, 0 = -2*j - 5*d. Factor j*z**2 - 1/2*z**3 + 0 + 0*z - 1/2*z**5 + z**4.
-z**3*(z - 1)**2/2
Suppose 4*r = -2*y + 20, 28 = 5*r + y + 3*y. Suppose s + r*s - 15 = 0. Factor -2*z**5 - 10*z**s - 24*z**2 - 8*z - 12*z**4 - 8*z**3 - 8*z**3.
-2*z*(z + 1)**2*(z + 2)**2
Let f(h) be the second derivative of -h**6/90 + h**5/12 - h**4/4 + 7*h**3/18 - h**2/3 + 4*h. Factor f(w).
-(w - 2)*(w - 1)**3/3
Let j(i) be the third derivative of 0*i**4 - 3*i**2 + 1/270*i**5 + 0*i + 0 + 0*i**3. Factor j(k).
2*k**2/9
Factor 1/2*v**4 + 2*v**3 + 2*v**2 + 0*v + 0.
v**2*(v + 2)**2/2
Factor -68/7*u - 16*u**2 - 52/7*u**3 - 8/7.
-4*(u + 1)**2*(13*u + 2)/7
Let y(z) be the first derivative of -z**4/22 + 4*z**3/33 + z**2/11 - 4*z/11 - 3. Factor y(u).
-2*(u - 2)*(u - 1)*(u + 1)/11
Let u(a) = a**3 + 10*a**2 + 23*a - 4. Let y be u(-6). Factor 1/4*t**3 + 0 + 1/4*t**4 - 1/4*t**y - 1/4*t.
t*(t - 1)*(t + 1)**2/4
Let l(o) be the first derivative of 5*o**4/4 + 17*o**3/6 + 2*o**2 + o/2 - 1. Factor l(s).
(s + 1)*(2*s + 1)*(5*s + 1)/2
Let l(t) be the third derivative of -t**7/350 - t**6/100 + t**5/100 + t**4/20 - 20*t**2. What is h in l(h) = 0?
-2, -1, 0, 1
Suppose -4*f = -9*f - 5*z - 10, 4 = 4*f + z. Let o be 3/5 - 0/(30/(-2)). Solve o*j**f - 3/5*j + 0 + 3/5*j**3 - 3/5*j**4 = 0.
-1, 0, 1
Let m(y) be the third derivative of y**6/540 + y**5/135 - y**4/108 - 2*y**3/27 + 5*y**2. Determine s so that m(s) = 0.
-2, -1, 1
Solve 6/7*b**3 + 2*b - 4/7 - 16/7*b**2 = 0 for b.
2/3, 1
Let l = 3/191 - -101/5730. Let y(a) be the third derivative of 0*a + 0 + 4/3*a**3 - a**2 + l*a**5 + 1/3*a**4. Factor y(m).
2*(m + 2)**2
Let d(j) be the second derivative of -j + j**6 + j**2 + 1/6*j**7 + 5/2*j**3 + 0 + 10/3*j**4 + 5/2*j**5. Factor d(w).
(w + 1)**4*(7*w + 2)
Let v(m) be the first derivative of 20*m**3/3 - 9*m**2/2 + 11*m - 1. Let i(j) = -7*j**2 + 3*j - 4. Let c = 121 - 110. Let w(y) = c*i(y) + 4*v(y). Factor w(t).
3*t*(t - 1)
Determine i so that 5*i**4 + 52*i**2 + 8*i - 15*i**2 - 25*i**3 - 28*i + 3*i**2 = 0.
0, 1, 2
Let w(z) = -z**2 + 2. Let b(c) be the first derivative of -3*c + 4. Let t(m) = -2*b(m) - 3*w(m). Let t(n) = 0. What is n?
0
Let 1/4*l**3 + 0 + 1/2*l - 3/4*l**2 = 0. Calculate l.
0, 1, 2
Let l be 36/77 - (-2)/(-7). Solve 0*j + 0 - 2/11*j**2 + l*j**5 + 2/11*j**4 - 2/11*j**3 = 0 for j.
-1, 0, 1
Let d(s) be the third derivative of s**7/1155 - s**6/220 + s**5/110 - s**4/132 + 2*s**2. Factor d(a).
2*a*(a - 1)**3/11
Let b(v) = 3*v**2 + 3*v. Let k(c) = 39*c**2 + 39*c. Let a(m) = -27*b(m) + 2*k(m). Factor a(s).
-3*s*(s + 1)
Let a(s) = 103*s**2 + 6*s**3 - 25*s**2 + 36*s**2 + 174*s + 66. Let m(d) = d**3 + 23*d**2 + 35*d + 13. Let z(k) = -3*a(k) + 14*m(k). Factor z(n).
-4*(n + 1)*(n + 2)**2
Suppose -5*g = 20, 4*d - 5*g - 32 = -0*d. Find b such that 4*b**5 - 10*b**2 + 12*b**5 + 8*b**3 - 40*b**4 + 25*b**d + b = 0.
0, 1/4, 1
Let r = 1/59 + 54/295. Let b(o) be the first derivative of 2/3*o**3 - r*o - 2/15*o**6 - o**4 + 3/5*o**5 + 0*o**2 + 1. Factor b(j).
-(j - 1)**4*(4*j + 1)/5
Let o(f) be the first derivative of -2*f**3/5 - f**2 - 4*f/5 + 30. Determine z, given that o(z) = 0.
-1, -2/3
Let l = -1303/14382 - -1/423. Let a = 53/170 - l. Let -a*q**5 + 2/5*q + 0 - 4/5*q**2 + 0*q**3 + 4/5*q**4 = 0. What is q?
-1, 0, 1
Let l be 380/315 + 3/((-27)/(-2)). Solve 6/7*u + l*u**2 - 4/7 = 0.
-1, 2/5
Suppose -3/8*f**4 - 15/8*f**2 + 0 + 3/2*f**3 + 3/4*f = 0. Calculate f.
0, 1, 2
Let r = -70 + 49. Let q(m) = -15*m**2 - 81*m - 81. Let p(s) = 3*s**2 + 16*s + 16. Let l(x) = r*p(x) - 4*q(x). Factor l(f).
-3*(f + 2)**2