3*h(u) + 4*n(u). Factor r(f).
-(f - 4)**2
Let z(x) be the third derivative of x**7/1120 + x**6/480 + x**5/480 + x**4/12 + 4*x**2. Let q(i) be the second derivative of z(i). Solve q(n) = 0 for n.
-1/3
Let j(w) = w - 5. Let d be j(7). Find t such that 0*t - 3*t + 2*t**3 + d*t**5 + 2*t - 3*t**5 = 0.
-1, 0, 1
Factor 363/4*f**2 + 33*f + 3.
3*(11*f + 2)**2/4
Let h be (0 + 0/(-3))/(-1). Let s = 5 - h. What is g in -7*g**3 + 3*g**2 + s*g + 2*g**3 + 2 - 4*g**2 - g**2 = 0?
-1, -2/5, 1
Let t(u) be the second derivative of 0*u**5 + 1/2*u**4 - 1/10*u**6 - 3/2*u**2 + 0 - 2*u + 0*u**3. Factor t(c).
-3*(c - 1)**2*(c + 1)**2
Let r(s) be the third derivative of 0*s - s**2 + 0*s**6 + 0*s**5 + 0 + 0*s**4 - 1/735*s**7 - 1/1176*s**8 + 0*s**3. Factor r(g).
-2*g**4*(g + 1)/7
Factor 4/3*c**2 - 4/3 - 4/3*c + 4/3*c**3.
4*(c - 1)*(c + 1)**2/3
Let l(u) = u**2 - 27*u. Let w be l(27). Factor 0 + 3/2*x**5 + 0*x**2 + w*x + 0*x**4 - 3/2*x**3.
3*x**3*(x - 1)*(x + 1)/2
Let p(y) = -y**2 - 5*y - 4. Let c be p(-3). Suppose 5*w = -4*i + c*i, 2*w = -3*i. Determine g so that 2/7*g**4 + 0*g + 4/7*g**3 + 2/7*g**2 + i = 0.
-1, 0
Let -1/4*w**4 - 1/4 - 1/4*w + 1/2*w**3 - 1/4*w**5 + 1/2*w**2 = 0. What is w?
-1, 1
Let j(f) be the second derivative of -f**6/30 - 3*f**5/20 - f**4/12 + f**3/2 + f**2 + 9*f. Factor j(k).
-(k - 1)*(k + 1)**2*(k + 2)
Factor -2*y - 9*y**2 - 7*y**3 - 4*y + 7*y**3 + 3*y**4.
3*y*(y - 2)*(y + 1)**2
Let w(b) be the third derivative of -b**5/160 + b**4/8 - b**3 - 57*b**2. Solve w(p) = 0.
4
Suppose -19 = x - 21. Let u be 99/21 - (1 + x). Solve 4/7 + 2/7*w - u*w**2 = 0 for w.
-1/2, 2/3
Let q(j) be the second derivative of 1/25*j**5 + 0*j**2 + 1/60*j**4 + 0 - 1/50*j**6 + 4*j - 1/15*j**3. Factor q(h).
-h*(h - 1)**2*(3*h + 2)/5
Let b(a) be the first derivative of a**6/18 - a**5/15 - a**4/12 + a**3/9 - 8. Solve b(y) = 0.
-1, 0, 1
Let n = 13 - 10. Let k(l) be the third derivative of 0*l**n - 1/84*l**4 + 0*l + 2*l**2 - 1/210*l**5 + 0. Suppose k(g) = 0. Calculate g.
-1, 0
Let r be 20/(-70) + (-37)/(-7). Suppose 3*w + 2*f = 1, 3*w - 2*f = -3*f + r. Solve 1/2*m**w + 0 + 0*m**2 + 0*m + 0*m**4 - 1/2*m**5 = 0 for m.
-1, 0, 1
Factor 0*v**3 + 0*v + 0 + 2/11*v**5 + 0*v**2 + 2/11*v**4.
2*v**4*(v + 1)/11
Let t(o) be the second derivative of -o**6/60 - o**5/10 + 2*o**2 + 8*o. Let g(h) be the first derivative of t(h). Factor g(q).
-2*q**2*(q + 3)
Let s = -30 - -30. Suppose 2*i - 4 = -5*a - 20, 5*a = 2*i - 24. Factor -2/3 + s*r + 2/3*r**i.
2*(r - 1)*(r + 1)/3
Let k(j) be the third derivative of -1/24*j**6 + 0*j + 1/30*j**7 + 0 - 1/30*j**5 + 0*j**3 + j**2 + 0*j**4. Determine o, given that k(o) = 0.
-2/7, 0, 1
Suppose 3*m**3 + 0 - 3/2*m**2 + 3/2*m**4 - 3*m = 0. What is m?
-2, -1, 0, 1
Let a(b) = b**3 + b - 1. Let v(j) = -6*j**3 - 2*j**2 - 8*j + 8. Let l(h) = 8*a(h) + v(h). Factor l(q).
2*q**2*(q - 1)
Let v(k) be the third derivative of -1/12*k**4 + 0*k - k**2 + 1/60*k**6 + 1/15*k**5 - 2/3*k**3 + 0. Let v(i) = 0. Calculate i.
-2, -1, 1
Let n(g) be the second derivative of 2*g**6/15 - 3*g**5/2 + 29*g**4/6 - 7*g**3 + 5*g**2 + 12*g - 1. Factor n(o).
2*(o - 5)*(o - 1)**2*(2*o - 1)
Factor 2*m**3 - 2*m**3 + 28*m**4 + 8*m**2 - 30*m**4.
-2*m**2*(m - 2)*(m + 2)
Let d(u) be the second derivative of -2*u + 1/20*u**5 + 0*u**2 - 1/12*u**4 + 0 + 0*u**3. Factor d(q).
q**2*(q - 1)
Let f(d) = d**3 + 7*d**2 - 8*d + 5. Let a be f(-8). Suppose 15 = a*g + 5. Let -13*m**2 - 12*m**g + 12*m - 4 + 8*m = 0. What is m?
2/5
Let k(t) be the first derivative of 4 - 2/9*t**2 - 2/27*t**3 - 2/9*t. Find q such that k(q) = 0.
-1
Let x(t) be the first derivative of 0*t**2 + 0*t - 1 - 3/14*t**4 - 2/35*t**5 - 4/21*t**3. Determine s so that x(s) = 0.
-2, -1, 0
Let o be (-6)/(-2) + 10/(-15) + -2. Suppose o - u**2 - 2/3*u = 0. Calculate u.
-1, 1/3
Factor 4*x**2 - 11*x + 196 - 11*x + 8*x - 42*x.
4*(x - 7)**2
Factor 0*d**2 + 8/7*d**3 + 0*d + 0 - 8/7*d**4 + 2/7*d**5.
2*d**3*(d - 2)**2/7
Let p(x) be the second derivative of -x**6/60 + x**5/10 - x**4/6 + x**2 + 4*x. Let b(i) be the first derivative of p(i). Factor b(y).
-2*y*(y - 2)*(y - 1)
Let r(n) be the first derivative of n**9/19656 - n**8/10920 - n**7/5460 + n**6/2340 - 2*n**3 - 8. Let g(o) be the third derivative of r(o). Factor g(d).
2*d**2*(d - 1)**2*(d + 1)/13
Factor -1/4*g**3 + 0*g + 3/8*g**2 - 1/8.
-(g - 1)**2*(2*g + 1)/8
Let f be -4 + 1 - -4 - -1. Let p(d) be the third derivative of 0*d**3 - 1/30*d**5 + 1/12*d**4 + 0*d + 0 - d**f. Let p(r) = 0. What is r?
0, 1
Let c(n) = -5*n**3 + 13*n**2 - 19*n + 8. Let z(i) = 4*i**3 - 12*i**2 + 18*i - 8. Let y(q) = 2*c(q) + 3*z(q). Solve y(r) = 0.
1, 2
Suppose -3*k + 2*k = 0. Let w(i) be the third derivative of -i**2 + k*i**3 + 1/12*i**4 + 0*i - 1/60*i**6 + 0*i**5 + 0. Factor w(f).
-2*f*(f - 1)*(f + 1)
Let l = 41 - 11. Factor 2 + 1 + 56*u**3 - 3 + 4*u - l*u**2.
2*u*(4*u - 1)*(7*u - 2)
Let d(q) = -q**3 + q**2 + 1. Let o(x) = -2*x**3 - 4*x**2 + 6*x - 1. Let c(z) = -d(z) - o(z). Factor c(w).
3*w*(w - 1)*(w + 2)
Let w(o) = o**3 - 3*o**2 - 6*o + 10. Let a be w(4). Let -277 - 2*r**3 + 277 - 18*r - 12*r**a = 0. Calculate r.
-3, 0
Suppose -3*k + 0 = -6. Factor k*t - 6 + 4*t - 3*t + 3*t**2.
3*(t - 1)*(t + 2)
Let c(s) = -s**2 + 9*s - 6. Let z be c(6). Let a be 6/27*z + -2. Factor -4/3*b**2 + a*b**3 + 2*b**4 + 0 + 0*b.
2*b**2*(b + 1)*(3*b - 2)/3
Let r be (-51)/(-42) + 6/21. What is u in 1/2*u**4 - r*u**3 + 3/2*u**5 - 1/2*u**2 + 0 + 0*u = 0?
-1, -1/3, 0, 1
Suppose 0*i + 2*i + 0*i**4 - 6*i**2 + 6*i**3 - 2*i**4 = 0. What is i?
0, 1
Let w(m) be the first derivative of m**6/60 + 11*m**5/75 + 7*m**4/15 + 8*m**3/15 - 7*m**2/2 + 3. Let h(o) be the second derivative of w(o). Factor h(f).
2*(f + 2)**2*(5*f + 2)/5
Let g be (-3)/(2 - -7)*(-36)/42. Let q be -1 + 1 + 2/7. Factor 2/7 + g*m**3 - q*m**2 - 2/7*m.
2*(m - 1)**2*(m + 1)/7
Suppose 0 = -0*c + 3*c. Suppose 4*r + c = 8. Factor 1/2*w**4 - 1/2*w + 3/2*w**r - 3/2*w**3 + 0.
w*(w - 1)**3/2
Let v be 5 + (1 - (-4 + 8)). Factor -1/3*f**3 + 1/3 - f + f**v.
-(f - 1)**3/3
Let z(w) be the third derivative of w**6/120 - w**5/20 + w**4/8 - 2*w**3/3 - 4*w**2. Let a(y) be the first derivative of z(y). Let a(l) = 0. What is l?
1
Suppose -75*d = -80*d + 35. Let b(o) be the second derivative of -43/48*o**4 + 5/8*o**3 - 1/4*o**2 + 29/40*o**5 - 3/10*o**6 + 0 - 4*o + 1/21*o**d. Factor b(c).
(c - 2)*(c - 1)*(2*c - 1)**3/4
Suppose z - 5*z = 0. Suppose -3*u = -z*u - 6. Factor -7 - 12*i - 4 + 3 - 4 + 9*i**u.
3*(i - 2)*(3*i + 2)
Let x(f) = 2*f**3 - 3 - f + f**3 - 5*f**2 - 4*f - 2*f**3. Let g be x(6). Suppose -2/7*b + 2/7 + 2/7*b**g - 2/7*b**2 = 0. Calculate b.
-1, 1
Let a(j) be the first derivative of -j**6/12 + j**4/8 - 6. Determine y, given that a(y) = 0.
-1, 0, 1
Let p(o) be the first derivative of -o**4/8 + o**3/6 + o**2/2 - 24. Determine b, given that p(b) = 0.
-1, 0, 2
Factor -o**4 + 2/5*o**2 + 3/5 - 7/5*o + 1/5*o**5 + 6/5*o**3.
(o - 3)*(o - 1)**3*(o + 1)/5
Let j = -67 + 203/3. Factor -j*g + 2/3*g**3 + 2/3*g**2 + 0 - 2/3*g**4.
-2*g*(g - 1)**2*(g + 1)/3
Let h(a) be the third derivative of a**7/1155 - a**5/330 + a**2. Factor h(i).
2*i**2*(i - 1)*(i + 1)/11
What is d in -25/2 - 1/2*d**2 + 5*d = 0?
5
Let j(w) be the first derivative of w**6/120 - w**4/24 + 3*w**2/2 - 3. Let s(d) be the second derivative of j(d). Factor s(p).
p*(p - 1)*(p + 1)
Let m = -7561/15 + 505. Let a = -4/15 + m. Factor 4/9 + 2/9*r**2 - a*r.
2*(r - 2)*(r - 1)/9
Let x(y) be the second derivative of -1/6*y**4 + 0*y**2 - 2*y + 2/3*y**3 - 3/10*y**5 + 0. Factor x(v).
-2*v*(v + 1)*(3*v - 2)
Let o(f) be the second derivative of f - 1/4*f**2 + 1/8*f**3 + 0 - 1/48*f**4. Factor o(y).
-(y - 2)*(y - 1)/4
Let w = -453239/40 - -11332. Let m = w - 5/8. Factor 14/5*k**3 - m*k + 0 - 4/5*k**2 - 8/5*k**4.
-2*k*(k - 1)**2*(4*k + 1)/5
Let h(d) be the first derivative of -2*d**3/27 + d**2/6 - d/9 - 24. Determine t, given that h(t) = 0.
1/2, 1
Let g(c) be the third derivative of -c**7/126 + 7*c**6/360 + c**5/60 - 7*c**4/72 + c**3/9 - 7*c**2. Find u, given that g(u) = 0.
-1, 2/5, 1
Suppose 51 = -3*b + 66. Let y(d) be the first derivative of -b*d**2 + 3/2*d**4 + 2 + 8/3*d**3 - 4*d. Factor y(q).
2*(q - 1)*(q + 2)*(3*q + 1)
Let o(h) be the first derivative of 2*h**5/15 + h**4/3 - 2. Factor o(s).
2*s**3*(s + 2)/3
Suppose 4*a - 101 = 5*b + 280, 2*b - 6 = 0. Find x, given that -1089/2*x**2 