 o/7. Let -8/7*a**3 - 8/7*a + 2/7*a**4 + 2/7 + c*a**2 = 0. What is a?
1
Let w(n) be the third derivative of 0 - 11/15*n**5 + 0*n**3 + 1/3*n**4 + 7/10*n**6 - 34/105*n**7 + 0*n + 5/84*n**8 + 3*n**2. Factor w(z).
4*z*(z - 1)**3*(5*z - 2)
Suppose 12 - 6 + 3*y**2 + 6*y - 3 = 0. Calculate y.
-1
Factor -3/2*p**2 - 5/4*p**3 - 1/4*p**4 + p + 2.
-(p - 1)*(p + 2)**3/4
Let g(q) be the first derivative of 4*q**5/5 + 2*q**4 - 4*q**3 - 16*q**2 - 16*q + 52. Factor g(i).
4*(i - 2)*(i + 1)**2*(i + 2)
Let x(r) = 54*r**3 - 29*r**2 - 336*r - 288. Let p(t) = 18*t**3 - 10*t**2 - 112*t - 96. Let l(b) = -11*p(b) + 4*x(b). Let l(k) = 0. Calculate k.
-4/3, 3
Suppose -3*s = -7*s. Let d be ((-2)/(-6))/((-7)/(-42)). Factor n**2 + 6*n**4 + 4*n**3 + s*n**4 - 4*n**4 + n**d.
2*n**2*(n + 1)**2
Let h(c) be the first derivative of -c**4/6 - 10*c**3/9 - c**2 + 6*c - 5. Suppose h(f) = 0. Calculate f.
-3, 1
Suppose -4*t + 14 = j, 0 = -6*j + 7*j - t + 1. Let u(b) be the third derivative of -b**j - 1/120*b**6 - 1/6*b**3 - 1/8*b**4 + 0 + 0*b - 1/20*b**5. Factor u(f).
-(f + 1)**3
Let c(n) be the second derivative of -n**6/900 - n**5/150 - 2*n**3/3 + 2*n. Let w(h) be the second derivative of c(h). Solve w(z) = 0 for z.
-2, 0
Suppose -47*i + 44*i = 0. Find p, given that i*p + 0*p**2 + 0 - 1/3*p**3 = 0.
0
Let k = 53249 - 8786036/165. Let v = k + 10/33. Determine h, given that -6/5*h**4 + 6/5*h**2 - v*h**5 + 0*h**3 + 3/5*h + 0 = 0.
-1, 0, 1
Let u(l) be the third derivative of -l**6/1440 - l**5/240 - l**4/96 + l**3/2 + l**2. Let q(c) be the first derivative of u(c). Factor q(i).
-(i + 1)**2/4
Let u(a) be the first derivative of -16*a**5/5 - 87*a**4 - 616*a**3 + 242*a**2 + 4. What is r in u(r) = 0?
-11, 0, 1/4
Let i be (-9)/2*(-392)/882. Factor -1/2*m + 0 - 1/2*m**i - 1/8*m**3.
-m*(m + 2)**2/8
Let a(w) be the third derivative of -w**8/210 + 2*w**7/105 - w**6/36 + w**5/60 - w**3/2 + w**2. Let i(b) be the first derivative of a(b). Factor i(y).
-2*y*(y - 1)*(2*y - 1)**2
Let a(d) = 3*d**3 + 18*d**2 + 24*d - 45. Suppose -2*v - 15 = -7*v. Let n(l) = 6*l**3 + 35*l**2 + 48*l - 89. Let x(j) = v*n(j) - 7*a(j). Factor x(h).
-3*(h - 1)*(h + 4)**2
Factor -4*s**3 + 576 - 672*s + s**3 + 73*s**2 - s**3 + 27*s**2.
-4*(s - 12)**2*(s - 1)
Let k = 130/57 - -1/19. Let 5/3*p**5 + 0 - 2/3*p - 7/3*p**4 - p**3 + k*p**2 = 0. What is p?
-1, 0, 2/5, 1
Find k, given that -2/3*k**2 - 10/3 + 4*k = 0.
1, 5
Let z be (1 - 0) + (-12 - -13). Let h(a) be the first derivative of 2/9*a**3 - 2/15*a**5 - 1/9*a**6 - 1 + 0*a**z + 1/6*a**4 + 0*a. Find n such that h(n) = 0.
-1, 0, 1
Factor 0 + 0*r + 8/7*r**3 + 0*r**2 - 4*r**4 - 36/7*r**5.
-4*r**3*(r + 1)*(9*r - 2)/7
Factor 5*o**2 + 7*o**3 + 0*o + o**4 + 2*o - 2*o**3 - o**3.
o*(o + 1)**2*(o + 2)
Suppose -3*m + 3*z + 3 = 2*z, -2*z - 6 = -m. Suppose 4*p - 7*p + 6 = m. Factor -2/7*v + 0 - 2/7*v**3 + 4/7*v**p.
-2*v*(v - 1)**2/7
Let j(m) be the first derivative of -12*m**5/25 + m**4/5 + 8*m**3/15 + 10. Factor j(n).
-4*n**2*(n - 1)*(3*n + 2)/5
Factor -w**3 - 1/2 - 1/2*w**5 + 3/2*w**4 - w**2 + 3/2*w.
-(w - 1)**4*(w + 1)/2
Let v(o) = -o**3 - 11*o**2 - 1. Let y be v(-11). Let f be y*(-4 - (-22)/6). Find j such that -f*j + 1/3*j**2 - 1/3*j**4 + j**3 + 0 - 2/3*j**5 = 0.
-1, 0, 1/2, 1
Let m(x) be the first derivative of -x**6/15 + 2*x**5/25 + x**4/10 - 2*x**3/15 + 4. Let m(y) = 0. Calculate y.
-1, 0, 1
Let a = -8555 - -42421/5. Let h = 71 + a. Let h*n + 1/5*n**2 - 2/5 = 0. What is n?
-2, 1
Let h = 31 - 31. Let c(n) be the second derivative of 0*n**3 + h - 1/48*n**4 - n + 0*n**2. Let c(p) = 0. What is p?
0
Let t(q) be the second derivative of -q**5/165 + q**4/132 - 9*q**2/2 + 7*q. Let a(o) be the first derivative of t(o). Factor a(b).
-2*b*(2*b - 1)/11
Let i be (-2)/2 - (-9)/(-21). Let f = -33/28 - i. Factor -1/4*h + 1/2*h**3 - f - 1/4*h**4 + 1/2*h**2 - 1/4*h**5.
-(h - 1)**2*(h + 1)**3/4
Let n be 0 - 12/3*-1. Let z(w) be the second derivative of 0*w**2 + 0 + 0*w**3 + 2*w + 1/60*w**n. Suppose z(g) = 0. What is g?
0
Let j(y) = y**2 + 13*y + 8. Let n be j(-12). Let h be 8/3 + n/6. Let 14/9*r - 14/9*r**3 - 4/9*r**h + 4/9 = 0. Calculate r.
-1, -2/7, 1
Factor -2/5 + 2/5*h - 2/5*h**3 + 2/5*h**2.
-2*(h - 1)**2*(h + 1)/5
Let m(p) be the third derivative of 3*p**8/1120 - p**7/105 + p**6/90 + p**4/8 - p**2. Let y(c) be the second derivative of m(c). Factor y(v).
2*v*(3*v - 2)**2
Let x(r) be the second derivative of r**7/14 + r**6/10 - 3*r**5/20 - r**4/4 - 10*r. Determine l, given that x(l) = 0.
-1, 0, 1
Let s(g) be the first derivative of 4*g**3/9 - 2*g**2 + 8*g/3 - 2. Factor s(f).
4*(f - 2)*(f - 1)/3
Factor 0 + r**4 + 0*r + 1/2*r**2 - 5/4*r**3 - 1/4*r**5.
-r**2*(r - 2)*(r - 1)**2/4
Factor -d**3 + 2*d - 36*d**2 - 3*d**3 + 30*d + 8*d.
-4*d*(d - 1)*(d + 10)
Factor 11 + 2 + 5*w**2 - 29 - 14 - 25*w.
5*(w - 6)*(w + 1)
Let 1/3 - 2/3*m + 1/3*m**2 = 0. What is m?
1
Let g = 4/3 + -2/3. Suppose -1/6 - p**2 + 2/3*p - 1/6*p**4 + g*p**3 = 0. What is p?
1
Suppose 0 = 4*r - 5*s + 42 - 19, 3*s = r + 4. Let j = -5 - r. Find d such that -2/5 - 4/5*d + 6/5*d**j = 0.
-1/3, 1
Let k(d) be the third derivative of 2*d**7/175 - 29*d**6/200 + 67*d**5/100 - 51*d**4/40 + 9*d**3/10 + 45*d**2. Find t, given that k(t) = 0.
1/4, 1, 3
Let j(x) be the second derivative of x**5/90 - x**4/36 - x**2 - 4*x. Let o(d) be the first derivative of j(d). Suppose o(h) = 0. Calculate h.
0, 1
Let z(g) be the first derivative of -g**4/4 + g**3/3 + g**2 - 6. Solve z(h) = 0 for h.
-1, 0, 2
Let b = 0 - -2. Let z = -2 + b. Factor -w**5 + w**3 + 0*w**3 + z*w**3.
-w**3*(w - 1)*(w + 1)
Let t(a) be the third derivative of a**8/21 + 2*a**7/21 - 11*a**6/30 - 23*a**5/15 - 13*a**4/6 - 4*a**3/3 - 4*a**2. Find y such that t(y) = 0.
-1, -1/4, 2
Let c(m) = -m**3 - m**2 + m + 1. Let z(a) = -a**4 + 3*a**3 + 5*a**2 - 5*a - 5. Let w(i) = -10*c(i) - 2*z(i). Factor w(n).
2*n**3*(n + 2)
Solve h**3 + 0*h - 39*h**2 + 4*h + 15*h**2 + 19*h**2 = 0.
0, 1, 4
Suppose -3*q + 9 - 126 = -3*p, -3*p = 3*q + 93. Let z = q + 141/4. Factor z*x**3 - 1/4*x - 1/4 + 1/4*x**2.
(x - 1)*(x + 1)**2/4
Let w be (-1092)/16 - (-6)/(-8). Let i be 2*w/6*-1. Factor 2*j + 34*j**4 + 7*j**3 + 14*j**2 - 8*j**4 + i*j**3 + 8*j**5.
2*j*(j + 1)**3*(4*j + 1)
Suppose -1 - 138*i**2 - 8*i + 9 + 140*i**2 = 0. What is i?
2
Solve -j**2 + 0*j + 0*j**3 + 1/2 + 1/2*j**4 = 0.
-1, 1
Let t be 2/4 - (-3)/2. Let s be (6/5)/(8/20). Factor t*b**2 - 2*b**3 + 5*b**3 - b**s.
2*b**2*(b + 1)
Let k = 8 + -6. Let a(n) be the second derivative of -4/5*n**2 + 0*n**3 + 1/50*n**5 + 0 - k*n + 1/10*n**4. Factor a(r).
2*(r - 1)*(r + 2)**2/5
Let j be -4 + 14*2/4. Let h(m) be the third derivative of 0 - 1/150*m**5 + 2*m**2 + 2/15*m**j + 1/60*m**4 + 0*m. Determine i, given that h(i) = 0.
-1, 2
Suppose 8 = 19*c - 15*c. Let b(f) be the first derivative of -1 + 2/45*f**5 - 1/18*f**4 - 2/27*f**3 + 0*f + 1/9*f**c. Factor b(l).
2*l*(l - 1)**2*(l + 1)/9
Let v(w) be the first derivative of w**7/350 - 3*w**6/200 + w**5/100 + 3*w**4/40 - w**3/5 - 2*w**2 + 3. Let p(u) be the second derivative of v(u). Factor p(h).
3*(h - 2)*(h - 1)**2*(h + 1)/5
Let t = -5 + 7. Factor t*m**3 - 5*m**3 + 11 - 4*m**2 + m**5 + m**3 + m - 9 + 2*m**4.
(m - 1)**2*(m + 1)**2*(m + 2)
Let o(h) be the second derivative of -h**6/20 - 27*h**5/40 - 29*h**4/8 - 39*h**3/4 - 27*h**2/2 + 17*h. Find x, given that o(x) = 0.
-3, -2, -1
Let o = 6 - 3. Factor -4*q**3 + 3*q**o + q + 0*q**2 - q**4 + q**2 + 0*q**3.
-q*(q - 1)*(q + 1)**2
Let f(g) be the third derivative of -1/56*g**4 + 1/21*g**3 + 4*g**2 + 0*g + 0*g**5 + 0 + 1/840*g**6. Factor f(z).
(z - 1)**2*(z + 2)/7
Let o(w) be the first derivative of 2*w**5/5 + w**4 + 2*w**3/3 + 9. Factor o(g).
2*g**2*(g + 1)**2
Suppose 1/2*q + q**2 + 0 = 0. Calculate q.
-1/2, 0
Let 285*w + 210*w**2 + 90 + 25*w**3 - 51*w**2 + w**2 = 0. What is w?
-3, -2/5
Let q(t) be the third derivative of -t**8/11760 + t**7/1260 - t**6/360 + t**5/210 - 5*t**4/24 + 5*t**2. Let p(r) be the second derivative of q(r). Factor p(j).
-2*(j - 2)*(j - 1)*(2*j - 1)/7
Let v(u) = 2*u + 6. Let r be v(-6). Let x be (-2 + 1)*r/12. What is j in -6*j - x*j**3 - 4 - 3*j**2 = 0?
-2
Let a(k) = -k**2 + 6*k + 4. Let q be a(6). Let c = 0 + q. Suppose -70*o**4 + 26*o**3 + 25*o**5 + 0*o - 28*o**2 + 43*o**3 + c*o = 0. Calculate o.
0, 2/5, 1
Let y(a) = -5*a + 20. Let d be y(4). Let q(u) be the third deriv