 Let f(j) be the first derivative of 1 + 0*j**2 - 2/15*j**3 + 0*j - 1/20*j**t. Determine q so that f(q) = 0.
-2, 0
Let p(m) = m**2 - 2*m - 3. Let w be p(3). Let s = 3 + w. Factor -24*d - 14*d**2 + d**s - 16 - 2*d**2 + 4*d**2 - 3*d**3.
-2*(d + 2)**3
Let q(m) be the first derivative of -2*m**3/21 + 3*m**2/7 + 12. Suppose q(p) = 0. Calculate p.
0, 3
Let p(h) = -4*h**4 - 22*h**3 + 17*h**2 - 19*h + 7. Let t(u) = -u**4 - 7*u**3 + 6*u**2 - 6*u + 2. Let b(r) = -2*p(r) + 7*t(r). Factor b(z).
z*(z - 2)**2*(z - 1)
Let p be -10 - -7 - 22/(-6). Let j be (2 - 1)*(-10)/(-2). Factor -4/3*b**4 + 0 - p*b**2 + 0*b + 5/3*b**3 + 1/3*b**j.
b**2*(b - 2)*(b - 1)**2/3
Let w(y) = -3*y**4 + 36*y**3 + 108*y**2 + 168*y + 87. Let f(l) = l**4 - l**3 - l - 1. Let c(p) = -6*f(p) - w(p). Determine z so that c(z) = 0.
-3, -1
Let w(z) = 12*z**4 - 4*z**3 - 12*z**2 + 6*z. Let x(c) = 23*c**4 - 8*c**3 - 23*c**2 + 13*c. Let b(j) = 5*w(j) - 2*x(j). Determine a so that b(a) = 0.
-1, 0, 2/7, 1
Factor 3*x**2 + 81*x - 162 - 5*x**2 - 45*x.
-2*(x - 9)**2
Let g(m) be the first derivative of 3*m + 1/12*m**3 - 1/8*m**2 - 3 - 1/48*m**4. Let q(a) be the first derivative of g(a). Factor q(j).
-(j - 1)**2/4
Suppose 2*j + 14 = 3*u, 0*j - 18 = -u + 4*j. Suppose -5*d = -u*d. Factor d*w + 2/7*w**2 + 0.
2*w**2/7
Suppose 3*y - 9 + 3 = 0. Let -4*f**2 + 6*f**4 - 10*f**4 + f + 6*f**3 - y*f**5 + 3*f**5 = 0. What is f?
0, 1
Let d(p) be the second derivative of -49*p**6/30 + 7*p**5/5 - p**4/3 + 2*p. Factor d(c).
-c**2*(7*c - 2)**2
Let b(i) be the second derivative of -i**4/30 + 6*i. Factor b(h).
-2*h**2/5
Let j(p) be the second derivative of 1/15*p**6 + 1/5*p**5 + 0*p**4 - 2/3*p**3 + 3*p - p**2 + 0. Determine t, given that j(t) = 0.
-1, 1
Suppose -6 = -3*i, -6*i = -2*w - i - 4. Factor -8/3*f - 10*f**w + 0 + 28/3*f**2 + 3*f**4.
f*(f - 2)*(3*f - 2)**2/3
Let k(r) be the first derivative of r**8/5880 - r**7/1470 - r**6/1260 + r**5/210 - 4*r**3/3 - 4. Let c(i) be the third derivative of k(i). Factor c(j).
2*j*(j - 2)*(j - 1)*(j + 1)/7
Let n(c) = -c**2 - c. Let y be n(0). Suppose -o = -m - 5, -12 = o + 5*m + 1. Find p such that -1/2*p + y - 1/2*p**o = 0.
-1, 0
Let c be (-2)/(-2) - (-5)/(-10). Let l(u) be the first derivative of 1 - u - 1/12*u**3 + c*u**2. Suppose l(o) = 0. What is o?
2
Let s(y) = -7*y + 3. Let c be s(0). Let g(j) be the second derivative of 0 + 1/50*j**6 - 1/20*j**5 - 1/5*j**2 + 4*j + 1/6*j**c - 1/60*j**4. Factor g(m).
(m - 1)**2*(m + 1)*(3*m - 2)/5
Let j = 1/9 - -7/18. Factor j*r**2 + 1/2 - r.
(r - 1)**2/2
Let r = 129/2 - 64. Factor 0 + 0*n - r*n**3 + n**2.
-n**2*(n - 2)/2
Let j(h) be the second derivative of h + 0*h**3 - 1/42*h**4 + 0 + 1/7*h**2. Solve j(n) = 0.
-1, 1
Let a(v) = -6*v**3 - 2*v**2 - 5. Let g(j) = 5*j**3 + j**2 + 4. Let x(k) = -4*a(k) - 5*g(k). Factor x(n).
-n**2*(n - 3)
Factor -5/6*h**5 - 11/3*h**3 + 1/2*h + 3*h**4 - 1/3 + 4/3*h**2.
-(h - 1)**4*(5*h + 2)/6
Let u = 1/75 + 49/75. Let f(t) be the first derivative of 1 + 0*t + 0*t**2 - 2/5*t**5 + t**4 - u*t**3. Factor f(z).
-2*z**2*(z - 1)**2
Let h(d) be the first derivative of d**8/5880 + d**7/2940 - d**6/1260 - d**5/420 - d**3 + 3. Let t(c) be the third derivative of h(c). Factor t(a).
2*a*(a - 1)*(a + 1)**2/7
Let b(f) be the second derivative of f**6/300 - f**5/75 - f**4/60 + 2*f**3/15 - 9*f**2/2 - 2*f. Let z(n) be the first derivative of b(n). Factor z(l).
2*(l - 2)*(l - 1)*(l + 1)/5
Let k(i) be the third derivative of -i**6/90 - 2*i**5/45 - 69*i**2. Factor k(p).
-4*p**2*(p + 2)/3
Let x be 4/(-35)*(-7 + -3). Let q = 2 + -10/7. Factor -10/7*r + q - 2/7*r**3 + x*r**2.
-2*(r - 2)*(r - 1)**2/7
Let d be ((-7)/(-252))/(2/10). Let q(y) be the third derivative of 0*y + d*y**4 + 0 + 3*y**2 - 1/9*y**3 - 7/90*y**5 + 1/60*y**6. Determine a so that q(a) = 0.
1/3, 1
Let g(o) = o + 3. Let d be g(-4). Let b(a) = 2*a**2 - a. Let c be b(d). Determine h, given that 2*h**c + 2*h**3 - 5*h**3 + h**4 = 0.
0, 1
Suppose 5*v - 3*x + 8 = 9*v, 2*x - 8 = -4*v. Determine l, given that -16/3*l**3 - 64/3*l + 16*l**v + 32/3 + 2/3*l**4 = 0.
2
Let j(q) be the second derivative of -q**8/2240 - q**7/420 - q**6/240 + q**4/3 + 4*q. Let w(r) be the third derivative of j(r). Factor w(c).
-3*c*(c + 1)**2
Find v such that 8/13*v**2 + 0 + 2/13*v**4 + 8/13*v**3 + 0*v = 0.
-2, 0
Let y(v) = v**4 - 4*v**3 + 6*v**2 + 16*v + 11. Let u(i) = 5*i**4 - 25*i**3 + 35*i**2 + 95*i + 65. Let g(j) = 6*u(j) - 35*y(j). Let g(t) = 0. Calculate t.
-1, 1
Let p(a) be the third derivative of -a**5/100 - a**4/10 + a**3/2 - 11*a**2. Suppose p(d) = 0. What is d?
-5, 1
Let o(m) be the second derivative of -m**5/5 - 5*m**4/3 - 4*m**3 - 24*m. Factor o(y).
-4*y*(y + 2)*(y + 3)
Let m(f) be the first derivative of f**6/720 + f**5/120 - f**3 - 1. Let l(s) be the third derivative of m(s). Let l(r) = 0. What is r?
-2, 0
Let f(s) = -s**3 - 5*s**2 - 5*s - 4. Let t be f(-4). Let w = 11 + -8. Factor t*r + 2/5*r**4 - 4/5*r**w + 0 + 2/5*r**2.
2*r**2*(r - 1)**2/5
Let q(g) be the third derivative of -g**6/40 + g**5/5 - 3*g**4/8 - 39*g**2. Suppose q(j) = 0. What is j?
0, 1, 3
Let u(b) be the first derivative of -b**5 + 5*b**4/2 - 5*b**2 + 5*b - 1. Factor u(g).
-5*(g - 1)**3*(g + 1)
Let f be 3 - (1 + -1)*(-4)/(-8). Factor -1/3*w**f + 0 + 4/3*w**2 - 4/3*w.
-w*(w - 2)**2/3
Let g be 36/8 + (-40)/(-20). Let -g*r**3 - 2*r + 0 + 6*r**2 + 3*r**4 - 1/2*r**5 = 0. Calculate r.
0, 1, 2
Let z(a) be the first derivative of -a**8/32 - a**7/21 + a**6/80 + a**5/60 + a**2/2 - 4. Let m(t) be the second derivative of z(t). Solve m(s) = 0 for s.
-1, -2/7, 0, 1/3
Suppose 2*x**2 - 1/4*x**4 + 0 - 1/2*x**3 + 0*x = 0. What is x?
-4, 0, 2
Let b(f) be the third derivative of -f**5/12 + 55*f**4/12 - 605*f**3/6 - 31*f**2. Factor b(q).
-5*(q - 11)**2
Suppose 0 = 17*c - 18*c + 4. Let u(k) be the third derivative of 0 + 1/30*k**5 + 0*k**c - 2*k**2 + 0*k**3 + 0*k. Let u(x) = 0. What is x?
0
Let q(k) be the third derivative of -k**5/150 - k**4/30 - k**2. Factor q(v).
-2*v*(v + 2)/5
Factor -4*b + 7*b - 6 + 3*b**3 + b**3 + 6*b**2 - 7*b**3.
-3*(b - 2)*(b - 1)*(b + 1)
Let s(h) = -9*h**4 - 24*h**3 - 42*h**2 - 18*h + 6. Let z(w) = -26*w**4 - 71*w**3 - 125*w**2 - 55*w + 17. Let m(i) = -17*s(i) + 6*z(i). Factor m(t).
-3*t*(t + 2)**3
Let t = -4 - -1. Let m be t - -1 - 1*-4. Suppose j**2 + 10*j**3 + 8*j**4 - 2*j**m + 3*j**2 = 0. Calculate j.
-1, -1/4, 0
Let i(y) = -7*y. Let n be i(1). Let v = n - -11. Let 0*h**2 + 4/7*h**3 - 4/7*h - 2/7 + 2/7*h**v = 0. Calculate h.
-1, 1
Let 61*z**4 + 53*z + 828*z**3 - 336*z**2 - 385*z**4 - 32 - 293*z + 104*z**2 = 0. Calculate z.
-2/9, 1, 2
Find h such that -1/4*h**3 + 0 + 3/2*h**2 - 9/4*h = 0.
0, 3
Suppose 3*c = 150 + 12. Suppose -z - z = -c. Factor -j**2 - 2*j**2 + 27*j + 6 - z*j**3 - 3*j**2.
-3*(j - 1)*(j + 1)*(9*j + 2)
Let u(w) be the first derivative of w**7/315 + w**6/225 + 9*w - 2. Let k(q) be the first derivative of u(q). Find h, given that k(h) = 0.
-1, 0
Suppose -4/9*s**3 - 4/3*s**2 + 16/9 + 0*s = 0. Calculate s.
-2, 1
Let b = -3791/24 + 158. Let w(x) be the third derivative of 2*x**2 + 0*x - 1/30*x**5 + 1/336*x**8 + b*x**4 + 0 - 1/60*x**6 + 1/210*x**7 + 1/6*x**3. Factor w(j).
(j - 1)**2*(j + 1)**3
Let l be (-2)/3*27/(-6). Suppose 1 = l*m - 8. Determine r so that 7*r - 4*r + 4 - 2 - r**m = 0.
-1, 2
Let g(t) be the first derivative of 2/15*t**3 - 2/25*t**5 + 1/5*t**2 - 2 + 0*t - 1/10*t**4. Factor g(c).
-2*c*(c - 1)*(c + 1)**2/5
Let 8/3*b + 8/3 + 2/3*b**2 = 0. What is b?
-2
Let w(j) = 6*j**3 + 5*j**2 + 23*j. Let o(q) = 2*q**3 + 2*q**2 + 8*q. Let u(g) = -17*o(g) + 6*w(g). What is x in u(x) = 0?
0, 1
Let t(u) be the first derivative of -2/5*u**5 + 14/9*u**3 - 3 - 1/6*u**4 + 0*u**2 + 1/9*u**6 - 8/3*u. Determine k so that t(k) = 0.
-1, 1, 2
Let g(s) = -2*s**3 + s**2 - 7*s + 1. Let n(v) = v**3 - v**2 + 4*v. Suppose 5*d + 0*d + 35 = 0. Let y(m) = d*n(m) - 4*g(m). Factor y(c).
(c - 1)*(c + 2)**2
Let w be 63/36 - (-2)/8. Let u be ((-8)/16)/(-3 + w). Suppose 0 + 9/4*r**2 + u*r = 0. What is r?
-2/9, 0
Let a(s) be the second derivative of -s**4/3 - 8*s**3/3 - 6*s**2 - 27*s. Factor a(z).
-4*(z + 1)*(z + 3)
Let r(s) be the second derivative of 3*s**8/224 - s**7/20 + s**6/16 - s**5/40 - 2*s**2 + 4*s. Let b(q) be the first derivative of r(q). Factor b(d).
3*d**2*(d - 1)**2*(3*d - 1)/2
Let w(b) be the first derivative of -2*b**3/21