st derivative of -s**6/21 + 2*s**5/7 - 9*s**4/14 + 2*s**3/3 - 2*s**2/7 + 2. Suppose b(x) = 0. Calculate x.
0, 1, 2
Let x(f) be the first derivative of -2*f**3 + 2*f**2 + 2*f + 1. What is j in x(j) = 0?
-1/3, 1
Let x(u) = u**2 - u - 13. Let i be x(5). Suppose -6*s = -i*s. Factor 1/4*b**5 + 1/2*b**4 + s*b**2 + 0 + 0*b**3 + 0*b.
b**4*(b + 2)/4
Let z be 2/(-3 + (-16)/(-5)). Factor 3 - 6*h**2 - 14*h**3 - 3 + z*h**4 - 4 + 11*h + 3*h.
2*(h - 1)**2*(h + 1)*(5*h - 2)
Let d(u) be the third derivative of u**7/2520 - u**6/720 - u**4/8 - 3*u**2. Let s(x) be the second derivative of d(x). Solve s(z) = 0 for z.
0, 1
Solve 29*z**3 + 4 + 0 - 25*z**3 - 4*z**2 - 4*z = 0.
-1, 1
Factor -2/3 - 1/3*t**2 - t.
-(t + 1)*(t + 2)/3
Suppose -9 = -w - 7. Let b(f) be the first derivative of -1 + 2*f**3 - 49/20*f**5 - 1/2*f**w - 21/16*f**4 + 0*f. Suppose b(u) = 0. Calculate u.
-1, 0, 2/7
Let q = 14 + -9. Factor -3 - 2*w**2 - 2*w + 3*w**3 - w + q*w**2.
3*(w - 1)*(w + 1)**2
Suppose -36 = -2*v + h, 3*v - 24 = v + 4*h. Factor -2 + 25*o**2 - 4*o**2 + 69*o + v.
3*(o + 3)*(7*o + 2)
Let z be (-1 + 5)*(10 - 1020/105). Find l such that 8/7*l + z*l**3 + 12/7*l**2 + 2/7*l**4 + 2/7 = 0.
-1
Let b(g) be the second derivative of 1/5*g**5 + 1/21*g**7 - 1/5*g**6 + 1/3*g**4 + 0 + 2*g - g**3 + g**2. Factor b(i).
2*(i - 1)**4*(i + 1)
Let w(n) be the third derivative of 5*n**5/12 - 65*n**4/24 + 5*n**3 + 18*n**2. Factor w(u).
5*(u - 2)*(5*u - 3)
Let m(y) be the third derivative of -y**8/280 + 16*y**7/525 - 29*y**6/300 + 2*y**5/15 - y**4/15 + 14*y**2. Determine d, given that m(d) = 0.
0, 1/3, 1, 2
Let a(b) be the second derivative of -3*b**5/10 - 5*b**4/8 - b**3/2 - b**2 + 4*b. Let t(i) be the first derivative of a(i). Let t(u) = 0. What is u?
-1/2, -1/3
Let z(v) be the third derivative of v**7/630 + v**6/360 - 7*v**2. Determine a so that z(a) = 0.
-1, 0
Let a(n) be the third derivative of n**6/40 - n**5/10 + n**4/8 + 2*n**2. Factor a(z).
3*z*(z - 1)**2
Let g be (-2)/(-1 + 1/2). Let z be ((-4)/6)/(g/(-18)). Factor -z*d + 6*d - 4*d - 3*d + 2*d**2 + 2.
2*(d - 1)**2
Let g(k) be the third derivative of -k**11/166320 + k**9/30240 + k**5/60 + 5*k**2. Let u(j) be the third derivative of g(j). Factor u(w).
-2*w**3*(w - 1)*(w + 1)
Let x(t) be the first derivative of 5*t**6/24 - t**5/4 - 15*t**4/16 + 25*t**3/12 - 5*t**2/4 + 3. Factor x(u).
5*u*(u - 1)**3*(u + 2)/4
Let d(z) be the first derivative of z**2 + 2/9*z**3 + 4 + 4/3*z. Find y, given that d(y) = 0.
-2, -1
Let h(l) be the second derivative of -l**6/10 + 3*l**4/4 - l**3 - 9*l. Solve h(r) = 0 for r.
-2, 0, 1
Let c be 4/(-22) + 24/(-154)*-3. Determine p so that 0*p**2 - 2/7*p - c*p**5 + 4/7*p**3 + 0*p**4 + 0 = 0.
-1, 0, 1
Let g(k) be the second derivative of -2*k**7/63 + 2*k**6/15 + 4*k**5/15 - 12*k. Find h, given that g(h) = 0.
-1, 0, 4
Let c(o) be the second derivative of -o**7/2100 + o**6/450 - o**5/300 - o**4/6 - 3*o. Let f(y) be the third derivative of c(y). What is b in f(b) = 0?
1/3, 1
Let j(d) be the second derivative of -d**5/140 - 10*d. What is w in j(w) = 0?
0
Let c(b) be the third derivative of -b**5/36 + 25*b**4/72 + 27*b**2. Factor c(p).
-5*p*(p - 5)/3
Let 0*l - 1/2*l**3 - 3/2*l**2 + 2 = 0. What is l?
-2, 1
Suppose -5*h = 2*h - 3*h. Let r(o) be the first derivative of -2/21*o**3 - 2 + 2/7*o**2 + h*o. Factor r(a).
-2*a*(a - 2)/7
Suppose -3 - 7 = 2*s. Let i(c) = -182*c**4 + 72*c**3 + 36*c**2 - 7*c. Let b(d) = 121*d**4 - 48*d**3 - 24*d**2 + 5*d. Let l(q) = s*i(q) - 7*b(q). Factor l(w).
3*w**2*(3*w - 2)*(7*w + 2)
Let c(u) be the second derivative of -u**4/36 + 2*u**3/9 + 9*u. Factor c(o).
-o*(o - 4)/3
Let n = 50 + -30. Let h = n + -18. Factor 1/4*j**h + 0 - 1/4*j**3 + 0*j.
-j**2*(j - 1)/4
Let z = -1603/15 + 107. Let p(f) be the second derivative of f + 0*f**2 + z*f**3 - 1/30*f**4 + 0. Factor p(c).
-2*c*(c - 2)/5
Let z = -2 - -2. Factor z + 4/5*w + 2/5*w**2.
2*w*(w + 2)/5
Let q(m) be the third derivative of -m**5/240 - m**4/32 - 4*m**2. Find x, given that q(x) = 0.
-3, 0
Let f be ((-1)/2)/((-75)/(-40) + -2). Suppose -6*s**3 + 0*s - 4*s**2 - 1/2*s**5 + 0 - 3*s**f = 0. What is s?
-2, 0
Let m = 16/15 - 21/20. Let v(d) be the third derivative of -m*d**5 - 1/12*d**4 + 0*d + 1/120*d**6 + 0 - 2*d**2 + 0*d**3. Factor v(c).
c*(c - 2)*(c + 1)
What is u in -25*u**5 + 82*u**3 - 5*u - 25*u**5 + 2*u**2 - 27*u - 3*u**4 + 8 - 7*u**4 = 0?
-1, 2/5, 1
Let w be (-30)/(-8) - 1/(-4). Let 3*r**2 - 2 - r**2 + 4*r - w*r = 0. What is r?
-1, 1
Solve -2/3*n - 2/3*n**2 + 2/3*n**3 + 2/3 = 0 for n.
-1, 1
Let y(u) = -u + 7. Let w be y(7). Let r(h) be the third derivative of h**2 + 1/180*h**5 + 0*h + w + 1/36*h**4 + 0*h**3. Let r(x) = 0. What is x?
-2, 0
Let x(i) be the first derivative of -i**5/20 - i**4/4 - i**3/3 + i - 3. Let w(v) be the first derivative of x(v). Factor w(k).
-k*(k + 1)*(k + 2)
Let f(j) = j + 14. Suppose 9 = 2*z - 3*z - x, 2*z + 24 = x. Let s be f(z). Find b, given that b**2 + 0*b**2 + s*b - 4*b**2 = 0.
0, 1
Let p(v) be the first derivative of -2/3*v**3 - 1/180*v**5 + 0*v**2 + 3 + 1/1080*v**6 + 0*v + 0*v**4. Let r(g) be the third derivative of p(g). Factor r(u).
u*(u - 2)/3
Let o(d) be the third derivative of -d**6/40 + 13*d**5/60 - 13*d**4/24 + d**3/2 + 3*d**2. Find a, given that o(a) = 0.
1/3, 1, 3
Let f be 558/14 + 12/84. Factor 36 - 64 + f + 5*j**2 + 34*j + 5*j**2.
2*(j + 3)*(5*j + 2)
Let k be ((-2)/(-4)*0)/1. Let z(h) be the first derivative of 2/9*h**3 + 2 + 0*h**2 + k*h. Factor z(t).
2*t**2/3
Let x(n) = n**4 - n**2 + n + 1. Let o(l) = -7*l**4 - 9*l**3 + 7*l**2 + 5*l - 4. Let s(y) = -o(y) - 4*x(y). Determine z, given that s(z) = 0.
-3, -1, 0, 1
Let p(i) = i - 7. Let k be p(9). Let f(l) be the third derivative of 0 + 0*l**6 + 0*l**4 - l**k + 0*l**3 + 0*l + 1/105*l**7 + 0*l**5. Let f(r) = 0. What is r?
0
Let o = 8/31 - -6/217. Let b(v) = v**3 + 2*v**2 - v - 2. Let f be b(-2). Factor -o*l**3 + 2/7*l**2 + 0*l + f.
-2*l**2*(l - 1)/7
Let z = -12 + 18. Factor -2 - 2*q + 10*q**2 + 0*q**3 - z*q**3 + 0*q**3.
-2*(q - 1)**2*(3*q + 1)
Let a(u) be the second derivative of u**6/15 - u**5/10 - u**4/6 + u**3/3 - 2*u. Factor a(p).
2*p*(p - 1)**2*(p + 1)
Factor 0 - 4/9*q - 2/9*q**3 - 2/3*q**2.
-2*q*(q + 1)*(q + 2)/9
Let h(m) be the first derivative of 1/42*m**4 + 1/105*m**6 - 2*m + 0*m**2 + 2 + 0*m**3 - 1/35*m**5. Let r(v) be the first derivative of h(v). Factor r(t).
2*t**2*(t - 1)**2/7
Solve 76/3*d**3 - 8/3*d**2 + 0*d + 0 = 0 for d.
0, 2/19
Determine u so that 2/15*u**2 - 14/15 + 4/5*u = 0.
-7, 1
Let x(v) be the second derivative of v**4/30 + v**3/5 + 2*v**2/5 - 19*v. Factor x(g).
2*(g + 1)*(g + 2)/5
Factor -11*a - 5 - 3*a**2 + 1 - 2.
-(a + 3)*(3*a + 2)
Determine m so that 0*m + 1/8 - 1/8*m**2 = 0.
-1, 1
Let d(s) = -5*s**2 - 3*s + 32. Let f(k) = -85*k**2 - 50*k + 545. Let r(l) = 35*d(l) - 2*f(l). Factor r(j).
-5*(j - 2)*(j + 3)
Let w be (8/(-10))/(12/(-90)). Suppose -2*g = -w*g. Factor 4 - 5 + 2 - k**2 + g.
-(k - 1)*(k + 1)
Let u(v) be the first derivative of 3*v**4/16 - v**3/4 - 15*v**2/8 - 9*v/4 - 61. What is i in u(i) = 0?
-1, 3
Let m(g) be the first derivative of 2*g**3/3 - 4*g**2 + 8*g - 8. Factor m(v).
2*(v - 2)**2
Let u be (-1)/(-1) - 12/(-12). Suppose 1/3*t**u + 4/3 + 4/3*t = 0. Calculate t.
-2
Let h(m) be the first derivative of -7 - 2/3*m**3 - 1/6*m**4 - m**2 - 2/3*m. Factor h(t).
-2*(t + 1)**3/3
Let x(n) = -n**2 + 9*n - 9. Let z be x(7). Factor -109*l**4 + 117*l**4 - 2*l - 2*l**z + 9*l**2 - 12*l**3 - l**2.
-2*l*(l - 1)**4
Factor 133*f**3 - 32 + 67*f**3 + 99*f**4 + 151*f**4 + 224*f - 480*f**2.
2*(f + 2)*(5*f - 2)**3
Let f(g) = 6*g**5 - 9*g**4 + 6*g**3 - 4*g**2 - 4*g - 5. Let d = -13 + 8. Let i(j) = -j**5 + j**4 + j + 1. Let z(m) = d*i(m) - f(m). Suppose z(p) = 0. What is p?
0, 1
Suppose -2*o - 3*x = -9, 0 = 3*o - 0*x - x + 3. Suppose -w + o + 3 = 0. Factor 10 + 81*g**2 - 3 - w + 0 - 36*g.
(9*g - 2)**2
Let u(k) = k**3 - k + 1. Let z(v) = -2*v**2 - 2*v + 1. Let x(p) = 2*u(p) - 2*z(p). Solve x(h) = 0 for h.
-1, 0
Suppose 3*i + 24 = 6. Let b(c) = -c**4 - c**3 + c**2 - 5*c - 6. Let f(h) = h + 1. Let z(r) = i*f(r) - b(r). Factor z(p).
p*(p - 1)*(p + 1)**2
Let d(o) = -o**3 - 15*o**2 + 2. Let c be d(-15). Let w(r) be the second derivative of 1/4*r**4 - 3/2*r**3 + 3*r**c - r + 0. Factor w(t).
3*(t - 2)*(t - 1)
Let o(t) be the second derivative of 5*t**4/3 - 115*t