g = 54/29 - -260/203. Suppose -b*r**3 + g*r**2 + 2*r**4 - 4/7*r + 0 = 0. Calculate r.
0, 2/7, 1
Factor -6*i + 15 - 3/4*i**2.
-3*(i - 2)*(i + 10)/4
Let d be 172/32 + (-3)/8. Factor -d*y**2 - 2*y**4 - 5*y + y**3 + 4*y**3 + 7*y**4.
5*y*(y - 1)*(y + 1)**2
Find x such that -3/7*x**2 + 24/7 - 6/7*x = 0.
-4, 2
Let d(y) be the first derivative of 1/21*y**3 - 6/7*y - 5/14*y**2 + 25. Determine x, given that d(x) = 0.
-1, 6
Suppose -l - 8/3*l**2 + 0*l**4 + 1/3*l**5 - 2*l**3 + 0 = 0. Calculate l.
-1, 0, 3
Let c be (-89)/324 - 0 - 3/(-12). Let l = 214/81 - c. Factor -2/3*r**2 - l*r - 2.
-2*(r + 1)*(r + 3)/3
Let l(s) be the third derivative of -s**6/150 - s**5/15 + 6*s**4/5 + 16*s**2 - 3. Factor l(q).
-4*q*(q - 4)*(q + 9)/5
Let o(z) be the first derivative of z**6/2 - 3*z**5/5 - 3*z**4/2 + 2*z**3 + 3*z**2/2 - 3*z - 76. Factor o(k).
3*(k - 1)**3*(k + 1)**2
Let g be (20/25)/((-2)/(-15)). Suppose 7*q - g*q = 4*q. Let 9/4*p**2 + q - 9/4*p**3 - 3/4*p + 3/4*p**4 = 0. Calculate p.
0, 1
Let q(r) be the third derivative of -1/35*r**7 - 1/60*r**6 - 1/4*r**4 - 2/3*r**3 + 3/10*r**5 + 11*r**2 + 0*r + 0. Determine v, given that q(v) = 0.
-2, -1/3, 1
Let c(x) be the first derivative of -1/4*x**4 + 7 - 11/2*x**2 - 3*x - 19/9*x**3. Let c(w) = 0. Calculate w.
-3, -1/3
Factor 174*s**2 - 84*s**2 - 5*s**3 + 5*s - 25 - 65*s**2.
-5*(s - 5)*(s - 1)*(s + 1)
Let s(m) be the third derivative of -m**8/3360 + m**7/1512 - m**6/2160 - 5*m**4/8 - 5*m**2. Let k(z) be the second derivative of s(z). Factor k(h).
-h*(2*h - 1)*(3*h - 1)/3
Let u = -23373/26 - -899. Let m(r) be the first derivative of -9 - 2/13*r - u*r**4 + 2/39*r**3 + 1/13*r**2. Factor m(z).
-2*(z - 1)**2*(z + 1)/13
Solve -3/2*q + 1/2 + 3/2*q**2 - 1/2*q**3 = 0 for q.
1
Let v be 0 - 1 - 143/(-121). Let q be ((-81)/(-198))/(-2 + (-11)/(-4)). Solve q*b + v*b**2 + 0 = 0.
-3, 0
Suppose 10 - 10*n + 5/2*n**2 = 0. Calculate n.
2
Let j be ((-4)/(-2))/((-10)/(-15)). Let y be (-1 + -1)/((-62)/186). Let 8/3*i**j + 4/3*i + y*i**2 + 0 = 0. Calculate i.
-2, -1/4, 0
Let 69/5*g**4 + 1/5*g**5 - 38016/5*g + 1514/5*g**3 + 27648/5 + 8784/5*g**2 = 0. Calculate g.
-24, 1, 2
Let f(c) = 3*c**2 - 32*c. Let a(r) = 3*r**2 - 33*r. Let i(p) = -5*a(p) + 6*f(p). Solve i(y) = 0 for y.
0, 9
Let u(m) be the second derivative of -m**6/105 - 11*m**5/70 - 23*m**4/42 + 11*m**3/21 + 24*m**2/7 - 85*m. Solve u(j) = 0 for j.
-8, -3, -1, 1
Factor 3/7*g**5 + 2448/7*g - 1728/7 + 387/7*g**3 - 54/7*g**4 - 1380/7*g**2.
3*(g - 4)**3*(g - 3)**2/7
Let x be ((-1)/((-21)/(-18)))/((-2)/(-4)). Let k = x + 2. Factor 1/7*j**3 + 0 + 1/7*j**2 - k*j.
j*(j - 1)*(j + 2)/7
Let s(o) be the first derivative of o**5/25 + o**4/5 - o**3/5 - o**2 + 8*o/5 - 495. Factor s(n).
(n - 1)**2*(n + 2)*(n + 4)/5
Let f(m) be the third derivative of 6*m**2 - 3/4*m**4 + 8/35*m**7 + 3/5*m**6 + 1/20*m**5 + 0 + 1/2*m**3 + 0*m. Factor f(u).
3*(u + 1)**2*(4*u - 1)**2
Solve 21 + 11*g**2 - 96*g + 15 + 15*g**3 - 2*g**2 = 0.
-3, 2/5, 2
Let l = 29 - 21. Suppose -k = -0*k - l. Suppose k - 20*g - 9*g**4 - 3*g**4 + 5*g**3 + 4*g**2 + 15*g**3 = 0. What is g?
-1, 2/3, 1
Let q(p) = 70*p**2 - 123*p + 11. Let v(k) = 206*k**2 - 368*k + 32. Let f(r) = -8*q(r) + 3*v(r). Factor f(s).
2*(s - 2)*(29*s - 2)
Let -3*s - 45/2 + 3/2*s**2 = 0. What is s?
-3, 5
Let b be (-6)/16 - ((-7007)/(-56) - -6). Let z = 132 + b. Suppose r + 0 + z*r**2 = 0. Calculate r.
-2, 0
Let p be 2/(-22) - (-136)/1496. Solve p + 3/7*b**3 - 3/7*b**2 + 0*b = 0.
0, 1
Let w(t) be the first derivative of 1/2*t**4 + 32*t - 19 + 8*t**3 - 2/5*t**5 - 28*t**2. Factor w(i).
-2*(i - 2)**2*(i - 1)*(i + 4)
Factor 25338 - 22*q**2 + 25224 + 24*q**2 + 636*q.
2*(q + 159)**2
Let k(v) = 639*v + v**2 - 639*v. Let b(u) = u**3 + 2*u**2 - 3*u - 2. Let s(m) = b(m) - 2*k(m). Determine h so that s(h) = 0.
-1, 2
Let t(z) be the third derivative of z**6/240 - z**5/12 + 3*z**4/16 - 4*z**2 - 19*z. Factor t(f).
f*(f - 9)*(f - 1)/2
Suppose 0 = 4*o - 275 + 2779. Let l = 4392/7 + o. Determine h so that 24/7*h**2 + l*h**3 + 0 + 8/7*h = 0.
-2, -2/5, 0
Let 72/7 - 2/7*i**2 - 32/7*i = 0. What is i?
-18, 2
Let k be (60/(-21))/((-6)/21). Let m be k/4*3/(-18)*-3. Let 1/2*p**5 - p**2 - p - 1/4 + m*p**4 + 1/2*p**3 = 0. What is p?
-1, -1/2, 1
Let g(o) be the second derivative of o**5/60 - 7*o**4/36 + 5*o**3/6 - 3*o**2/2 + 42*o. Factor g(j).
(j - 3)**2*(j - 1)/3
Suppose -6*z = -39 - 105. Factor 2 - l**4 + 6 - 3*l**4 - z*l + 26*l**2 + 6*l**4 - 12*l**3.
2*(l - 2)**2*(l - 1)**2
Let p(w) be the first derivative of 7/30*w**4 - 8/75*w**5 + 0*w + 4/45*w**3 + 0*w**2 - 8. What is r in p(r) = 0?
-1/4, 0, 2
Let s(f) be the third derivative of -f**5/240 - 35*f**4/96 - 11*f**3/4 + 361*f**2. Let s(r) = 0. Calculate r.
-33, -2
Let y(b) = -2*b**2 - 4*b - b**2 - 3 + 2*b**3 + b**2 - 3. Let z(h) = 4*h**2 - h + 1 - 3*h**2 + 0*h**2. Let u(m) = -y(m) - 2*z(m). Determine i so that u(i) = 0.
-1, 2
Let o(c) = -2*c**3 + 255*c**2 - 4338*c + 24562. Let m(q) = 5*q**3 - 510*q**2 + 8675*q - 49125. Let v(l) = 3*m(l) + 5*o(l). Factor v(h).
5*(h - 17)**3
Determine w, given that -232*w - 21*w - 11*w**2 + 15*w**2 - 3*w**2 + 42849 - 161*w = 0.
207
Let f(k) be the third derivative of 1/1260*k**7 - 1/720*k**6 + 0*k**3 + 0*k - 1/360*k**5 + 0 + 1/144*k**4 + 10*k**2. Factor f(a).
a*(a - 1)**2*(a + 1)/6
Let j(w) = w**3 + 4*w**2 - 20*w + 2. Let i be j(0). Find p, given that -3/5*p**i - 12/5*p - 12/5 = 0.
-2
Let f be (-102)/(-24) - 3/12. Let n be 2 + (-8 - -4) + f. Factor t**2 - 2*t**2 - 32*t + 3*t**n + 64 + 2*t**2.
4*(t - 4)**2
Let f(m) be the second derivative of m**8/1680 - m**7/315 + m**6/180 - 29*m**4/6 + 27*m - 2. Let l(i) be the third derivative of f(i). Factor l(w).
4*w*(w - 1)**2
Let c(f) be the second derivative of -f**6/3 + 33*f**5/4 - 275*f**4/4 + 1015*f**3/6 + 735*f**2/2 - 99*f. Find j, given that c(j) = 0.
-1/2, 3, 7
Let b = 229 + -2281/10. Let x(p) be the second derivative of 2/5*p**3 + 10*p + b*p**2 + 1/20*p**4 + 0. Factor x(k).
3*(k + 1)*(k + 3)/5
Let h(l) be the third derivative of l**6/90 + 4*l**5/9 + 32*l**4/9 + 14*l**2 + 12*l. Factor h(o).
4*o*(o + 4)*(o + 16)/3
Let g(b) = b + 2. Let s(t) = -2*t**2 - 41*t + 22. Let m(h) = -14*g(h) - 2*s(h). What is u in m(u) = 0?
-18, 1
Let p be (-4)/((-108)/123)*42/245. Let l = 2/105 + p. Determine a, given that -l*a**2 - 32/5*a - 64/5 = 0.
-4
Let h(f) be the third derivative of -1/40*f**6 + 1/168*f**8 + 5*f**2 + 1/210*f**7 - 1/60*f**5 + 0*f**3 + 0 + 0*f + 1/24*f**4. Find v such that h(v) = 0.
-1, 0, 1/2, 1
Let t(u) be the third derivative of -13/120*u**6 - 15*u + 1/35*u**7 - 1/6*u**3 + 0 - 2*u**2 + 7/60*u**5 + 1/24*u**4. Suppose t(f) = 0. What is f?
-1/3, 1/2, 1
Let j(x) be the second derivative of 9*x - 5*x**2 - 5/6*x**3 + 5/12*x**4 + 0. Factor j(o).
5*(o - 2)*(o + 1)
Let s = -1341 - -1346. Let c(z) be the second derivative of 1/10*z**s + 2*z + 1/2*z**4 + z**2 + 0 + z**3. Factor c(u).
2*(u + 1)**3
Let r(t) = 3*t**3 - 7*t**2 + 9*t - 5. Let p(w) = 19*w**3 - 43*w**2 + 55*w - 31. Let l(k) = 6*p(k) - 39*r(k). What is n in l(n) = 0?
1, 3
Factor -3*q**4 + 40*q**3 - 10 + 18*q**2 - 37*q**3 + 10.
-3*q**2*(q - 3)*(q + 2)
Suppose -m + 2*m - 2 = 0. Factor m - 2 - 2*l + 2*l**2 + 0*l - 4.
2*(l - 2)*(l + 1)
Let x = 24 + -10. Factor -12*o - x + 5 + 5*o**2 - 8*o**2.
-3*(o + 1)*(o + 3)
Factor 4*o - 566*o**3 + 0*o + 4*o**4 + 8 - 12*o**2 + 562*o**3.
4*(o - 2)*(o - 1)*(o + 1)**2
Let s(h) be the third derivative of h**9/151200 + h**8/25200 + 11*h**5/60 + 17*h**2. Let z(u) be the third derivative of s(u). Factor z(p).
2*p**2*(p + 2)/5
Let h(o) be the third derivative of o**7/630 - 19*o**6/360 + 28*o**5/45 - 8*o**4/3 - 90*o**2 - 2. Suppose h(z) = 0. Calculate z.
0, 3, 8
Determine d so that 6/7*d**2 - 10/7*d - 24/7 = 0.
-4/3, 3
Let l be -2 + 4/3 + 10/1440*132. Let a = 1 - 1. Solve a - l*v**2 - 1/4*v = 0 for v.
-1, 0
Suppose 2*t = -5*d - 6, 0 = -2*t - 0*t - 3*d - 2. Let i(b) be the first derivative of -7/16*b**4 - b - 23/12*b**3 - 5/2*b**t - 1. Factor i(j).
-(j + 1)*(j + 2)*(7*j + 2)/4
Let r(u) = -3*u**3 + 5*u**2 - 8*u + 2. Let m(q) = 7*q**3 - 9*q**2 + 15*q - 5. Let i(a) = 4*m(a) + 10*r(a). What is p in i(p) = 0?
0, 2, 5
Find i, given that 3*i**2 + 4*i**5 - 36*i**4 - 33552*i + 84*i**3 + i**2 + 33432*i = 0.
-1, 0, 2, 3, 5
Suppose 431*r + 33 = 442*r. Let y(a) be the first derivative of -2/21*a**r + 2/7*a + 0*a**2 + 13. F