(d - 1)**3*(d + 1)
Let v = 298/21 - 97/7. Let c(r) be the second derivative of -r**3 + 0 - 2*r**2 + 6*r - 2/5*r**5 - 4/5*r**6 + v*r**7 + 7/3*r**4. Let c(s) = 0. Calculate s.
-1, -2/7, 1
Let n = -30848 - -925577/30. Let s = n + -25/6. Solve -2/5 - 4/5*w - s*w**2 = 0 for w.
-1
Let j(y) = 24*y**3 - 42*y**2 - 183*y - 45. Let f(w) = w**3 - 2*w**2 - w + 1. Let p(u) = -3*f(u) + j(u). Factor p(x).
3*(x - 4)*(x + 2)*(7*x + 2)
Let s(l) be the second derivative of -l**7/14 - 3*l**6/10 - 3*l**5/10 + l**4/2 + 3*l**3/2 + 3*l**2/2 - 93*l. Let s(g) = 0. What is g?
-1, 1
Let g(m) be the first derivative of 2*m**3/33 - 86*m**2/11 + 170*m/11 - 339. Let g(a) = 0. What is a?
1, 85
Let y(b) = -6*b**5 - 3*b**4 + 6*b**3 + 3*b**2 - 4*b. Let j(s) = 13*s**5 + 7*s**4 - 13*s**3 - 7*s**2 + 9*s. Let c(f) = 4*j(f) + 9*y(f). Solve c(d) = 0.
-1, 0, 1/2, 1
Let 10*t**3 - 18*t**4 + 13*t**3 + 296*t**2 + 2*t**5 - 28*t + 3*t**3 - 278*t**2 = 0. What is t?
-1, 0, 1, 2, 7
Let w = 43 - 40. Factor -4*y - y**2 - 2*y**w + 11*y**2 - y**2 - 3*y**2.
-2*y*(y - 2)*(y - 1)
Let d(h) = 242*h**2 + 93*h + 8. Let o(v) = 121*v**2 + 46*v + 4. Suppose -5*i = -4*i - 2. Let a(y) = i*d(y) - 5*o(y). Factor a(x).
-(11*x + 2)**2
Determine t, given that -24/7 + 40/7*t + 2/7*t**3 - 18/7*t**2 = 0.
1, 2, 6
Let h = -65 - -70. Factor -1145*v**4 + 10*v**3 + 1160*v**4 + 6*v**5 - v**h.
5*v**3*(v + 1)*(v + 2)
Factor -2/5*q**2 + 3/5*q + 0 - 1/5*q**3.
-q*(q - 1)*(q + 3)/5
Let b = -95 + 97. Factor 6*f + 24*f**2 - 42*f**b + 39*f**2.
3*f*(7*f + 2)
Let g be (2/(-4))/((-2)/80). Let y be 7*(g/(-14) - -2). Factor -4*r**5 + 3*r**3 + 2*r**4 + y*r**5 - 3*r**2 + r**4 - 3*r**5.
-3*r**2*(r - 1)**2*(r + 1)
Let z(p) = p**3 + 5*p**2 - 4*p - 5. Let s be z(-4). Suppose -s = l - 2*l. Factor 0*x**2 - x**2 - l + 25 + 0*x**2 + 3*x.
-(x - 2)*(x - 1)
Let n(r) = 12*r - 5*r**3 - r**3 + 6*r**2 + r**2 - 7 + 6*r**2. Let f(v) = -3*v**3 + 6*v**2 + 6*v - 3. Let b(d) = 7*f(d) - 3*n(d). Factor b(q).
-3*q*(q - 2)*(q + 1)
Let x(s) be the first derivative of -1/6*s**6 - 4*s**2 + 0*s - 13 - 9/2*s**4 + 20/3*s**3 + 7/5*s**5. Let x(b) = 0. Calculate b.
0, 1, 2
Let g(r) be the second derivative of r**7/3360 - r**6/320 + r**5/80 - 11*r**4/12 + 20*r. Let m(s) be the third derivative of g(s). Factor m(i).
3*(i - 2)*(i - 1)/4
Suppose 27*c - 30*c = -9. Let u(w) be the first derivative of -4/7*w**c - 8/21*w**6 - 16/7*w**4 + 0*w**2 + 2 + 0*w - 68/35*w**5. Suppose u(b) = 0. What is b?
-3, -1, -1/4, 0
Let o = -239543180194/5495 - -43592936. Let k = o - -2/785. Suppose -5/7 + k*l + 1/7*l**2 = 0. Calculate l.
-5, 1
Let i be (30/(-18))/(1/45). Let a be (i/30)/((-2)/4). Factor 4*r**3 + r**3 + 45*r**5 - 50*r**a.
-5*r**3*(r - 1)*(r + 1)
Let f(x) = -x - 1. Let g be f(-7). Suppose -5*k = -2*k - g. Factor -w**k - 21*w + 12*w + 8*w.
-w*(w + 1)
Let p be 2*(-15)/10 - 721/(-240). Let h(m) be the third derivative of 0 + 1/24*m**3 - p*m**5 + 0*m**4 + 0*m - 4*m**2. What is r in h(r) = 0?
-1, 1
Let m(s) be the first derivative of -9/5*s**3 - 4/5*s + 9/25*s**5 - 12/5*s**2 + 1/10*s**4 + 8. What is d in m(d) = 0?
-1, -2/9, 2
Suppose 0 = 5*s + 9 + 71. Let i be (-28)/s*1*(3 - 2). Suppose -i*a - 1/2 - 5/4*a**2 = 0. Calculate a.
-1, -2/5
Let s be (-25)/20*(-4)/1. Suppose s*k - 5*m = 20, 2*k - 4*m - 12 + 4 = 0. Factor -2*c**k + 6 + 3*c**3 + 0*c**4 - 6 - c.
-c*(c - 1)**2*(2*c + 1)
Let t(p) be the first derivative of 3*p**4/16 - 5*p**3/4 + 3*p**2 - 3*p - 59. Determine w, given that t(w) = 0.
1, 2
Let v(y) = -y**3 - 6*y**2 + 2*y + 7. Let q be v(-6). Let h be (4/q)/((-2)/20). Factor 10*a + 2*a**5 - 3*a**2 - a**2 + h - 2*a**4 + 6*a**2 - 10*a**3 + 6*a.
2*(a - 2)**2*(a + 1)**3
Let i = -37 - -37. Let c(x) = x**3 + x**2 - 2*x + 3. Let y be c(i). Factor 12*g**4 + 80*g**5 - 77*g**5 + 11*g**y + 7*g**3 + 12*g**2 + 3*g.
3*g*(g + 1)**4
Let j be ((-18)/24 - (-7)/(-28)) + 3. Let g(o) be the first derivative of 0*o - 1/6*o**3 - 7 + 0*o**4 + 0*o**j + 1/10*o**5. Factor g(h).
h**2*(h - 1)*(h + 1)/2
Find u, given that 76/13*u**4 + 2/13*u**5 + 2656/13*u**2 + 1156/13 + 860/13*u**3 + 3026/13*u = 0.
-17, -2, -1
Suppose 4*l = -l - 435. Let r = -32 - l. Let s(v) = -11*v**2 + 21*v - 10. Let n(i) = 100*i**2 - 190*i + 90. Let o(t) = r*s(t) + 6*n(t). Factor o(w).
-5*(w - 2)*(w - 1)
Suppose -25*i = -26*i + 36. Determine b, given that 142*b**2 + 119*b**2 - 243*b**2 + 3*b - i*b**4 + 15*b**3 = 0.
-1/3, -1/4, 0, 1
Suppose 3*x = 3*l - 24, 0 = -4*l + 5*l - 5*x. Let i be -3 + 0 + 45/l. Factor -i*s + 3/4*s**2 + 3/4.
3*(s - 1)**2/4
Let k(v) be the third derivative of 1/20*v**5 - 1/40*v**6 + 1/4*v**4 + 0*v + 0 - 17*v**2 + 0*v**3. Factor k(j).
-3*j*(j - 2)*(j + 1)
Let h(x) be the first derivative of -x**5/130 - x**4/78 + 5*x + 11. Let v(m) be the first derivative of h(m). Suppose v(f) = 0. What is f?
-1, 0
Find p, given that -2/23*p**5 - 8186/23*p**3 - 256/23*p**4 + 772/23*p**2 + 16384/23 + 25088/23*p = 0.
-64, -1, 2
Let q be 54/8*(-27)/81*20/(-7). Solve 0 + 9/7*k**5 + 33/7*k**4 + 27/7*k**2 + 6/7*k + q*k**3 = 0.
-1, -2/3, 0
Let i(n) be the first derivative of n**5 + 1865*n**4/4 + 77500*n**3 + 4881880*n**2 + 9533120*n + 384. Factor i(g).
5*(g + 1)*(g + 124)**3
Suppose 15*i**2 + 36*i + 3/2*i**4 - 39/2*i**3 + 0 = 0. Calculate i.
-1, 0, 2, 12
Let j = 311/192 + 3/64. Let w(d) be the second derivative of 0 + 8/3*d**6 + j*d**4 + 3*d - 33/10*d**5 - 16/21*d**7 - 1/3*d**3 + 0*d**2. Factor w(x).
-2*x*(x - 1)**2*(4*x - 1)**2
Let v be (-2)/2*15/(-100). Let d(r) be the first derivative of 3/8*r**2 - 3/16*r**4 + v*r**5 + 5 - 1/4*r**3 + 0*r. Factor d(s).
3*s*(s - 1)**2*(s + 1)/4
Let v(w) be the first derivative of w**6/18 + w**5/15 - w**4/6 - 32. Determine m so that v(m) = 0.
-2, 0, 1
Let j(k) = -2*k**3 + 4*k**2 - 5*k - 3. Let p = -47 - -45. Let b(t) = -t**3 + 3*t**2 - 4*t - 2. Let n(o) = p*j(o) + 3*b(o). Solve n(d) = 0.
-2, 0, 1
Let h(v) be the third derivative of 0 - 1/2*v**3 + 1/40*v**5 + 0*v - 1/16*v**4 + 12*v**2. Solve h(t) = 0.
-1, 2
Let y(j) = j**2 + 66. Let f be y(0). Determine w, given that 5324 + 1452*w + 56*w**2 + 142*w**2 + 4*w**3 - f*w**2 = 0.
-11
Let m(u) be the third derivative of -25*u**2 + 0*u + 1/12*u**6 + 5/6*u**3 + 1/7*u**7 - 5/96*u**8 + 5/16*u**4 - 7/12*u**5 + 0. Determine q so that m(q) = 0.
-1, -2/7, 1
Suppose -2*d = 3*z + 70, -2*d + 3*z - 26 - 32 = 0. Let v be ((-5)/(-3))/((-80)/d). Suppose 0 - v*j**3 - 2/3*j - 4/3*j**2 = 0. Calculate j.
-1, 0
Let i(f) be the second derivative of -f**6/15 + f**5/10 + 5*f**4/6 + f**3 + 17*f. Determine q so that i(q) = 0.
-1, 0, 3
Let c = 1990/99 + -176/9. Let u = c - 20/77. Factor 2/7 + 4/7*x + u*x**2.
2*(x + 1)**2/7
Let o(w) = 4*w**5 - 7*w**4 + 17*w**3 - 4*w**2 - 5. Let k(s) = -6*s**5 + 10*s**4 - 26*s**3 + 6*s**2 + 8. Let y(a) = -5*k(a) - 8*o(a). Factor y(t).
-2*t**2*(t - 1)**3
Factor -887*r**2 + r**3 + 0*r**3 + 882*r**2 - 4*r + 20.
(r - 5)*(r - 2)*(r + 2)
Let -10/9*x**2 + 0 + 2/9*x - 4/3*x**3 = 0. Calculate x.
-1, 0, 1/6
Let h(i) be the second derivative of 0*i**2 + 2/75*i**6 + 0*i**5 + 8*i - 4/15*i**3 - 1/5*i**4 + 0. Factor h(d).
4*d*(d - 2)*(d + 1)**2/5
Suppose 3*x - 5*i - 138 = 0, -5*x + 0*i - 4*i = -267. Factor -x*j**2 + 17*j**2 - 6*j - 5 + 23 - 2*j**3 + 24*j**2.
-2*(j - 1)*(j + 3)**2
Let u = 40 + -38. Let x be ((-2)/3)/(6 + (-406)/63). Factor 0*m - x*m**4 + 0*m**u + 0 - m**3 - 1/2*m**5.
-m**3*(m + 1)*(m + 2)/2
Let u(j) = -6*j**5 + j**4 + 3*j**3 - j**2 + 3*j - 5. Let y(i) = 7*i**5 - 2*i**4 - 4*i**3 + 2*i**2 - 3*i + 6. Let z(a) = 6*u(a) + 5*y(a). Factor z(o).
-o*(o - 1)*(o + 1)**2*(o + 3)
Factor 2/3*u**3 - 8/3*u**2 - 2/3*u + 8/3.
2*(u - 4)*(u - 1)*(u + 1)/3
Let u = -21886/15 - -4382/3. Factor u*d + 2/5*d**3 + 8/5*d**2 + 0.
2*d*(d + 2)**2/5
Let y(o) be the first derivative of 5*o**4/16 + 2*o**3 + 9*o**2/2 + 4*o + 93. What is q in y(q) = 0?
-2, -4/5
Suppose 4*g = -0*g + 20. Factor -5*o**2 - 8*o**3 + g*o**3 + 5 + 8*o**3 - 5*o.
5*(o - 1)**2*(o + 1)
Let g be -3*(-1)/(-1) + 5. Suppose 2*f = -i - 2*f - 17, 3*f + 27 = 4*i. Factor i + 2*w + 6*w**2 - 3*w**g + 4*w.
3*(w + 1)**2
Let w be 67 + -49 + (-1690)/100. Solve 1/10*c**5 + 1/5*c**2 + c**3 - w*c + 1/2 - 7/10*c**4 = 0 for c.
-1, 1, 5
Let b(q) be the second derivative of 3*q + 0*q**3 - 1/10*q**6 - 1/10*q**5 + 0*q**4 + 0 + 0*q**2 - 1/42*q**7. Factor b(c).
-c**3*(c + 1)*(c + 2)
Let o = 5/189 - -323/2079. Suppose 0*n + 2 = 2*s - 2*n, 0 = s + 2*n - 4.