 m(v).
-v**2*(4*v + 1)**3
Factor 66*g**2 + 2*g**4 + 33 + 19 - 20*g**3 + 52 - 80*g - 72.
2*(g - 4)**2*(g - 1)**2
Let j(i) be the second derivative of -81*i**5/10 - 6*i**4 - 4*i**3/3 - 49*i. Determine d so that j(d) = 0.
-2/9, 0
Suppose -g = 4*h - 18, -g + 0*h - 3*h = -14. Find x such that -2*x + 10*x + 2*x**2 + g*x**2 = 0.
-2, 0
Let j(f) be the third derivative of -f**8/168 + f**7/35 + f**6/60 - f**5/10 - 535*f**2. Solve j(p) = 0 for p.
-1, 0, 1, 3
Let o(h) be the second derivative of -h**5/180 - h**4/72 + h**3/9 + 17*h**2/2 + 19*h. Let n(v) be the first derivative of o(v). Factor n(p).
-(p - 1)*(p + 2)/3
Let v(x) = x**3 - 7*x**2 + 2*x + 3. Let u be v(7). Let h = u - 15. Factor -3*s**4 + s**2 + 3*s**h + 0*s**2 + s**4 - 2.
-2*(s - 1)**2*(s + 1)**2
Let p(w) be the first derivative of 1/24*w**4 - 1/60*w**5 - 11 - 5/2*w**2 + 0*w**3 + 0*w. Let m(i) be the second derivative of p(i). Factor m(b).
-b*(b - 1)
Let h = 142 - 91. Suppose h + 9 = 5*f - 5*o, -2*f + 15 = o. Solve -27*x**3 - f - 6 - 63*x**2 - 48*x + 3 = 0 for x.
-1, -2/3
Let q = 381 + 748. Let c = q - 23699/21. Factor -c*t**2 + 2/7 - 4/21*t.
-2*(t + 1)*(5*t - 3)/21
Factor 12*i - 176*i**3 - 174*i**3 + 530*i**3 - 183*i**3.
-3*i*(i - 2)*(i + 2)
Let m(f) = -f**2 + 13*f + 29. Let b be m(13). Suppose -21 = 4*h - b. Let 2/9*u + 2/3*u**3 - 8/9*u**h + 0 = 0. What is u?
0, 1/3, 1
Let i(u) = -u**2 - 33*u - 76. Let j(v) = 16*v + 40. Let p(n) = -4*i(n) - 7*j(n). Factor p(g).
4*(g + 2)*(g + 3)
What is h in -12/5 + 2/5*h**2 - 2/5*h = 0?
-2, 3
Suppose 0 = 4*r, -3*r = -7*g + 3*g + 40. Let u = g + -8. Factor 2/13*j**u - 12/13*j + 18/13.
2*(j - 3)**2/13
Let h(i) be the second derivative of -3*i**5/20 + 29*i**4/4 + 15*i**3 - 79*i. Solve h(u) = 0.
-1, 0, 30
Let m(c) = -c**2 - 9*c + 2. Let f be m(-9). Suppose f*g = 2*y - g - 16, 4*g = -3*y - 10. Factor -4*n**y - 2*n - 12*n**3 + 21*n**3 - 11*n**3.
-2*n*(n + 1)**2
Suppose 49/4 + 1/4*g**2 + 7/2*g = 0. Calculate g.
-7
Factor -12/13*y + 18/13 + 2/13*y**2.
2*(y - 3)**2/13
Let g(v) be the second derivative of 2/105*v**7 + 42*v + 8/75*v**6 - 4/5*v**2 - 2/15*v**4 + 0 - 2/3*v**3 + 4/25*v**5. Factor g(p).
4*(p - 1)*(p + 1)**3*(p + 2)/5
Let z(r) be the first derivative of -r**6/210 - 3*r**5/35 - 11*r**4/42 + 2*r**3 - 7*r**2/2 - 34*r - 39. Let y(i) be the first derivative of z(i). Factor y(s).
-(s - 1)**2*(s + 7)**2/7
Let y(d) be the first derivative of 1/9*d**3 + 0*d + 1/6*d**4 - 1/3*d**2 - 10 - 1/15*d**5. Factor y(k).
-k*(k - 2)*(k - 1)*(k + 1)/3
Let k be 24/20*5*-1. Let n be (k - -8) + (2 - 4)/(-6). Factor -n*m**2 + 0 - 2/3*m.
-m*(7*m + 2)/3
Suppose 5*j - 2 - 13 = 0. Factor -3*a**2 - 12*a**3 - 19*a**j + 4*a**4 + 42*a**3.
a**2*(a + 3)*(4*a - 1)
Let x = -587 + 587. Let k(c) be the third derivative of -4/15*c**5 + 0*c**4 + 0*c + 6*c**2 - 1/70*c**7 + 1/10*c**6 + x + 1/1344*c**8 + 0*c**3. Factor k(n).
n**2*(n - 4)**3/4
Let t(q) be the second derivative of q**4/18 - 5*q**3 + 86*q**2/3 + 2*q - 22. Solve t(o) = 0.
2, 43
Let j(i) be the first derivative of 1/10*i**4 - 12 - 2/5*i**3 + 4/5*i + 2/25*i**5 - 1/5*i**2. Factor j(d).
2*(d - 1)**2*(d + 1)*(d + 2)/5
Let n(c) be the third derivative of 2*c**2 + 0 + 0*c**3 - 1/560*c**7 - 3/160*c**5 + 3/320*c**6 + 1/64*c**4 + 0*c. Find l, given that n(l) = 0.
0, 1
Let 7/4*a**2 + 3/4 - 19/8*a - 1/4*a**4 + 1/8*a**3 = 0. What is a?
-3, 1/2, 1, 2
Let c(w) = 2*w**4 + 14*w**3 - 17*w**2 - 5*w + 3. Let i(p) = p**5 - 7*p**4 - 42*p**3 + 52*p**2 + 16*p - 8. Let o(y) = -8*c(y) - 3*i(y). Solve o(r) = 0.
-2, -1/3, 0, 2
Factor -6*h**3 + 36/7*h**2 + 2/7*h**4 + 0 + 80/7*h.
2*h*(h - 20)*(h - 2)*(h + 1)/7
Solve 1/7*v**2 + 1/7*v - 12/7 = 0 for v.
-4, 3
Let w(u) be the first derivative of -2/15*u**3 - 1/20*u**4 + 0*u + 9 + 0*u**2. Determine m so that w(m) = 0.
-2, 0
Let f(v) = v**3 - 2*v. Let a(u) = 2*u**4 + 21*u**3 + 16*u**2 - 46*u. Let d(t) = 2*a(t) - 14*f(t). Factor d(i).
4*i*(i - 1)*(i + 4)**2
Let j(d) be the second derivative of 0*d**2 - 5/6*d**3 + 9*d + 0 + 5/4*d**4. Determine c, given that j(c) = 0.
0, 1/3
Let v(x) be the second derivative of x**7/63 + 4*x**6/45 + x**5/5 + 2*x**4/9 + x**3/9 + 138*x - 1. Suppose v(g) = 0. What is g?
-1, 0
Let v(z) be the second derivative of -2/25*z**5 + 1/5*z**2 + 2/15*z**3 - 1/15*z**4 + 1/75*z**6 + 2/105*z**7 + 0 + 5*z. Let v(p) = 0. What is p?
-1, -1/2, 1
Let r(l) be the third derivative of 2/35*l**7 + 0*l**3 - 2/3*l**4 + 0*l - 1/5*l**5 + 2/15*l**6 + 29*l**2 + 0. Factor r(p).
4*p*(p - 1)*(p + 1)*(3*p + 4)
Let r be 84/8*(-2)/(-3). Let k be (-2760)/(-84) + 1/r. Factor k*p**2 - 17*p**2 - 19*p**2 + 3*p.
-3*p*(p - 1)
Let -390*h**3 + 784*h**3 - 210 + 210*h**2 - 389*h**3 - 5*h = 0. What is h?
-42, -1, 1
Let m = 752 + -11276/15. Let p(z) be the first derivative of 1/5*z**4 + 0*z**2 - m*z**3 + 0*z + 5. Find r, given that p(r) = 0.
0, 1
Suppose 5*u + 2*l = 10, 0 = 4*u - 6*l + 2*l - 8. Factor 61*q**5 - 86*q**2 - 65*q**5 - 10*q**u - 36*q - 88*q**3 - 32*q**4.
-4*q*(q + 1)**2*(q + 3)**2
Let p = -10 + 16. Find j such that -6*j**2 - p*j**5 + 10*j**3 + 4*j**5 - 8 - 2*j**4 + 8 = 0.
-3, 0, 1
Let l = 257 - 324. Let b = l - -269/4. Determine q, given that b*q**2 - 3/4 - 1/2*q = 0.
-1, 3
Let s = 4252/5 - 850. Factor -s + 1/5*o + 3/5*o**2.
(o + 1)*(3*o - 2)/5
Suppose 10 = -s - 3*l, 0*s - l = -4*s - 40. Let n be (-45)/27*12/s. Factor 0*g - 1/2*g**n + 0.
-g**2/2
Let i(c) be the second derivative of c**4/30 - 64*c**3/15 + 1024*c**2/5 - 28*c. Determine s, given that i(s) = 0.
32
Let m = 27 + -59. Let h be m/(-63) + 2*1/(-7). Factor 4/9*i**2 + h*i**3 - 4/9 - 2/9*i.
2*(i - 1)*(i + 1)*(i + 2)/9
Factor -3 + 17*q**2 + 52*q + 51 - 13*q**2.
4*(q + 1)*(q + 12)
Let d(g) be the third derivative of 2*g**7/105 - 3*g**6/10 + 9*g**5/5 - 31*g**4/6 + 8*g**3 + 429*g**2. Factor d(f).
4*(f - 4)*(f - 3)*(f - 1)**2
Let i be 3 + 1 + 2 + -1. Factor -6*y**2 + 3*y**4 + 3 + i - y**4 + 8*y - 4*y**3.
2*(y - 2)**2*(y + 1)**2
Let k be (-90)/(-135)*1*4. Factor k*z**2 + 4/3*z**3 + 0 + 0*z.
4*z**2*(z + 2)/3
Suppose g - 2 = 4. Let a be 2 + 3/g - (-1 + 0). Factor -7/2*c + a*c**3 - 1 + c**2.
(c - 1)*(c + 1)*(7*c + 2)/2
Let j(o) = 10*o - 135. Let w be j(14). Let b(g) be the second derivative of 0*g**2 + 1/48*g**4 + 0 + 8*g + 1/160*g**w + 1/48*g**3. Factor b(n).
n*(n + 1)**2/8
Let y be 1530/150 + 54/(-6). Factor -3/5 - 8/5*w + 1/5*w**4 + 0*w**3 - y*w**2.
(w - 3)*(w + 1)**3/5
Suppose 0 = 16*s - 14*s + 194. Let w = -93 - s. Factor 2/7*f**w - 2/7*f**5 + 2/7*f**3 - 2/7*f**2 + 0*f + 0.
-2*f**2*(f - 1)**2*(f + 1)/7
Suppose -5*k - 3*v = -8, -k = -6*k - v + 6. Let i be 110/88 - (k - 14/8). Factor 0 - 2/9*x**i - 4/9*x.
-2*x*(x + 2)/9
Let d(j) = -216*j - 648. Let g be d(-3). Find s such that g - 8/7*s**3 - 2/7*s + 8/7*s**2 = 0.
0, 1/2
Let s(c) = -17*c + 40. Let f be s(2). Let m(n) be the second derivative of -2/3*n**3 + f*n - 1/2*n**4 - 1/10*n**5 + 0 + 0*n**2. Find p such that m(p) = 0.
-2, -1, 0
Let s(l) be the second derivative of -l**4/60 + 28*l**3/15 - 11*l**2/2 + 199*l. Factor s(f).
-(f - 55)*(f - 1)/5
Let q be (-204)/(-15) - 430/43. Factor 0 + 2/5*l**3 + q*l - 12/5*l**2.
2*l*(l - 3)**2/5
Factor -2342*j + 264*j**2 + 4*j**3 + 3098*j + 5052*j + 42592.
4*(j + 22)**3
Let i(r) be the second derivative of r**10/105840 + r**4 - 13*r. Let a(s) be the third derivative of i(s). Solve a(f) = 0 for f.
0
Let 4/3 + 4/3*s**3 - s**2 - 1/3*s**4 - 4/3*s = 0. What is s?
-1, 1, 2
Let x(i) be the second derivative of 18*i + 0 + 7/12*i**5 - 20/3*i**2 - 70/9*i**3 + 5/18*i**4. Factor x(g).
5*(g - 2)*(g + 2)*(7*g + 2)/3
Suppose -17*b + 873 - 839 = 0. Let y(h) be the second derivative of 9*h + 0 - 1/3*h**3 - 1/3*h**4 + 0*h**b. Factor y(d).
-2*d*(2*d + 1)
Suppose -15*p - 693 + 2493 = 0. Let w be 5/((-250)/8)*p/(-16). Factor -4/5*n + 2/5*n**2 - w.
2*(n - 3)*(n + 1)/5
Let q(c) be the first derivative of c**6/540 + c**5/20 + 2*c**4/9 - 15*c**3 + 32. Let d(i) be the third derivative of q(i). Factor d(v).
2*(v + 1)*(v + 8)/3
Let r = -649 + 652. Let h(v) be the first derivative of 0*v**2 - 12 - 1/15*v**r + 1/20*v**4 + 0*v. Suppose h(w) = 0. Calculate w.
0, 1
Suppose -6*k + 5*k = 2*p - 13, -p + 2 = -k. Let m(l) = 3*l - 6. Let s be m(k). Factor -2/9*y + 0*y**2 + 2/9*y**s + 0.
2*y*(y - 1)*(y + 1)/9
Let h(r) be the first derivative of r**6/300 - r**4/60 + 15*r**2 - 1. Let c(i) be the second derivative of h(i). Determine m, g