t derivative of k(q). Factor r(g).
2*g*(g - 7)/7
Suppose 1072 = -2*z + w - 96, -4*z + 4*w = 2332. Let j = -276 - z. Let -5*x**2 + 314 - j + 3*x**3 - 4*x**3 + 5*x - 4*x**3 = 0. Calculate x.
-1, 1
Factor -240*k**3 - 164*k**2 - 3120*k - 944 - 5*k**4 - 901 - 1494*k**2 + 148*k**2.
-5*(k + 1)*(k + 3)**2*(k + 41)
Suppose 144 = -26*u + 29*u. Determine o so that 4 + 356*o - u*o**2 - 4 - 340*o + 20*o**3 = 0.
0, 2/5, 2
Let -6/5*p**4 - 46/5*p**3 - 16 - 8/5*p + 28*p**2 = 0. What is p?
-10, -2/3, 1, 2
Let f(h) be the second derivative of -h**4/4 + 361*h**3/2 + 543*h**2 + 4623*h. Suppose f(v) = 0. Calculate v.
-1, 362
Let t(h) be the first derivative of 5*h**3 + 11/4*h**4 + 9/2*h**2 + 3/5*h**5 + 2*h - 45. Factor t(z).
(z + 1)**3*(3*z + 2)
Let 998*j**4 + 2640*j - 1752*j**3 + 288 + 7325*j**2 + 21*j**2 + 32*j**5 - 182*j**4 + 7530*j**3 = 0. Calculate j.
-12, -1, -1/4
Let o be 23/((-24)/(-16) - (-2)/(-4)). Solve -88*m**4 + 74*m**3 - 92*m + 20*m**5 + o + 55*m**3 + 64*m**2 - 57*m**3 + 1 = 0 for m.
-1, 2/5, 1, 3
Let c(r) be the third derivative of r**5/45 - 4*r**4/3 + 238*r**3/9 + 5425*r**2. Factor c(t).
4*(t - 17)*(t - 7)/3
Let h(d) be the first derivative of -1/2*d**3 - 70 - 216*d - 18*d**2. Determine f, given that h(f) = 0.
-12
Let c(p) be the second derivative of -1 - 25/2*p**3 - 5/8*p**4 - 3*p - 1/80*p**5 - 125*p**2. Find f, given that c(f) = 0.
-10
Let b(g) be the second derivative of g**7/504 + g**6/24 - 9*g**5/8 + g**4/6 + 8*g**2 + 58*g. Let t(c) be the third derivative of b(c). Factor t(a).
5*(a - 3)*(a + 9)
Find v such that -224/3*v**3 - 16/3*v + 130/3*v**2 + 122/3*v**4 - 4*v**5 + 0 = 0.
0, 1/6, 1, 8
Let w(i) = -i**3 + 5*i**2 - i + 14. Let g be w(5). Let f be ((-134)/4)/((45/(-10))/g). Factor -27*b**4 - 49*b**3 - 225*b**2 - 19*b**3 - 135*b - f*b**3 + 10*b.
-b*(3*b + 5)**3
Let f(o) be the first derivative of -7/15*o**3 + 62 - 1/10*o**2 + 7/5*o + 1/20*o**4. Find r such that f(r) = 0.
-1, 1, 7
Let n(m) be the third derivative of -m**7/840 + 17*m**6/120 - 289*m**5/40 + m**4 + 85*m**2. Let q(c) be the second derivative of n(c). Factor q(f).
-3*(f - 17)**2
Suppose -94*p + 5936 = 128*p + 109*p + 40*p. Factor -v**2 + p + 70/3*v.
-(v - 24)*(3*v + 2)/3
Suppose 0*h - 5*w + 610 = 5*h, -5*w = 3*h - 358. Let s = -123 + h. Factor -1/7*a**s + 4/7*a + 2/7*a**2 - 8/7.
-(a - 2)**2*(a + 2)/7
Let v(w) be the first derivative of -20/3*w**3 + 0*w + 100*w**2 + 1/8*w**4 - 14. Factor v(k).
k*(k - 20)**2/2
Let b(u) = -u**3 + 5*u**2 + 2*u - 4. Let o be b(5). Let m be 11 - o*(-2)/4. What is q in -4 + 2*q**3 + 2*q - 4*q**4 + m*q**2 - 15*q**2 + 13*q**2 = 0?
-1, 1/2, 2
Let t(o) be the first derivative of 5*o**7/42 - o**6/6 - 9*o**5/4 - 55*o**4/12 - 10*o**3/3 - 122*o + 35. Let d(h) be the first derivative of t(h). Factor d(y).
5*y*(y - 4)*(y + 1)**3
Let m(s) be the third derivative of s**5/15 + 13*s**4/2 - 80*s**3/3 + s**2 + 133*s. Solve m(t) = 0 for t.
-40, 1
Let j be -1*5/(-75) + -33*(-23)/1265. Factor -4 + 8*o**3 + j*o**2 - 23/3*o + 10/3*o**4 - 1/3*o**5.
-(o - 12)*(o - 1)*(o + 1)**3/3
Let h(g) be the third derivative of 2*g**7/105 - 21*g**6/10 + 12*g**5 + 2*g**4/3 - 160*g**3 + 10*g**2 - 40*g. Let h(a) = 0. Calculate a.
-1, 2, 60
Let r be 22/6 + 2/6. Determine s, given that 6*s**4 - 11*s**2 + 5*s**2 - r*s**3 - s**5 + 5*s - 12*s**2 - 3 + 15 = 0.
-1, 1, 3, 4
Let x = -1848 + 1873. Suppose 27*g - x*g = 4. Suppose 2/3*c**g + 8/3*c - 8 = 0. What is c?
-6, 2
Let h be 316958/74100 + 20/(-650) - 12/150. Factor 49/12 + 1/12*c**2 - h*c.
(c - 49)*(c - 1)/12
Suppose 157 = 36*c - 59. Let b(o) = -33*o + 201. Let a be b(c). Factor -9/5*y - 9/5*y**2 - 3/5 - 3/5*y**a.
-3*(y + 1)**3/5
Let k(w) be the second derivative of w**4/30 + 37*w**3/15 + 32*w**2 - 300*w - 5. Factor k(l).
2*(l + 5)*(l + 32)/5
Let u(f) be the first derivative of -f**4/18 - 248*f**3/27 + 1315*f**2/9 - 6700*f/9 + 2387. Factor u(a).
-2*(a - 5)**2*(a + 134)/9
Let v = -112772 - -112776. Suppose -2/3*y**3 + 0*y**2 + 0 + 2/9*y**v + 8/9*y = 0. What is y?
-1, 0, 2
Let c(i) be the first derivative of -720*i - 5/3*i**3 + 60*i**2 - 26. Factor c(f).
-5*(f - 12)**2
Let h(r) be the second derivative of 3/28*r**7 - 7/4*r**3 + 2/5*r**6 - 3/4*r**4 - 1 - 3/2*r**2 + 3/10*r**5 + 4*r. Solve h(a) = 0 for a.
-1, -2/3, 1
Let m(s) be the third derivative of -s**5/135 - 4*s**4/9 + 224*s**3/27 + 1236*s**2. Factor m(i).
-4*(i - 4)*(i + 28)/9
Let l be (-6)/(-88) + 7642/42031. Suppose 5 - 1/4*v**2 - l*v = 0. Calculate v.
-5, 4
Let n(p) be the first derivative of p**5/10 + p**4 - 43*p**3/6 + 29*p**2/2 - 12*p + 789. Suppose n(r) = 0. What is r?
-12, 1, 2
Let a(t) be the third derivative of t**6/840 - 617*t**5/210 + 2465*t**4/168 - 88*t**3/3 - 3611*t**2. Let a(w) = 0. Calculate w.
1, 1232
Let c(s) be the first derivative of -125*s + 15*s**4 - s**5 + 2 + 150*s**2 - 230/3*s**3. Determine t so that c(t) = 0.
1, 5
Let p(s) be the third derivative of 1/35*s**5 + 0*s - 2 + 6*s**2 + 8/21*s**3 - 5/28*s**4 + 1/420*s**6. Factor p(i).
2*(i - 1)**2*(i + 8)/7
Find r, given that 367/2*r**3 - 333*r + 69/2*r**4 - 1/2*r**5 + 231/2*r**2 + 0 = 0.
-3, 0, 1, 74
Let v(n) be the second derivative of 0*n**2 + 5/14*n**7 + 0 + 5/6*n**3 - 318*n - 1/3*n**6 - n**5 + 5/6*n**4. Determine i so that v(i) = 0.
-1, -1/3, 0, 1
Factor 19*x**2 + 35/2*x - 37 + 1/2*x**3.
(x - 1)*(x + 2)*(x + 37)/2
Let y(g) = 47*g + 426. Suppose -b + 4*j = 17, -28*j - 15 = b - 31*j. Let x be y(b). Factor p**x - 7/4*p - 5/4*p**2 + 1/2.
(p - 2)*(p + 1)*(4*p - 1)/4
Suppose -42*s + 71670 = 71670. Factor -98/9*j**5 + 28/9*j**4 + 0 + 0*j + s*j**2 - 2/9*j**3.
-2*j**3*(7*j - 1)**2/9
Suppose -18445 = -94*n - 18445. What is w in 4/3*w - 4/3*w**2 + 2/3*w**4 + 1/3*w**5 + n - w**3 = 0?
-2, 0, 1
Let c(l) = 12*l - 84. Let h be c(17). Suppose a + 35*a**2 + 125*a**4 - 7*a - h*a**4 - 9*a - 25*a**3 = 0. What is a?
0, 1, 3
Let z(m) be the third derivative of m**10/30240 + m**9/4032 - m**7/252 + m**5/30 + m**3 + 18*m**2. Let f(n) be the third derivative of z(n). Factor f(v).
5*v*(v - 1)*(v + 2)**2
Let n be -6 + (-30)/(-6) - 4 - 782. Let w = n - -3936/5. Suppose -w + 14/5*j**2 + 26/5*j**3 + 19/5*j**4 + 1/5*j + j**5 = 0. What is j?
-1, 1/5
Let f(g) = -100*g**2 - 235*g + 3565. Let l(i) = -11*i**2 - 25*i + 396. Let t(m) = 6*f(m) - 55*l(m). Determine z, given that t(z) = 0.
-6, 13
Let v be (-64)/(-24) + 2/(-3). Find a, given that -16*a**v - 3*a**4 - 8*a**2 - 100 + 180 + 68*a - 104 + 23*a**3 - 38*a**2 = 0.
2/3, 2, 3
Let i = -10 + 8. Let a be (i/(-3))/(60/36). Suppose -a*u - 8/5 + 8/5*u**2 + 2/5*u**3 = 0. What is u?
-4, -1, 1
Determine a so that 2/9*a**3 - 2194/9 - 2198/9*a**2 + 4390/9*a = 0.
1, 1097
Let u(z) = -6*z**2 + 99*z - 397. Let o be u(7). Determine j, given that -35/4*j**o + 7/4*j**5 + 59/4*j**3 + 3/2*j + 0 - 37/4*j**4 = 0.
0, 2/7, 1, 3
Let c(k) = -147*k + 3969. Let m be c(27). Let y(j) be the second derivative of -1/120*j**6 - 1/20*j**5 - 14*j - 1/12*j**4 + m*j**3 + 0*j**2 + 0. Factor y(a).
-a**2*(a + 2)**2/4
Suppose 28*o = 214 + 178. Let s(r) be the first derivative of -1/3*r + o + 1/2*r**2 - 2/9*r**3. Solve s(n) = 0 for n.
1/2, 1
Let i(h) be the second derivative of h**6/135 - 13*h**5/90 + 20*h**4/27 - 4*h**3/3 - 37*h + 75. Let i(u) = 0. Calculate u.
0, 2, 9
Let u = 16451/4458 + -35/1486. Factor 0 - 2*x**4 - 1/6*x**5 + 14*x**2 - u*x**3 - 49/6*x.
-x*(x - 1)**2*(x + 7)**2/6
Factor 1936 + 1928 - 3864 + 4*u**2 - 3100*u.
4*u*(u - 775)
Let o(a) be the first derivative of 15/4*a**4 - 3*a**3 - 3/5*a**5 + 79 + 0*a**2 - 1/2*a**6 + 0*a. Find s, given that o(s) = 0.
-3, 0, 1
Let c(r) = 5*r**3 + 39*r**2 + 38*r - 74. Let f(i) = -23*i**3 - 157*i**2 - 151*i + 295. Let g(u) = 9*c(u) + 2*f(u). Let g(v) = 0. What is v?
-2, 1, 38
Let z(j) be the first derivative of 0*j**2 - 12*j + 5/16*j**4 + 1/40*j**6 - 1/4*j**3 - 10 - 3/20*j**5. Let f(m) be the first derivative of z(m). Factor f(i).
3*i*(i - 2)*(i - 1)**2/4
Let n be (1*40/(-15))/((-2)/3). Suppose 4*d - 2*c = -6*c + 12, 2 = 4*d - 6*c. Determine z, given that 4/7*z**d + 0 - 4/7*z**n - 8/7*z**3 + 6/7*z + 2/7*z**5 = 0.
-1, 0, 1, 3
Let i = 35 - 14. Let s be i/(-6)*-2 + -3. Factor -3*q - 10*q**2 + 9*q**2 + s + 0*q**2.
-(q - 1)*(q + 4)
Factor 5*c**4 - 7*c**2 + 20*c**3 + 73582*c - 73572*c + 32*c**2.
5*c*(c + 1)**2*(c + 2)
Let g(c) = -11*c**3 - 99*c**2 + 196*c - 121. Let u = 182 + -178. Let z(s) = -6*s**3 - 50*s