x**7/420 - 19*x**6/960 - 19*x**5/480 + 79*x**4/192 - 15*x**3/16 - 9846*x**2. Factor j(w).
(w - 5)*(w - 1)**2*(4*w + 9)/8
Let t = -722731 + 1445463/2. Factor -7/3*g**2 - 17/6*g - t.
-(g + 1)*(14*g + 3)/6
Let j(q) = -q - 1. Let h(t) = t**4 - 4*t**3 + 5*t**2 + t + 3. Let u = -224 - -223. Let l(f) = u*h(f) - 3*j(f). Determine c so that l(c) = 0.
0, 1, 2
Let s(o) be the first derivative of 150*o**6 - 852*o**5 - 1646*o**4 - 1520*o**3/3 - 48*o**2 - 978. What is f in s(f) = 0?
-1, -2/15, 0, 6
Factor -98 + 91*i - 289*i + 3*i**2 + 257 + 183 - 147*i.
3*(i - 114)*(i - 1)
Let v(b) be the second derivative of -1/135*b**6 + 0*b**2 - 1/90*b**5 + 0*b**3 + 1/27*b**4 - 3*b + 7. Factor v(u).
-2*u**2*(u - 1)*(u + 2)/9
Let n = -260849 - -260853. Factor 2/3*o**2 - 2/9*o**n - 8/9 + 8/9*o - 4/9*o**3.
-2*(o - 1)**2*(o + 2)**2/9
Suppose 0 = -14*v + 10 + 74. Find u, given that -220*u**4 - 210*u**4 + v*u**3 - 2*u**5 - 8*u - 8*u**2 + 434*u**4 = 0.
-1, 0, 2
Determine o so that -79*o**2 + 288 + 12*o**2 + 39*o**2 + 136*o + 24*o**2 = 0.
-2, 36
Let t be (37/7 - 2) + (-4)/14. Suppose -5*u = -2*f - 303, f = t*u - 4*f - 178. Factor -u*i - 3*i**5 + 16*i - 2*i**5 + 2*i**3 + 8*i**3 + 20*i**4 - 60*i**2.
-5*i*(i - 3)**2*(i + 1)**2
Let -2620/3*o + 1716100/3 + 1/3*o**2 = 0. What is o?
1310
Let v(g) = 5*g**2 - 13*g + 1. Let r(k) = -3*k**2 + 7*k. Let i = 98 + -96. Suppose -i*n - 18 = -4*c, 4 + 3 = 2*c - 3*n. Let x(z) = c*r(z) + 2*v(z). Factor x(p).
-(p - 2)*(5*p + 1)
Let n(f) be the second derivative of -25/2*f**3 + 29*f + 35*f**2 + 5/12*f**4 - 4. Let n(t) = 0. Calculate t.
1, 14
Suppose 30929574619/4 + 29559963/4*f + 1/4*f**3 + 9417/4*f**2 = 0. What is f?
-3139
Let v = 234868 - 1644073/7. Factor 0 - 3/7*c**2 - v*c.
-3*c*(c + 1)/7
Suppose 16 = -6*v + 16. Determine s, given that 3471*s**4 + 40 - 3465*s**4 - 48*s - 22*s**2 + v*s**5 + 26*s**3 - 2*s**5 = 0.
-2, 1, 5
Let p = -1016400 + 1016404. Factor -1/4*y**p + 0 + 53/4*y**2 + 27/4*y + 25/4*y**3.
-y*(y - 27)*(y + 1)**2/4
Suppose 33*m - 34*m + 3 = 0. Find r such that 3*r**4 + 0*r**4 + 11*r**3 - 11*r**3 + 39*r**m - 2*r**4 = 0.
-39, 0
Let -2*x**3 - 4524 - 400*x - 830*x - 150*x**2 - 135*x + 1144 - 3*x**3 = 0. What is x?
-13, -4
Let d(k) = k**2 - 27*k + 164. Let b be d(18). Let n be 5/(7 - 9/b). Factor 3/2*i**n + 0 - 9*i.
3*i*(i - 6)/2
Let r = -3 + -165. Let z = -164 - r. Find c such that 8/5 + 6/5*c**z - 14/5*c**2 - 8/5*c + 8/5*c**3 = 0.
-2, -1, 2/3, 1
Let m(d) be the second derivative of 0*d**2 + 4/3*d**4 - 2/7*d**7 + 4 - 5/6*d**6 - 2/3*d**3 - 4*d + 7/20*d**5. Solve m(g) = 0.
-2, -1, 0, 1/4, 2/3
Let x(h) be the third derivative of 0 - 1/320*h**6 - 3/80*h**5 - 3/16*h**4 - 29*h - 2*h**2 - 1/2*h**3. Suppose x(f) = 0. What is f?
-2
Let a = 32557/8684 - -2/2171. Find b, given that -a*b - 3/8 - 27/8*b**2 = 0.
-1, -1/9
Solve -73/4*p**2 - 77/4*p + 1/4*p**4 + 5/4*p**3 + 0 = 0 for p.
-11, -1, 0, 7
Let d(u) = -u - 4. Let a be d(-11). Suppose 13 + 1 = a*w. Factor 5*c**5 - w*c**4 + 0*c**2 + 2*c**2 + c - 6*c**5.
-c*(c - 1)*(c + 1)**3
Let d(h) be the first derivative of -h**5/4 + 5*h**4 + 25*h**3/2 - 65*h**2 - 112*h + 168. Let n(z) be the first derivative of d(z). Let n(w) = 0. Calculate w.
-2, 1, 13
Let i(x) be the third derivative of -x**5/60 + x**4/4 - 4*x**3/3 + 43*x**2 + 22*x. Factor i(j).
-(j - 4)*(j - 2)
Let f(v) be the third derivative of 0*v - 1/84*v**7 - 1/2016*v**8 - 1/24*v**6 + 2 - 6*v**2 - 25/16*v**4 + 19/36*v**5 + 9/4*v**3. Find w, given that f(w) = 0.
-9, 1
Let v(p) = p**2 + 32*p - 1858. Let z be v(-62). Factor -4*u**z - 5/3 + 1/3*u**4 + 2/3*u**3 + 14/3*u.
(u - 1)**3*(u + 5)/3
Let q(k) = -7*k**4 + 38*k**3 - 140*k**2 + 169*k - 65. Let s(w) = 10*w**4 - 56*w**3 + 208*w**2 - 253*w + 98. Let p(c) = 7*q(c) + 5*s(c). Factor p(u).
(u - 7)*(u - 5)*(u - 1)**2
Let k = -363 - -364. Let h be -20 + 20 + 2 + k. Suppose -24/11*m - 4/11 - 21/11*m**2 + 49/11*m**h = 0. What is m?
-2/7, 1
Suppose -4*q - 74 = 3*l - 2*q, -5*q = -5*l - 115. Let f be l/2*(-1)/2. Suppose 49 + 4*v - 54 + f*v - 5*v**2 = 0. Calculate v.
1
Let t(c) be the second derivative of c**5/180 - c**4/4 + 9*c**3/2 + 16*c**2 + 6*c - 2. Let i(s) be the first derivative of t(s). Factor i(q).
(q - 9)**2/3
Let k(d) = 13*d**2 - 6*d + 4. Let s be k(1). Let o be 45/(-10)*(-4)/6. Solve -8*g**3 + 21*g**3 - s*g**o = 0 for g.
0
Factor 19260/7*g**3 - 192/7*g**5 + 0 - 4821/7*g**2 - 25584/7*g**4 + 402/7*g.
-3*g*(g + 134)*(4*g - 1)**3/7
Let c(n) = n**3 + 10*n**5 + 27*n**5 - n**2 + n - 38*n**5. Let y(x) = 20*x**5 - 20*x**4 + 48*x**3 - 70*x**2 + 22*x. Let i(q) = 36*c(q) + 2*y(q). Factor i(v).
4*v*(v - 5)*(v - 2)**2*(v - 1)
Let i(q) be the first derivative of q**6/4 - 9*q**5/5 - 27*q**4/4 + 34*q**3 + 243*q**2/4 - 189*q - 159. Let i(v) = 0. Calculate v.
-3, -2, 1, 3, 7
Let z(q) be the second derivative of q**6/15 - 38*q**5/5 + 134*q**4 - 768*q**3 - 3602*q - 1. Solve z(p) = 0.
0, 6, 64
Let a = 1403890 + -7019438/5. Factor -1/5*k**4 + 31/5*k + 9/5*k**3 - a - 27/5*k**2.
-(k - 4)*(k - 3)*(k - 1)**2/5
Factor 6/5*q**3 + 0 + 128/5*q**2 - 88/5*q.
2*q*(q + 22)*(3*q - 2)/5
Let a = 160101 - 480277/3. What is u in -14/3*u**2 + 4/3 - a*u = 0?
-2, 1/7
Solve 522*i**3 + 0*i + 3/2*i**4 + 1041/2*i**2 + 0 = 0 for i.
-347, -1, 0
Let i(y) = -y**3 - 9*y**2 - 13*y + 45. Let f be i(-8). Suppose 3*d = 4*d - 3. Factor 23*g + 22*g + 25*g**d + f*g**2 + 35*g + 20.
5*(g + 1)*(g + 2)*(5*g + 2)
Let p(l) be the third derivative of -l**5/120 + l**4/8 + 28*l**3/3 + 1199*l**2 - 2*l. Let p(k) = 0. Calculate k.
-8, 14
Let y(k) = -297*k + 56729. Let h be y(191). Factor 0 + 2/13*m - 18/13*m**h + 48/13*m**3 - 32/13*m**4.
-2*m*(m - 1)*(4*m - 1)**2/13
Let x(j) be the first derivative of 8*j**5 - 195*j**4/4 - 25*j**3/3 - 8126. Suppose x(f) = 0. What is f?
-1/8, 0, 5
Let a(f) = -7 - 4*f - 4 + 11 - f**2 + 5 + 2*f**3. Let b be a(1). Suppose -3/4*y - 3/8 - 3/8*y**b = 0. What is y?
-1
Let 64/3 - 20*t**2 + 8/3*t**3 + 32*t = 0. What is t?
-1/2, 4
Factor -35*o**2 + 116*o - 32*o**2 - 29*o**2 - 38*o**2 + 138*o**2 - 248.
4*(o - 2)*(o + 31)
Let a(w) be the second derivative of w**6/75 + 41*w**5/25 + 1837*w**4/30 + 2132*w**3/5 + 6084*w**2/5 - 1070*w. Suppose a(u) = 0. What is u?
-39, -2
Let t be 2/90*2*4*(-75)/(-96). Let d(m) be the first derivative of -7/45*m**5 + 1/9*m**6 - 33 - 1/18*m**2 + 7/27*m**3 + 0*m - t*m**4. Solve d(w) = 0.
-1, 0, 1/6, 1
Let z = -13513/42 + 7019/21. Factor 5*p + 1/2*p**2 + z.
(p + 5)**2/2
Let m(k) be the first derivative of -k**7/21 - k**6/3 - k**5 - 5*k**4/3 - 5*k**3/3 - k**2 + 34*k + 67. Let l(b) be the first derivative of m(b). Factor l(v).
-2*(v + 1)**5
Let y(h) be the first derivative of -h**6/51 + 42*h**5/85 - 143*h**4/34 + 734*h**3/51 - 384*h**2/17 + 280*h/17 + 2200. Find s such that y(s) = 0.
1, 2, 7, 10
Let o(d) be the third derivative of -d**6/1260 - 89*d**5/210 - 7921*d**4/84 - 19*d**3 + 3*d**2 + 19. Let l(j) be the first derivative of o(j). Factor l(m).
-2*(m + 89)**2/7
Let w be (-6)/(-12)*(-9)/(-36). Let u(k) be the third derivative of 3/10*k**6 + 0 - w*k**4 + 2/5*k**5 + 0*k - 1/2*k**3 + 2*k**2. Factor u(o).
3*(2*o + 1)**2*(3*o - 1)
Factor 200*a + 208*a**3 - 5*a**4 + 175*a**3 + 290*a**2 - 446*a**3 + 148*a**3.
-5*a*(a - 20)*(a + 1)*(a + 2)
Let u(k) be the second derivative of -3*k**5/110 + 54*k**4/11 + 219*k**3/11 + 30*k**2 + 12*k + 36. Determine f, given that u(f) = 0.
-1, 110
Let p(d) be the third derivative of 0*d**3 + 1/35*d**5 + 1/2352*d**8 + 0*d - 1/210*d**6 + 2*d**2 - 1/490*d**7 + 0*d**4 - 79. Solve p(v) = 0 for v.
-2, 0, 2, 3
Factor -1/7*m**3 - 202/7*m**2 + 613/7*m - 410/7.
-(m - 2)*(m - 1)*(m + 205)/7
Let v = -484 + 489. Suppose 2*w + 7*k = 2*k + 4, -5*w - v*k + 10 = 0. Solve -4/7*b**w - 100/7 - 40/7*b = 0.
-5
Factor 264/7 - 2/7*f**2 + 82/7*f.
-2*(f - 44)*(f + 3)/7
Let v(l) = 8*l**4 - 24*l**3 + 12*l**2 + 54*l. Let r(z) = -7*z**4 + 24*z**3 - 15*z**2 - 54*z. Let c(y) = 5*r(y) + 4*v(y). Let c(q) = 0. Calculate q.
-1, 0, 3, 6
Let i(k) be the first derivative of -101 - 4/3*k**3 - 3600*k - 120*k**2. Factor i(r).
-4*(r + 30)**2
Let q(z) be the first derivative of -z**6/270 + z**5/45 - 23*z**3/3 + z**2/2 + 40. Let r(k) be the third derivative of q(k). Factor r(p).
-4*p*(p - 2)/3
Let i be 0/(-16*(-4)/64). Let s(p) be the first derivative of -p**5 + 4/3*p**3 + 19 + 1/6*p**6 + i*p - 4*p**2 + 3/2*p**4. Let s(b) = 0. What is b?
-1, 0, 2