 - -110. Let z(g) = 8*g**3 - 19*g**2 + 11*g + 5. Let i(r) = x*f(r) + 8*z(r). Factor i(y).
4*y*(y - 2)*(y - 1)
Let q = -7463/3 - -2488. Let o(b) be the third derivative of -2*b**3 + 0 + 0*b - 4*b**2 + q*b**4 + 1/15*b**5. Find z, given that o(z) = 0.
-3, 1
Let 1646 + 5*t**3 - 3068 - 100*t + 1602 - 85*t**2 = 0. What is t?
-2, 1, 18
Let r(d) be the third derivative of -d**7/7560 - 13*d**6/2160 - d**5/12 - 63*d**4/8 + 3*d**2 + 37. Let v(z) be the second derivative of r(z). Factor v(h).
-(h + 3)*(h + 10)/3
Let a = 110723/30 - 21367/6. Determine c so that 2/5*c**4 - 1224/5*c + 68/5*c**3 + a + 506/5*c**2 = 0.
-18, 1
Let m(t) be the first derivative of 14/3*t + 2/15*t**5 + 16/3*t**3 - 22/3*t**2 - 5/3*t**4 + 209. Factor m(w).
2*(w - 7)*(w - 1)**3/3
Let j be (-1090)/(-26) + 127264/(-3104). Suppose -10/13*a**4 + 10/13*a**3 - j*a + 10/13*a**2 + 0 + 2/13*a**5 = 0. What is a?
-1, 0, 1, 2, 3
Suppose 20/3 - 2/15*i**3 - 16/5*i**2 + 18/5*i = 0. Calculate i.
-25, -1, 2
Suppose -2/21*l**3 - 286/3*l**2 - 166666/7*l + 167334/7 = 0. What is l?
-501, 1
Let w = 9277/46260 - 5/9252. Solve -w*b**2 - 4/5 + 4/5*b = 0.
2
Let a(f) be the first derivative of 5*f**4/4 + 2408*f**3/3 + 289441*f**2/2 - 116162*f - 264. Determine b, given that a(b) = 0.
-241, 2/5
Let d(x) = 6*x**2 - 774*x - 1554. Let i(k) = -3*k**2 + 386*k + 776. Let b(m) = -4*d(m) - 9*i(m). Let b(v) = 0. What is v?
-2, 128
Suppose 0 = -31*v + 1326 + 4750. Factor -419*l**3 - 12*l**2 + v*l**3 + 21 + 7*l - 6*l**2 + 199*l**3 + 17*l - 3*l**4.
-3*(l - 1)*(l + 1)**2*(l + 7)
Let l = -11342 - -11342. Let z(k) be the third derivative of -1/24*k**4 + l*k + 39*k**2 + 0 - 7/60*k**5 + 1/120*k**6 + 7/6*k**3. Solve z(p) = 0.
-1, 1, 7
Let x(n) = -4*n**4 + 227*n**3 - 2746*n**2 - 2248*n + 722. Let c(b) = 4*b**4 - 229*b**3 + 2745*b**2 + 2249*b - 721. Let u(l) = -7*c(l) - 8*x(l). Factor u(g).
(g - 27)**2*(g + 1)*(4*g - 1)
Let g(n) be the first derivative of 2*n**3/9 + 124*n**2/3 + 488*n/3 + 1972. Suppose g(c) = 0. What is c?
-122, -2
Let q be 4 - (0 - (0 - 1)). Suppose 232*h = 3*r + 227*h - 518, -5*r + 2*h + 876 = 0. Let -170*c**q - c - c**4 + r*c**3 + 5*c + 0*c - 9*c**2 = 0. What is c?
0, 1, 4
Find m, given that 0*m**4 - 4*m**4 + 7*m**4 + 60*m**3 - 59*m**2 - 13*m**2 - 129*m**3 = 0.
-1, 0, 24
Let g(h) be the first derivative of 2*h**5/15 - 25*h**4 + 296*h**3/3 - 442*h**2/3 + 98*h + 3500. Solve g(s) = 0 for s.
1, 147
Let r = 586759 + -586757. Factor 6/7 - t + 1/7*t**3 + 0*t**r.
(t - 2)*(t - 1)*(t + 3)/7
Determine b, given that 3092/9*b - 770*b**2 - 9*b**3 - 344/9 = 0.
-86, 2/9
Suppose -3*m - 27 = 45*s - 39*s, 5*s = -2*m - 24. Factor 0 + 2/13*p**4 + 2/13*p**2 - 4/13*p**m + 0*p.
2*p**2*(p - 1)**2/13
Let h be (12/(-30))/((-81)/4 + 20). Let 0*m - h*m**2 - 2/5*m**5 - 2*m**4 - 16/5*m**3 + 0 = 0. What is m?
-2, -1, 0
Suppose 0 = -5*q + 2*s + 37 + 31, 0 = s - 1. Suppose 5*l = -3*h + q, l - 2*h - 16 = -2*l. Suppose 0 + 2*x**2 - 2 + 0 + l*x + 4 = 0. Calculate x.
-1
Suppose 3 = -v + 43. Let l(r) = 7*r**2 + 7*r - 8. Let p(j) = -j**2 - j + 1. Suppose 0 = -2*m - 6 + 16. Let z(d) = m*l(d) + v*p(d). Suppose z(h) = 0. What is h?
-1, 0
Suppose -42*h + 3744 = -16*h. Suppose -h = -21*w - 51*w. Solve 5/7*c**3 - 1/7*c**4 - 2/7 + c - 9/7*c**w = 0 for c.
1, 2
Let w(a) be the second derivative of -a**4/78 + 119*a**3/39 + 492*a**2/13 + 1905*a. Factor w(x).
-2*(x - 123)*(x + 4)/13
Let c(p) = p**3 + 10*p**2 - p + 2. Let u(w) = -8*w**4 + 340*w**3 + 2025*w**2 + 422*w - 223. Let l(t) = -6*c(t) + u(t). Solve l(j) = 0.
-5, -1/2, 1/4, 47
Let h(f) be the third derivative of -f**7/735 - 3*f**6/35 - 107*f**5/210 + 8*f**4 - 3499*f**2. What is i in h(i) = 0?
-32, -7, 0, 3
Suppose -4*p = -3*a + 61, a = -3*a + 4*p + 76. Factor 5*u**2 - 26*u**4 - a*u**4 + 21*u**4 + 25*u**3 - 15*u**2 + 5*u**5.
5*u**2*(u - 2)*(u - 1)**2
Let t(w) be the second derivative of -5/12*w**4 + 1/5*w**5 + 0 - 1/30*w**6 + 1/3*w**3 + 0*w**2 - 110*w. Factor t(g).
-g*(g - 2)*(g - 1)**2
Let 49/5*q**4 + 864/5 - 1728/5*q - 162/5*q**2 + 2/5*q**5 + 299/5*q**3 = 0. Calculate q.
-12, -3, 1/2, 2
Determine f so that -3/4*f**3 + 75/4*f + 33/4*f**2 + 39/4 = 0.
-1, 13
Let u(f) = 3*f**3 + 2356*f**2 + 17687*f + 15378. Let h(x) = -4*x**3 - 3298*x**2 - 24761*x - 21529. Let i(s) = 22*h(s) + 31*u(s). What is r in i(r) = 0?
-88, -7, -1
Let z = 8612 + -25835/3. Let i(j) be the second derivative of -2*j**2 + 14*j - z*j**3 + 0 + 1/6*j**4. Suppose i(f) = 0. Calculate f.
-1, 2
Suppose z + 5*m = -13, 2*z + 184*m - 180*m = -8. Let v(s) be the second derivative of -5/3*s**3 + 2/3*s**4 - 1/10*s**5 + 2*s**z + 0 - 13*s. Factor v(w).
-2*(w - 2)*(w - 1)**2
Let -230 - 1376*p**2 - 418*p**3 - 1016*p + 2516*p**2 + 310 + 46*p**4 = 0. What is p?
2/23, 2, 5
Suppose 3*r = 3*t - 5*t + 4, 0 = -2*r - t + 4. Factor 44*s**3 + 34*s**2 - 345 - 20*s - 11*s**4 + s**r + 345.
-2*s*(s - 5)*(s + 1)*(5*s - 2)
Suppose -5*x + 522 = 2*u, -43 + 253 = 2*x + 2*u. Factor 12*b + 571 + 487 + 2*b**2 - x*b.
2*(b - 23)**2
Let d be (((-23)/(-46))/((-40)/(-44)))/(210/560). What is q in d*q - 12/5 - 2/15*q**2 = 0?
2, 9
Let t be 11 + -26 + (-30)/120*-100. Factor 1/3*f**2 - 13/3*f + t.
(f - 10)*(f - 3)/3
Let t be (-2)/(-6)*(0 - (6 - 3)). Let h(k) = k**3 + 2*k**2 + k - 4. Let s(a) = -a + a**2 + 6*a**2 - 6*a**2. Let d(j) = t*s(j) - h(j). Factor d(x).
-(x - 1)*(x + 2)**2
Let q(p) be the first derivative of -1/34*p**4 + 2/17*p**2 - 6/85*p**5 + 0*p + 2/17*p**3 - 1/51*p**6 - 69. Let q(v) = 0. What is v?
-2, -1, 0, 1
Let b be 2286/635*(-10)/(-12). Let n(x) be the second derivative of 35*x - 1/3*x**b + 0 + 0*x**4 + 6/7*x**2 + 1/70*x**5. Solve n(o) = 0 for o.
-3, 1, 2
Let z be (-17*(135/70 - 2))/((-279)/(-22320)). Factor 4/7*n**2 + z*n + 28900/7.
4*(n + 85)**2/7
Let f(u) = -20*u**3 + 56*u**2 - 88*u + 34. Let o(c) = -c**3 + c - 1. Let p = 255 - 291. Let t(h) = p*o(h) + 2*f(h). Factor t(k).
-4*(k - 26)*(k - 1)**2
Let n(p) be the third derivative of 0*p**3 + 0*p**5 + 0*p + 1/45*p**6 + 0*p**4 + 12*p**2 + 1/315*p**7 - 1. Solve n(s) = 0 for s.
-4, 0
Let j(i) = 5*i**2 - 160*i + 776. Let l(s) = 70*s**2 - 2240*s + 10865. Let x(m) = -55*j(m) + 4*l(m). Factor x(c).
5*(c - 26)*(c - 6)
Let f(i) be the second derivative of -33*i**5/80 + 115*i**4/8 - 1067*i**3/8 - 1089*i**2/2 - 2861*i. What is c in f(c) = 0?
-12/11, 11
Let m(q) = -98*q - 11. Let l be m(-2). Let d be (l/(-74))/(5/(-1)). Factor -9/2*r**2 + 5/2*r**3 + 7/2*r - d*r**4 - 1.
-(r - 2)*(r - 1)**3/2
Let o(k) be the second derivative of -k**5/240 - 11*k**4/24 - 121*k**3/6 + k**2 + 2*k + 10. Let i(a) be the first derivative of o(a). Solve i(t) = 0 for t.
-22
Let -3732 - 1744 + 70*r**2 - 81*r**3 - 77*r**3 - 1073*r - 68*r**3 + 225*r**3 = 0. Calculate r.
-4, 37
Let y(c) be the second derivative of -c**7/630 + 4*c**6/15 + 49*c**5/30 + 149*c**4/12 - 228*c. Let r(g) be the third derivative of y(g). Factor r(m).
-4*(m - 49)*(m + 1)
Let a be 3724/(-798)*(-72)/273. Find b such that -6*b + 2/13*b**5 + 28/13*b**3 + a*b**4 + 72/13 - 40/13*b**2 = 0.
-4, -3, 1
Factor -196*k**4 - 1096*k**2 + 26 + 4*k**5 - 194569*k**3 + 724*k + 195313*k**3 - 206.
4*(k - 45)*(k - 1)**4
Let w(v) = -38560*v + 192830. Let m be w(5). Let -357/2*h**2 + m + 195/4*h**3 + 93*h + 27/4*h**4 = 0. Calculate h.
-10, -2/9, 1, 2
Let a(t) be the third derivative of t**7/42 - 7*t**6/12 - 115*t**5/12 - 125*t**4/6 - 2239*t**2. Suppose a(h) = 0. Calculate h.
-5, -1, 0, 20
Factor 0 - 1/2*z**3 + 285/2*z + 2*z**2.
-z*(z - 19)*(z + 15)/2
Let g(y) be the first derivative of 4/3*y**3 - 40*y + 6*y**2 - 84. Solve g(d) = 0.
-5, 2
Let y be (-3 - -7)*1/(-1)*(-934)/16812. Factor 0*k + y*k**4 + 20/9*k**3 + 0 + 2*k**2.
2*k**2*(k + 1)*(k + 9)/9
Suppose -12 = 84*k - 86*k. Suppose -3*b - k = -6*b. Let h**2 + 8*h + 3 + 6 - 2*h**b + 0*h**2 = 0. What is h?
-1, 9
Find l such that 153/2 - 1/4*l**2 + 305/4*l = 0.
-1, 306
Let r(u) be the second derivative of -u**6/15 - 29*u**5/5 + 122*u**4/3 - 248*u**3/3 + 23*u + 15. Determine l so that r(l) = 0.
-62, 0, 2
Let -4*z**2 + 12/5*z**4 - 508/5*z + 168/5 + 92/5*z**3 = 0. What is z?
-7, -3, 1/3, 2
Let s = -2209 - -2231. Let o be 1 + (-5)/2*2. Let t(u) = -2*u**3 + 2*u**2. Let p(x) = -x**4 - 11*x**3 + 11*x**2. Let z(c) = o*p(c) + s*t(c). Solve z(a) = 0.
0
Let k = -118/9 + 16. Suppose 0 = -4*z - 3 - 17, 2*u - z - 9 = 0. Factor -2/3 - k*o - 8/9*o**u.
-2*(o + 3)*(4*o + 1)/9
Let m(