660 + 47*v**5/165 - 2825*v**4/132 + 2500*v**3/3 - 5220*v**2 - 2. Let m(b) = 0. What is b?
25, 44
Suppose 50/9*y**3 - 49/9*y - 1/9*y**5 + 10/3*y**2 + y**4 - 13/3 = 0. Calculate y.
-3, -1, 1, 13
Let o = -1 + 1. Let n be (585/(-39))/(6/12 + -8). Find w such that o - 2/9*w + 2/9*w**n = 0.
0, 1
Suppose 3*w - 3 = 0, -33 = -4*l + 2*l - w. Suppose -154*h**4 - l*h - 132*h**3 + 56*h**2 + 133*h**5 + 55*h**2 - 7*h**2 - 35*h**5 = 0. Calculate h.
-1, 0, 2/7, 2
Let v(p) be the second derivative of p**7/231 + 8*p**6/55 + 119*p**5/110 + 94*p. Factor v(q).
2*q**3*(q + 7)*(q + 17)/11
Find v such that -2/3*v**4 - 200 + 4/3*v**3 - 160/3*v + 86/3*v**2 = 0.
-6, -2, 5
Let u = -393413 - -1180240/3. Factor f**2 - 22/3*f - 16/3 + 8/3*f**3 - u*f**4.
-(f - 8)*(f - 2)*(f + 1)**2/3
Let x(s) = -54*s - 444. Let q be x(-8). Let i be (-7)/4*q/210. Determine h so that 0 + 0*h + 3/5*h**2 + i*h**4 + 7/10*h**3 = 0.
-6, -1, 0
Let 2/13*x**2 + 1460/13*x + 266450/13 = 0. Calculate x.
-365
Let z(m) be the second derivative of -7/12*m**2 - 2/9*m**3 - 1/72*m**4 + 2 - 72*m. Find b such that z(b) = 0.
-7, -1
Let k = -602 + -2015. Let s = -44475/17 - k. Factor 0 + 2/17*a**2 + s*a.
2*a*(a + 7)/17
Suppose t = 6*t - 25. Let b = -5816 + 5818. Suppose 15 - 5 + 0 - 2*v**b - t*v - 3*v = 0. What is v?
-5, 1
Determine c so that 2634117*c**3 + 48*c - 108 + 107*c**2 - 3*c**4 - 2634165*c**3 + 4*c**2 = 0.
-18, -1, 1, 2
Let r(y) be the third derivative of y**7/42 - y**6/4 - 5*y**5/4 + 125*y**4/6 + 1930*y**2 + 2*y. Factor r(j).
5*j*(j - 5)**2*(j + 4)
Suppose -9*c = -66 - 123. Let b be ((-12)/7)/4 + 23/c. Find s, given that -4/3 + 4/3*s**2 - b*s**3 + 2/3*s = 0.
-1, 1, 2
Let k(u) = 861*u**2 + 102*u - 3. Let o(t) = -t**3 + 7*t**2 - 8*t + 11. Let b be o(6). Let p(m) = -m**2 - 1. Let x(j) = b*k(j) + 6*p(j). Factor x(c).
-3*(17*c + 1)**2
Suppose 5*s = 224 - 19. Let y = s - 35. Factor 10*n + 8*n**2 - 2*n**4 - 4*n - y*n - n**5 + 4*n**3.
-n**2*(n - 2)*(n + 2)**2
Let i(a) be the third derivative of -a**8/840 + a**7/75 + 3*a**6/100 - 23*a**5/30 + 5*a**4/3 + 1057*a**2 + 2*a. What is b in i(b) = 0?
-4, 0, 1, 5
Let y(t) be the third derivative of 128*t**2 + 0*t + 1/9*t**6 + 0 - 1/630*t**7 - 361/18*t**3 + 95/9*t**4 - 73/30*t**5. Factor y(z).
-(z - 19)**2*(z - 1)**2/3
Suppose -r = -3*r + 24. Let u be (-9)/(-6) + 1 + 157/2. Solve r - 16 + 30*y - u*y**2 + 6*y = 0.
2/9
Let l = -3338/1095 + 242/73. Let x(m) be the second derivative of 1/5*m**2 - 25*m - l*m**3 + 0 + 32/25*m**5 - 8/15*m**4. What is v in x(v) = 0?
-1/4, 1/4
Let s(p) be the first derivative of p**3/12 - 79*p**2/8 - 83*p - 2390. Suppose s(h) = 0. Calculate h.
-4, 83
Let m = -347885/42 + 8283. Let n(d) be the second derivative of -m*d**4 + 0 + 1/7*d**2 + 1/21*d**3 - 1/70*d**5 - 17*d. Find p such that n(p) = 0.
-1, 1
Let q(a) be the first derivative of 1/5*a**5 + 107 - 27/2*a**2 + 1/3*a**3 + 7/4*a**4 + 18*a. Determine b so that q(b) = 0.
-6, -3, 1
Let j(s) be the third derivative of -7*s**6/1140 + 149*s**5/95 - 2368*s**4/19 - 8192*s**3/57 + 90*s**2 - 4. Factor j(x).
-2*(x - 64)**2*(7*x + 2)/19
Determine w so that -199 - 324*w + 48*w**3 - 4*w**4 + 335*w**2 - 339*w**2 - 84*w - 153 = 0.
-2, -1, 4, 11
Suppose -383 = 171*r - 896. Let y(q) be the third derivative of -22*q**2 - 13/30*q**5 + 1/6*q**4 + 0*q + 0 + 0*q**r - 1/4*q**6. Determine z so that y(z) = 0.
-1, 0, 2/15
Let w(h) be the first derivative of h**3/15 + 412*h**2/5 + 823*h/5 + 3381. Suppose w(s) = 0. What is s?
-823, -1
Let w(t) be the third derivative of t**7/70 + 7*t**6/40 - 11*t**5/10 - 7*t**4/2 + 36*t**3 + 219*t**2 - 22. Factor w(s).
3*(s - 2)**2*(s + 2)*(s + 9)
Let m be -10 + -11 + 4745/195. Factor -m*i**3 + 0 + 104/3*i**2 - 40/3*i.
-2*i*(i - 10)*(5*i - 2)/3
Let f = 274 - 272. Factor -63*d**2 - 157*d + 363 - 95*d - f*d - 43*d - 3*d**3.
-3*(d - 1)*(d + 11)**2
Factor 893/3*p + 5054/3 + 52/3*p**2 + 1/3*p**3.
(p + 14)*(p + 19)**2/3
Let d be 15*(-816)/(-1020)*(-2)/(-44) - (-1852)/154. Factor -50/7*c**3 - d*c - 20*c**2 - 16/7.
-2*(c + 2)*(5*c + 2)**2/7
Let d(x) be the third derivative of x**6/420 + 23*x**5/210 - 13*x**4/42 - 16*x**3/7 - x**2 - 203. Factor d(k).
2*(k - 2)*(k + 1)*(k + 24)/7
Let r(z) be the third derivative of -z**7/42 - 23*z**6/72 + z**5/4 + 61*z**3/6 + 13*z**2. Let s(a) be the first derivative of r(a). Factor s(l).
-5*l*(l + 6)*(4*l - 1)
Let z(c) be the first derivative of c**3/12 + c**2 + 4*c - 1900. Factor z(l).
(l + 4)**2/4
Let z(x) be the first derivative of -x**8/840 - x**7/210 + x**6/180 + x**5/30 + 34*x**3/3 + 2*x + 45. Let k(t) be the third derivative of z(t). Factor k(l).
-2*l*(l - 1)*(l + 1)*(l + 2)
Let o(s) be the third derivative of -13*s**5/6 - 4*s**4 - 7*s**3/3 - 2151*s**2. Factor o(h).
-2*(5*h + 1)*(13*h + 7)
Let f(z) be the third derivative of z**7/840 + 7*z**6/480 + 3*z**5/80 - 7*z**4/96 - 5*z**3/12 - 18*z**2 + 50*z. Let f(t) = 0. What is t?
-5, -2, -1, 1
Let r(y) be the first derivative of -y**4/6 - 80*y**3/9 - 73*y**2/3 + 76*y + 1104. Solve r(d) = 0.
-38, -3, 1
Let f(b) = 4*b**5 - b**4 + 2*b - 1. Let h(l) = -5*l**5 - 93*l**4 - 93*l**3 - 2*l + 1. Let i(n) = 5*f(n) + 5*h(n). Factor i(t).
-5*t**3*(t + 1)*(t + 93)
Suppose 210*p - 729 = -33*p. Factor 2*a**2 + 1/2*a**p - 2*a - 8.
(a - 2)*(a + 2)*(a + 4)/2
Let h(n) = 34*n**2 - 24*n + 124. Let m be h(5). Factor x**3 - 8*x**2 - 854 + m.
x**2*(x - 8)
Factor -21*i**2 - 47*i**2 + 94*i**2 - 14*i**2 - 3*i**3 + 14*i + i**3.
-2*i*(i - 7)*(i + 1)
Let v be -4 + (-18)/(-6) + 5. Suppose -3616*a + 1804*a + 1808*a + v*a**2 = 0. What is a?
0, 1
Let y(z) = 4*z**2 + 16*z + 26. Let k be y(-6). Suppose -s + 76 = k. Find u such that 210*u + u**s - 210*u = 0.
0
Factor -3/5*n**4 - 36*n + 6*n**3 - 39/5*n**2 - 108/5.
-3*(n - 6)**2*(n + 1)**2/5
Let g = -638065 - -638065. Suppose 1/3*z**2 + 2/3*z + g - 1/3*z**3 = 0. What is z?
-1, 0, 2
Let 3/8*i**2 - 7/2*i + 1/8*i**3 - 15/2 = 0. What is i?
-6, -2, 5
Let y(r) = r**2 + 10*r - 21. Let o be y(-12). Factor 3*w**3 - 20915*w**4 + 20910*w**4 - 8*w**o.
-5*w**3*(w + 1)
Let v = -62133/5 + 12427. Let g(x) be the second derivative of -1/2*x**3 + 0 - 30*x + 11/60*x**4 + v*x**2. Factor g(u).
(u - 1)*(11*u - 4)/5
Let n(b) = b - 1. Let u(h) = -2*h**2 + 37*h + 125. Let c(r) = r**2 - 36*r - 125. Let p(f) = 7*c(f) + 6*u(f). Let k(v) = 20*n(v) - p(v). Factor k(w).
5*(w + 3)*(w + 7)
Let p(f) = -f**2 + 372*f + 10352. Let u be p(-26). Factor -2/11*v**2 + 2/11*v**u - 2/11*v + 0 + 2/11*v**3.
2*v*(v - 1)*(v + 1)**2/11
Let v(u) be the third derivative of u**6/40 - 139*u**5/4 + 15051*u**4 + 60552*u**3 + 367*u**2. Find q, given that v(q) = 0.
-1, 348
Let i be 432/234 + (-4)/(-26). Let l be 256/192*1/i. Solve 0*v + 4/3*v**3 - l*v**2 + 0 - 2/3*v**4 = 0.
0, 1
Let i be -6 - -3 - 2*-2 - -1. Factor 0*v**2 + 3*v**i - 51 + 51 - 3*v.
3*v*(v - 1)
Let u(n) = 8*n**4 + 3*n**3 + n. Let m(j) = -29*j**4 + 1951*j**3 + 3935*j**2 + 1967*j. Let f(x) = -m(x) - 3*u(x). Factor f(k).
5*k*(k - 394)*(k + 1)**2
Let u(x) = -7*x + 60. Let f be u(8). Suppose r = 22 - 14. Factor -r*d - 1/2*d**3 + 0 - f*d**2.
-d*(d + 4)**2/2
Suppose v - 766 = -5*h, -2*v + 1521 = -0*v - h. Factor 475*g**2 - v*g - 707*g - 20 + 1582*g - 1054*g.
5*(g - 2)*(95*g + 2)
Suppose 0 = 7*t - 98 + 70. Solve -3877 - 12*q**3 + 3877 + 2*q**t - 14*q**2 = 0 for q.
-1, 0, 7
Let m be 3408/(-15336)*(-18)/2. Determine l, given that 5/3 - 2*l + 1/3*l**m = 0.
1, 5
Let a(n) be the third derivative of -n**6/180 - 3*n**5/10 + 10*n**4/3 - 124*n**3/9 - 2*n**2 - 2118*n - 3. Factor a(q).
-2*(q - 2)**2*(q + 31)/3
Let c = -9 - -45. Find l, given that c*l + 15*l**3 - 72*l**2 + 24*l**2 + 6*l**3 - l**3 - 8 = 0.
2/5, 1
Let d(a) be the first derivative of -2*a**3/9 - 280*a**2 - 1678*a/3 + 3135. Factor d(t).
-2*(t + 1)*(t + 839)/3
Let q(v) be the first derivative of 0*v - 9/2*v**4 + 3/5*v**5 + 52 + 0*v**2 + 5*v**3. Factor q(g).
3*g**2*(g - 5)*(g - 1)
Let c(v) be the second derivative of -33/17*v**2 - 31/102*v**4 + 0 + 170*v - 1/170*v**5 + 65/51*v**3. Suppose c(s) = 0. Calculate s.
-33, 1
Let -5*s - 14*s + 2*s**2 - 18*s**2 + 42*s + 45*s - 80 + s**3 = 0. What is s?
2, 4, 10
Let v = 3/156892 - -627553/784460. Find o, given that -v*o**2 - 24/5 - 4*o = 0.
-3, -2
Let m be (1335/534)/((-45)/16*(-4)/3). Factor 0 - 4/3*i**3 + 2/9*i**5 + 16/9*i**2 - m*i + 0*i**4.
2*i*(i - 1)**3*(i + 3)/9
Let t(c) be the first derivative of -51 + 3