- 24*t + 8*t**2 - 28*t**2 + 144 - f*t**3.
-2*(t - 2)*(t + 6)**2
Let n(d) = 7*d**3 - 5*d**2 - 5*d - 3. Suppose -3*p - 42 = 4*p. Let g(b) = -b**3 + b**2 + 1. Let v(h) = p*g(h) - n(h). Suppose v(w) = 0. What is w?
-3, 1
Factor -1081 + 768*g + 1798 + 0*g**3 + 2*g**3 + 68*g**2 + 1259 + 904.
2*(g + 10)*(g + 12)**2
Let m(o) be the third derivative of o**5/60 - 7*o**4/8 + 19*o**3/3 - o**2 - 1492*o. Factor m(n).
(n - 19)*(n - 2)
Let -136/5*f + 14/5*f**4 + 42*f**2 - 96/5*f**3 - 24/5 = 0. Calculate f.
-1/7, 2, 3
Suppose -21 = 48*x - 51*x + c, -104 = -16*x + 4*c. Solve 1/5*r**x - 7/5*r**3 - 6/5*r**2 + 0 + 0*r**4 + 0*r = 0 for r.
-2, -1, 0, 3
Factor -2/7*p**2 + 522/7*p - 520/7.
-2*(p - 260)*(p - 1)/7
Let g(u) = 30*u**2 + 693*u + 24200. Let o(v) = 8*v**2 + 169*v + 6050. Let h(x) = 6*g(x) - 22*o(x). Factor h(a).
4*(a + 55)**2
Let v(r) = -20*r**2 - 1820*r - 11120. Let q(u) = -u**2 - 107*u - 654. Let h(p) = 35*q(p) - 2*v(p). Factor h(f).
5*(f - 26)*(f + 5)
Let o(g) be the third derivative of g**7/105 - 37*g**6/60 + 78*g**5/5 - 180*g**4 + 576*g**3 + 396*g**2 + 4. Factor o(z).
2*(z - 12)**3*(z - 1)
Let d be (-4)/34 - (-10325)/11900. Factor -d*h - 3/4*h**2 + 3/2.
-3*(h - 1)*(h + 2)/4
Let j(q) = -q - q - 88*q**2 + 46*q**2 + 1 + 41*q**2. Let g(i) = 17*i**2 + 42*i + 17. Let t(z) = 2*g(z) - 2*j(z). Find w such that t(w) = 0.
-2, -4/9
Let d be (-20)/30 + 14/3. Factor 122*k**4 + 2*k**5 - 8*k**2 + 2*k**3 - 134*k**d + 16*k**3.
2*k**2*(k - 4)*(k - 1)**2
Let w(t) be the second derivative of -t**5/6 - t**4/18 + 5*t**3/9 + t**2/3 - 255*t - 2. Suppose w(c) = 0. What is c?
-1, -1/5, 1
Let u(d) be the third derivative of -2*d**6/135 - 442*d**5/135 + 887*d**4/216 - 37*d**3/18 - 2438*d**2. Solve u(w) = 0.
-111, 1/4
Let o(f) = -f**3 + 12*f**2 - 28*f - 29. Let w = 342 - 334. Let p be o(w). Let 1/7*h**p + 0*h + 0*h**2 + 0 + 2/7*h**4 + 1/7*h**5 = 0. What is h?
-1, 0
Let t(d) = 2*d**2 - 32*d + 2. Let i be t(16). What is f in -5108 + f**3 - 17*f + 16*f**i + 5108 = 0?
-17, 0, 1
Let v(b) be the first derivative of -32*b - 12*b**3 + 33*b**2 - 137 + 1/2*b**4. Find a such that v(a) = 0.
1, 16
What is g in -24112352934 + 13*g**3 - 29527054581 + 14317131317 - 3090*g**2 - 43707606*g - 13104*g**2 - 15*g**3 = 0?
-2699
Suppose 15*v + 319 = -v + 367. Factor -27/4*f**v + 27/4*f**4 - 9/2*f**2 + 7*f - 2.
(f + 1)*(3*f - 2)**3/4
Let x(t) = -t**3 - 3*t**2 + 3*t - 27. Let q be x(-6). Let h = 9 + q. Factor 63*j**2 - 2*j**3 + 0*j**3 - h*j**2 + 5*j**3.
3*j**2*(j - 3)
Let v(m) be the second derivative of 0 - 5/6*m**4 + 14/9*m**3 + 1/30*m**5 + 0*m**2 + 55*m. Let v(j) = 0. What is j?
0, 1, 14
Let y(s) be the second derivative of s**7/14 + 31*s**6/10 - 81*s**5/4 + 173*s**4/4 - 35*s**3 - 2*s + 67. What is t in y(t) = 0?
-35, 0, 1, 2
Let k be (-1 - -2)/(4/(-18872)*2). Let a = k + 2408. Factor a + 1/4*i**2 + 7*i.
(i + 14)**2/4
Suppose 0 = 12*o + 93 - 849. Let w be ((-6)/o)/1 - (-220)/105. Factor -6/7*a**w - 15/7 + 3*a.
-3*(a - 1)*(2*a - 5)/7
Let k(v) be the third derivative of 0*v**3 - 1/9*v**4 - 1/630*v**7 - 14*v + 1/45*v**6 + 3*v**2 + 0 + 1/180*v**5. Factor k(j).
-j*(j - 8)*(j - 1)*(j + 1)/3
Let u = -37/192 + -75463/960. Let a = u - -79. Factor a*w**5 + 0*w**4 - 3/5*w**3 + 0 + 2/5*w**2 + 0*w.
w**2*(w - 1)**2*(w + 2)/5
Let j(i) be the second derivative of i**6/540 - 2*i**5/45 + 5*i**4/12 - 50*i**3/27 - 48*i**2 + 11*i - 4. Let o(h) be the first derivative of j(h). Factor o(l).
2*(l - 5)**2*(l - 2)/9
Let s = -619880 + 619882. Solve 24/13*u**s + 0 - 40/13*u - 2/13*u**3 = 0.
0, 2, 10
Let p be (-6 + -2)*7*(-214)/2247. Factor 8/3*b + p - 4/3*b**2 - 2/3*b**3.
-2*(b - 2)*(b + 2)**2/3
Let h be ((210/(-4))/3)/((-2)/4). Suppose 5*n - 26 = 4*j, 0 = -5*j + 3 + 2. Factor -3*m**2 - 3*m**2 + 9*m - 47*m**3 + n + 3*m**5 + h*m**3.
3*(m - 2)*(m - 1)*(m + 1)**3
Factor -3*k**3 + 186 - 11*k**2 + 24*k**2 + 99*k - 48*k**2 - 12*k**2 - 43*k**2.
-3*(k - 2)*(k + 1)*(k + 31)
Let c(h) be the first derivative of -h**3/3 + 777*h**2/2 + 778*h - 971. Determine m, given that c(m) = 0.
-1, 778
Factor 7*v - 3*v**4 + 6897*v**3 - 4*v - 9*v**2 - 6888*v**3.
-3*v*(v - 1)**3
Let x be -5 - -9 - (-1*112/24 + 1 + 6). Factor 0*j - x*j**5 + 3*j**3 + 0 + 0*j**2 + 4*j**4.
-j**3*(j - 3)*(5*j + 3)/3
Let c(u) = 42*u**2 - 1774*u + 1742. Let b(k) = 4*k**2 - k - 2. Let n(i) = -20*b(i) + 2*c(i). Factor n(r).
4*(r - 881)*(r - 1)
Let r(s) = -4*s**2 - 2576*s - 2800. Let q(d) = 4*d**2 + 2576*d + 2914. Let x(a) = -2*q(a) - 3*r(a). Factor x(h).
4*(h + 1)*(h + 643)
Suppose -6*y + 2668 = -8*y + 2*q, -2671 = 2*y + q. Let p = -9313/7 - y. Factor 4 + 4/7*l**2 + p*l.
4*(l + 1)*(l + 7)/7
Let j(v) = 2*v + 24. Let f be j(-11). Suppose 0 = g + 14 - 16. What is z in -5*z**g - 23*z - f*z**2 - z - 36 + 3*z**2 = 0?
-3
Let v(d) be the third derivative of -d**7/315 - 7*d**6/90 + d**5/6 + 3097*d**2. Factor v(a).
-2*a**2*(a - 1)*(a + 15)/3
Let k = 7 + -3. Let o(u) = 53*u - 4*u - 48*u. Let i(v) = v**2 + 4*v. Let t(w) = k*o(w) - i(w). Factor t(q).
-q**2
Let x(m) be the second derivative of -m**7/126 - 53*m**6/90 - 154*m**5/15 + 196*m**4/3 - 94*m + 4. Solve x(a) = 0 for a.
-28, 0, 3
Let -64 - 12/5*d + 2/5*d**2 = 0. What is d?
-10, 16
Suppose 330 + 35*o**2 - 4432*o - 4260*o + 8927*o = 0. What is o?
-33/7, -2
Let k = -4297/15 - -1439/5. What is f in -10/3*f**3 - 2/3*f + 16/3*f**2 - k = 0?
-2/5, 1
Let l(g) = g**2 + 12*g - 40. Let m be l(-15). Determine z so that 7 + 0 - m*z**2 + 2 + z**4 - 5 = 0.
-2, -1, 1, 2
Factor 7/3*f**2 + 887/3*f - 254/3.
(f + 127)*(7*f - 2)/3
Suppose 0 = -8270*d + 8372*d - 408. Suppose -64 - 33*k**2 + 80*k + 5*k**3 - 1/4*k**d = 0. What is k?
2, 8
Let l(r) be the third derivative of -r**5/20 + 143*r**4/4 - 20449*r**3/2 - 1449*r**2. Factor l(o).
-3*(o - 143)**2
Let g = 67283 - 605539/9. Suppose 0 - 2/9*n**5 + 2/3*n - 4/9*n**3 + g*n**2 - 8/9*n**4 = 0. What is n?
-3, -1, 0, 1
Let t(c) be the third derivative of -16/45*c**3 - 4/225*c**5 - 65*c**2 + 0 - 1/9*c**4 - 1/900*c**6 + 0*c. Factor t(n).
-2*(n + 2)**2*(n + 4)/15
Let j be (546/60 - (-7 + 19)) + 5. Let g(p) be the third derivative of -j*p**6 + 0*p + 0*p**3 + 56/15*p**7 - 4/5*p**5 - 18*p**2 + 0 + 2/3*p**4. Factor g(n).
4*n*(4*n + 1)*(7*n - 2)**2
Let s(p) be the second derivative of -p**6/10 - 12*p**5/5 - 19*p**4/2 + 8*p**3 + 117*p**2/2 + 916*p. Find i such that s(i) = 0.
-13, -3, -1, 1
Let w(q) = 4*q**3 + 16*q**2 - 18*q + 2. Let s = 601 - 596. Let l(h) = 9*h**3 + 32*h**2 - 36*h + 5. Let f(k) = s*w(k) - 2*l(k). What is z in f(z) = 0?
-9, 0, 1
Let i(d) be the second derivative of 0 - 162*d**2 + 3*d - 3*d**3 - 1/48*d**4. Suppose i(q) = 0. What is q?
-36
Let l be (9 - 752/120) + -5*(-77)/(-165). Determine p, given that -l*p**2 - 32*p - 640 = 0.
-40
Let l(v) be the second derivative of 22/3*v**4 - 16*v**3 + 18*v**2 + 2/15*v**6 + 17*v + 0 - 8/5*v**5. Solve l(g) = 0 for g.
1, 3
Suppose 484*a - 11050 = 59*a. Let y(w) be the second derivative of a*w + 25/2*w**3 - 5/2*w**4 - 20*w**2 + 0 - 1/4*w**5. Factor y(j).
-5*(j - 1)**2*(j + 8)
Let f be (-11592)/12420*(-105)/49. Let j = -111/8 + 14. Determine h, given that -j*h**3 - 1 - 7/8*h**f - 7/4*h = 0.
-4, -2, -1
Let p(n) = -9*n**3 - 1262*n**2 - 496*n + 8. Let f(h) = 4*h**3 + 421*h**2 + 165*h - 3. Let v(b) = 8*f(b) + 3*p(b). Factor v(i).
i*(i - 84)*(5*i + 2)
Suppose -5*k = -4*j + 31, -5*j - k = 3*k - 8. Suppose -d + j - 1 = 0. Factor 0 - 3/2*z**2 - 1/2*z**d + 0*z.
-z**2*(z + 3)/2
Suppose -1628 = 9*s - 16874. Factor 2*u**5 + 11*u**3 - s*u + u**3 - 10*u**4 + 1694*u.
2*u**3*(u - 3)*(u - 2)
Let r(n) be the second derivative of n**4/12 + 7*n**3/3 + 24*n**2 - 641*n. Factor r(g).
(g + 6)*(g + 8)
Suppose 13*t = 3*w + 184 - 126, -5*t = 3*w - 14. Factor -38/13*n**3 - 14/13*n**t - 2/13*n**5 - 50/13*n**2 - 8/13 - 32/13*n.
-2*(n + 1)**3*(n + 2)**2/13
Let p(t) = -2*t**3 + 3*t + 2. Let f(k) = -8*k**3 + 386*k**2 - 757*k + 388. Let v(z) = -2*f(z) + 6*p(z). Suppose v(m) = 0. What is m?
1, 191
Let x(h) be the second derivative of -h**5/15 + 13*h**4/6 - 3*h**2 + 97*h. Let k(p) be the first derivative of x(p). Factor k(f).
-4*f*(f - 13)
What is m in 336*m**3 - 231*m**2 + 192*m - 78*m**4 + 3*m**5 - 217*m**2 - 3*m - 2*m**2 = 0?
0, 1, 3, 21
Let g(c) = 5*c**4 + 15*c**3 - 35*c**2 + 160*c + 115. Let d(h) = 3*h**4 - 17*h**2 + 80*h + 58. Let t(b) = -5*d(b) + 2*g(b). Factor t(v).
-5*(v - 6)*(v - 2)*(v + 1)**2
Solve -15