m(p) = 74*p**3 + 232*p**2 + 450*p - 660. Let i(t) = -6*t**3 - t**2 - 2*t + 1. Let x(c) = 12*i(c) + m(c). Factor x(q).
2*(q - 1)*(q + 3)*(q + 108)
Let d = 9 + -5. Let m be -1*(5 - d)*-19. Solve 1499*l**2 + 68*l**4 - 20*l**5 - m*l**3 - 45*l**3 - 1483*l**2 = 0.
0, 2/5, 1, 2
Let 170/7*s**3 + 156/7*s**2 + 30/7 + 6/7*s**4 - 23*s - 9/7*s**5 = 0. What is s?
-3, -2, 1/3, 5
Suppose 10 = 4*n - 6*n, n = -2*z + 5. Suppose 0 = -z*k + 5*g, 2*g = 3*k + g - 10. Suppose -5*j**3 - k*j**4 - 7 + 7 = 0. Calculate j.
-1, 0
Factor -2/23*l**2 - 128/23 - 130/23*l.
-2*(l + 1)*(l + 64)/23
Let y = -8740/3 + 218506/75. Let s(p) be the first derivative of 0*p**3 + 16/5*p**2 + 32/5*p - 37 - y*p**5 - 2/5*p**4. Factor s(b).
-2*(b - 2)*(b + 2)**3/5
Let f = 698 + -696. Solve -v**f - 95*v - 107 - 125 + 22 + 6*v**2 = 0.
-2, 21
Factor -15138/5*n - 2/5*n**3 + 0 - 348/5*n**2.
-2*n*(n + 87)**2/5
Let k(h) be the second derivative of 0 - 4/5*h**3 + 0*h**2 - 3/100*h**5 - 1/2*h**4 + 10*h + 1/50*h**6. Factor k(p).
3*p*(p - 4)*(p + 1)*(p + 2)/5
Let n(c) be the first derivative of c**3/7 + 99*c**2/7 + 3219*c/7 - 6162. Suppose n(p) = 0. What is p?
-37, -29
Let y(i) be the third derivative of -i**7/5040 - i**6/108 + 7*i**5/240 - 131*i**3/6 + 36*i**2. Let h(l) be the first derivative of y(l). Factor h(q).
-q*(q - 1)*(q + 21)/6
Let f(v) be the second derivative of v**5/180 + 869*v**4/36 + 188935*v**3/6 + 1697809*v**2/18 - 8*v - 434. Factor f(m).
(m + 1)*(m + 1303)**2/9
Let w(t) be the first derivative of 15*t**4/4 - 1825*t**3/3 + 30160*t**2 - 285940*t - 4662. Factor w(p).
5*(p - 58)**2*(3*p - 17)
Let v = 251 + -248. Factor 45*r**4 + 2531 - 40*r**v - 5*r**5 - 2531.
-5*r**3*(r - 8)*(r - 1)
Let z(g) be the first derivative of 0*g - 1/4*g**4 - 51 - 10/3*g**3 - 9/2*g**2. Suppose z(w) = 0. Calculate w.
-9, -1, 0
Find h, given that 52/5*h**2 + 32/5*h**3 + 2/5 - 23/5*h = 0.
-2, 1/8, 1/4
Let b(u) = -6*u**2 - 5*u - 10. Let d be b(-2). Let l = 27 + d. Solve h**l + 6*h + 0 + 0 - 7*h = 0 for h.
-1, 0, 1
Suppose w = 3, 0 = -2*o + 3*w + 15. Let k(h) = -h**3 + 10*h**2 + 13*h + 14. Let b be k(11). Factor -6 + 3 - 17 - 4*v**3 - o*v**2 + b*v.
-4*(v - 1)**2*(v + 5)
Let t(h) = 14*h**2 - 5050*h - 803879. Let i(r) = 4*r**2 - 1262*r - 200969. Let p(a) = -22*i(a) + 6*t(a). Factor p(o).
-4*(o + 317)**2
Suppose 60 = 2*w - 4*a + 350, -145 = w - a. Let m = w - -727/5. What is o in -8/5*o - 8/5 - m*o**2 = 0?
-2
Let z(o) be the second derivative of -o**4/3 - 26*o**3/3 + 126*o + 12. Solve z(f) = 0.
-13, 0
Let b(w) = -26*w**2 - 486*w + 529. Let l(n) = -124 + 162*n - 53 + 15*n**2 - 11*n**2 + 5*n**2. Let g(u) = -6*b(u) - 17*l(u). Factor g(t).
3*(t - 1)*(t + 55)
Let k be 192/102 + 82/697. Determine c so that -10/13*c - 2/13*c**3 - 8/13*c**k - 4/13 = 0.
-2, -1
Let l(w) be the first derivative of w**4/14 + 292*w**3/21 + 572*w**2/7 + 1136*w/7 + 132. Factor l(n).
2*(n + 2)**2*(n + 142)/7
Suppose 0 = 5*v - x - 12, -16 = -3*v + 2*x - 6. Suppose -5*g + v*q + 24 = 0, -36*g + 9 = -37*g + 5*q. Suppose 58/7*u + 8/7*u**3 - 12/7 - g*u**2 = 0. What is u?
1/4, 2, 3
Let m(k) be the third derivative of -k**8/336 + 11*k**7/35 + 7*k**6/120 - 38*k**5/5 - 33*k**4/2 + 5*k**2 + 671*k. Solve m(p) = 0.
-2, -1, 0, 3, 66
Find p such that -26*p - 4*p**2 - 362 - 15*p + 45*p - 478 + 112*p = 0.
14, 15
Let k(o) be the second derivative of 1/40*o**5 - 1/12*o**4 - 1/4*o**3 - o + 0*o**2 - 14. Find x such that k(x) = 0.
-1, 0, 3
Let i(a) = 10*a**3 + 1215*a**2 - 10140*a + 20650. Let l(k) = -5*k**3 - 607*k**2 + 5072*k - 10324. Let f(w) = 2*i(w) + 5*l(w). Find p, given that f(p) = 0.
-129, 4
Suppose 4*q - 56 = -2*v, 3*v - 3*q + 61 = 163. Factor v + 298*n - 109*n - 3*n**2 - 153*n + 7.
-3*(n - 13)*(n + 1)
Let o be 2356/7524 + 1/(-11)*(11 - 10). Determine f, given that 32/9 - o*f**3 + 2*f**2 - 16/3*f = 0.
1, 4
Let u(l) be the third derivative of 0 + 0*l + 25/3*l**3 + 1/30*l**5 - 210*l**2 - 5/6*l**4. Factor u(o).
2*(o - 5)**2
Let r(c) be the third derivative of -1/180*c**5 + 1/9*c**4 - 8/9*c**3 + 2*c**2 - 158 + 0*c. Factor r(s).
-(s - 4)**2/3
Let h(o) be the second derivative of 1/105*o**6 + 0*o**4 + 0*o**5 + 0*o**2 + 0*o**3 + 1/147*o**7 + 0 - 7*o. Determine k so that h(k) = 0.
-1, 0
Let m(o) be the first derivative of -2/21*o**3 + 0*o**2 + 2/7*o - 160. Solve m(g) = 0.
-1, 1
Let t = 9/428 - 7/1605. Let o(w) be the second derivative of -1/100*w**5 + 0*w**2 + 1/15*w**3 - t*w**4 - 7*w + 0. Find n such that o(n) = 0.
-2, 0, 1
Factor -1/2*z**3 - 4*z**4 + 0*z + z**2 + 0 - 5/2*z**5.
-z**2*(z + 1)**2*(5*z - 2)/2
Let l(w) be the third derivative of w**7/840 + w**6/120 - 43*w**3/3 + 5*w**2. Let q(o) be the first derivative of l(o). Solve q(z) = 0 for z.
-3, 0
Let p = 25361/3 + -8447. Let y(z) be the first derivative of -6*z**2 + 8*z - 24 - p*z**3. Let y(d) = 0. What is d?
-1, 2/5
Let i(v) be the first derivative of -v**4/78 - 8*v**3/39 + 48*v**2/13 - 170*v + 103. Let w(a) be the first derivative of i(a). Find f, given that w(f) = 0.
-12, 4
Suppose 5*v - 2*r = -3*r + 23, -v - 8 = -4*r. Let t be 0/(v*25/(-20)). Factor 3/4*j**2 + 0 + t*j.
3*j**2/4
Let y(r) be the second derivative of -r**5/50 - 67*r**4/30 - 203*r**3/3 + 735*r**2 + 9002*r. Factor y(d).
-2*(d - 3)*(d + 35)**2/5
Let q = -5771/15477 + 345/737. Factor 0 + 4/21*x**2 + 0*x - q*x**3.
-2*x**2*(x - 2)/21
Let z = 139 - -8. Suppose 7*b = z - 392. Let l(v) = 135*v**2 - 145*v - 180. Let h(t) = -15*t**2 + 16*t + 20. Let f(u) = b*h(u) - 4*l(u). Solve f(w) = 0.
-2/3, 2
Factor 1/5*z**2 + 1338/5*z + 447561/5.
(z + 669)**2/5
Let a(v) be the second derivative of 3*v + 5/2*v**4 - 3/2*v**5 + 9/2*v**3 + 1/14*v**7 - 27/2*v**2 - 8 - 1/10*v**6. Let a(k) = 0. What is k?
-3, -1, 1, 3
Suppose -435*j**3 + 477*j**3 - 765*j**2 - 3480*j + 288*j**3 - 21*j**4 - 924 = 0. Calculate j.
-2, -2/7, 7, 11
Let x(l) = 18*l - 155. Let m be x(10). Suppose -m*r + 5 = s - 23*r, -5*r = -5. Find f, given that -2/9*f**2 + 0*f + 0 + 1/9*f**s = 0.
0, 2
Let 111/2*w**2 + 35/2*w - 6 + 5/2*w**4 + 69/2*w**3 = 0. Calculate w.
-12, -1, 1/5
Let n(g) be the third derivative of -g**7/630 - g**6/15 - 319*g**4/24 - 17*g**2 + 6*g. Let j(o) be the second derivative of n(o). Find q such that j(q) = 0.
-12, 0
Factor -62/9*r**2 + 2/9*r**3 + 208/3*r - 224.
2*(r - 12)**2*(r - 7)/9
Let x(i) = -65*i**3 - 6*i**2 - 15*i - 5. Let b be x(-3). Factor 6*f**4 - 578 - b*f - 2*f**5 - 380*f**3 - 2376*f**2 + 844*f**2 + 56*f**4 + 75*f.
-2*(f - 17)**2*(f + 1)**3
Let z be (4 - -1)*3/(-9)*-3. Suppose -z*x = -5*i + 30, -5*i - 4 + 2 = 3*x. Factor -4/3 - 10/3*r - 8/3*r**i - 2/3*r**3.
-2*(r + 1)**2*(r + 2)/3
Determine x, given that -104/3*x - 2/9*x**3 + 50/9*x**2 + 0 = 0.
0, 12, 13
Let u(t) = t**2 + 3*t - 5. Let i(n) = -n + 11. Let d be i(9). Let f be u(d). Suppose 2*q**4 + f*q**3 - 4*q + 6*q**3 - 2 - 7*q**3 + 0*q**4 = 0. What is q?
-1, 1
Let c(s) be the first derivative of -s**5/5 - 16*s**4 + 66*s**3 - 100*s**2 + 67*s - 1103. What is p in c(p) = 0?
-67, 1
Let q(c) = c**2 - 336*c + 14065. Let d be q(287). Factor -d*u**3 + 2/5*u**4 + 4/5 - 14/5*u + 18/5*u**2.
2*(u - 2)*(u - 1)**3/5
Let a(m) be the first derivative of -m**4/32 - 5*m**3/12 + 443*m**2/16 - 54*m - 1079. Factor a(o).
-(o - 16)*(o - 1)*(o + 27)/8
Let 123 + 3/2*q**5 + 57*q**3 - 186*q**2 + 63*q**4 - 117/2*q = 0. Calculate q.
-41, -2, -1, 1
Let h be ((-24)/(-14))/((-11)/((-770)/(-20))). Let n be (h/(-4))/(0 - (-99)/44). Determine x so that n - 7/3*x**2 - 5/3*x = 0.
-1, 2/7
Let b be (4/(-6))/(((-15367)/363)/127). Determine t so that -3 - 1/9*t**b - 4/3*t = 0.
-9, -3
Factor -10/9 - 14/9*d**2 + 2/9*d**3 + 22/9*d.
2*(d - 5)*(d - 1)**2/9
Let k(m) be the first derivative of m**7/7980 + m**6/1140 - m**4/57 - 56*m**3/3 - 29. Let n(t) be the third derivative of k(t). Factor n(x).
2*(x - 1)*(x + 2)**2/19
Let q(i) be the third derivative of -i**5/300 - 5*i**4/24 + 112*i**3/15 + 1349*i**2. Suppose q(o) = 0. What is o?
-32, 7
Factor -1/3*h**3 - 463/3*h**2 - 7280/3 - 3656/3*h.
-(h + 4)**2*(h + 455)/3
Let k(g) be the first derivative of g**4 + 40*g**3 + 600*g**2 + 4000*g + 774. Factor k(l).
4*(l + 10)**3
Let z(w) be the third derivative of w**7/420 - 7*w**6/180 + 35*w**3/6 - 69*w**2. Let f(q) be the first derivative of z(q). Factor f(r).
2*r**2*(r - 7)
Let t be ((-5)/(-160)*8)/((-12)/114 + (-938)/(-6384)). Let 16/5 + 2/5*q**5 - 32/5*q**3 - 12/5*q**4 + t*q - 4/5*q*