645*w**3/6 - 2529*w**2. Factor f(q).
-5*(q - 1)**2*(q + 173)**2
Let l(p) be the first derivative of -p**6/120 + p**5/80 + p**4/96 + 53*p**2/2 - 47. Let t(m) be the second derivative of l(m). Suppose t(s) = 0. Calculate s.
-1/4, 0, 1
Let q(k) be the first derivative of k**4/2 - 128*k**3/3 + 235*k**2 + 600*k - 3215. Suppose q(g) = 0. What is g?
-1, 5, 60
Let o(l) = 6*l**2 - 3022 - 26*l + 2996 - 4*l**2. Let u be o(14). Factor -5/2*w - 25/4 - 1/4*w**u.
-(w + 5)**2/4
Suppose -x = 4*s + 15 + 8, -28 = 4*s. Let l(z) be the second derivative of 1/200*z**x + 6*z + 0 + 0*z**3 + 0*z**2 - 1/120*z**4. Factor l(i).
i**2*(i - 1)/10
Let d(b) = -8*b**2 - 87*b + 16. Let v be d(-11). Let s = 3569/5 + -713. Let -s - 6/5*q - 24/5*q**4 - 8/5*q**3 + 14/5*q**v + 28/5*q**2 = 0. What is q?
-1, -2/7, 1
Suppose 5*s - 5*q - 60 = 0, q + 23 = 4*s + 2*q. Suppose -21 = -s*r - 0. Find x, given that -3*x**2 - 4*x**2 + 10*x**2 + 3*x**r - 6*x**3 = 0.
0, 1
Suppose -3*s = -n + 4, 2*s + 0*s = -n - 1. Let q(u) = u**3 + u**2 + 1. Let d(y) = 6*y**3 + 16*y**2 - 56*y + 65. Let i(w) = s*d(w) + 5*q(w). Factor i(h).
-(h - 2)**2*(h + 15)
Suppose 0 = -27*o + 32*o + 4*q - 175, -3*q + 140 = 4*o. Let g(k) be the third derivative of 0*k + 0 + 0*k**3 + 1/240*k**5 + 1/96*k**4 - o*k**2. Factor g(d).
d*(d + 1)/4
Let r be -2*(5 - (1 - 1)). Let h(j) = 32*j**2 - 53*j + 18. Let n(v) = 16*v**2 - 26*v + 9. Let l(i) = r*n(i) + 4*h(i). Find p, given that l(p) = 0.
3/4
Let r(c) = 17*c**2 + 57*c. Let q(z) be the third derivative of -z**5/15 - 7*z**4/12 - 2*z**2 + z. Let s(a) = 9*q(a) + 2*r(a). Factor s(t).
-2*t*(t + 6)
Suppose -5*h - 7*w = -80, -42 = 1388*h - 1389*h - 4*w. Factor -2187/2 + 3/2*s**3 - 81/2*s**h + 729/2*s.
3*(s - 9)**3/2
Let z(l) = -14*l**3 - 21*l**2 - 25*l - 8. Let n be (4/(-12))/(16/96). Let m(t) = 6*t**3 + 10*t**2 + 12*t + 4. Let g(p) = n*z(p) - 5*m(p). Factor g(r).
-2*(r + 1)**2*(r + 2)
Suppose 2*k**2 - k**2 - 13045 - 26*k + 13114 = 0. What is k?
3, 23
Let r(a) = 41*a**3 + 7 + 12*a**2 + 13*a**2 + 3*a**4 - 348*a + 349*a. Let u(q) = 2*q**4 + 20*q**3 + 13*q**2 + q + 3. Let g(t) = -3*r(t) + 7*u(t). Factor g(p).
p*(p + 1)*(p + 2)*(5*p + 2)
Let a be 273/91 + (2/(-2))/(-1). Let l be (a/28)/((-32)/(-112)). Factor 0 + 2*h**2 - l*h**3 - 2*h.
-h*(h - 2)**2/2
Suppose -54*t = -267 - 235 + 178. Determine l, given that t*l**2 + 0 + 6*l - 6*l**4 - 9/2*l**3 - 3/2*l**5 = 0.
-2, -1, 0, 1
Let o = -31 - -36. Suppose 0 = -6*y + o*y + 2. Factor 3*c**5 + c**5 - 2*c**5 + 6*c**4 - 8*c**y.
2*c**2*(c - 1)*(c + 2)**2
Let a(i) be the second derivative of 0 - 2*i + 1/90*i**6 + 3/2*i**4 + 8/3*i**3 - 1/5*i**5 + 0*i**2. Let m(h) be the second derivative of a(h). Factor m(u).
4*(u - 3)**2
Suppose 171*a - 89 - 454 = -10*a. Let p(t) be the second derivative of -10*t - 2/3*t**3 + 0 + 1/6*t**4 - a*t**2. Factor p(m).
2*(m - 3)*(m + 1)
Let a(k) be the second derivative of 0*k**2 + 3/140*k**5 + 3 + 0*k**3 + 22*k + 1/7*k**4. Factor a(p).
3*p**2*(p + 4)/7
Let d(c) be the second derivative of 9/20*c**5 + 8*c**3 + 6*c + 3*c**4 - 9*c**2 + 1/40*c**6 + 0. Let n(a) be the first derivative of d(a). Factor n(s).
3*(s + 1)*(s + 4)**2
Let v(p) be the second derivative of p**7/630 + p**6/45 + 2*p**5/15 + 4*p**4/3 - 46*p + 2. Let s(g) be the third derivative of v(g). Factor s(k).
4*(k + 2)**2
Let w(m) be the first derivative of m**5/45 - 5*m**4/18 + m**3/3 + 989. Solve w(x) = 0.
0, 1, 9
Let d = -182 + 188. Let k(q) = 9*q**3 - 2*q**2 + 3*q**3 + 6*q + 6 - 2*q**3. Let t(h) = h**3 - h**2 + h + 1. Let v(g) = d*t(g) - k(g). Factor v(n).
-4*n**2*(n + 1)
Let x(j) be the first derivative of 18 + 4/3*j**3 + 12*j**2 - 28*j. Factor x(i).
4*(i - 1)*(i + 7)
Suppose -2*j + 5854 = 4*n, -5*j - 4*n + 14630 = n. Suppose 0 = 2*g + 3*g - j. What is a in 14*a**3 + g*a - 527*a + 60*a**2 - 3 + 15 = 0?
-3, -1, -2/7
Let j(w) be the second derivative of w**4/48 - 721*w**3/3 + 1039682*w**2 - 8620*w. Factor j(f).
(f - 2884)**2/4
Suppose -269*j + 982*j = 0. Factor 0*t + 2*t**4 + j - 8/3*t**3 + 2/3*t**2.
2*t**2*(t - 1)*(3*t - 1)/3
Let b = -61 - -73. Suppose -b = 2*w - 16. Factor -3 - 4 + 4*y**2 - w*y**2 + 5.
2*(y - 1)*(y + 1)
Let u(q) be the first derivative of 5*q**6/18 - 32*q**5/15 - 103*q**4/12 + 706*q**3/9 - 482*q**2/3 + 280*q/3 - 3196. Suppose u(f) = 0. Calculate f.
-5, 2/5, 2, 7
Let v(s) be the third derivative of 0*s + 0*s**3 + 0*s**4 - 4*s**2 - 1/60*s**6 + 21 - 19/15*s**5. Suppose v(r) = 0. What is r?
-38, 0
Let r be 0/(1 + -2) - (-9741 + 21). Factor -6*j**4 - 90452 - 360*j**3 + 11*j**4 + 615332 + r*j**2 - 116640*j.
5*(j - 18)**4
Suppose 4*q - 8 = 0, -4*o + 19 = -3*q + 5. Suppose 3038*p**4 - 220*p - 369*p**5 + 1315*p**3 - 2198*p**4 - 250*p**5 - 130*p**2 - 101*p**o + 40 = 0. What is p?
-2/3, 1/4, 2
Let m be 32/(-1952) + 2755/610. Factor -6 + 3/4*v**3 + 9/4*v**2 - m*v.
3*(v - 2)*(v + 1)*(v + 4)/4
Solve -426*m - 36396*m**2 + 3528 - 2*m**3 + 0*m**3 + 36470*m**2 - 470*m = 0 for m.
9, 14
Let d be ((-77)/21)/((-2)/6). Let i = 14 - d. Factor -45 - 6*q - 5*q**3 - 6*q - 6*q + 25*q**2 + i*q.
-5*(q - 3)**2*(q + 1)
Let r(h) = 54*h - 1186. Let g be r(22). Let i(n) be the third derivative of 11*n**g - 5/8*n**4 + 0*n + 0 + 1/10*n**5 + 3/2*n**3. Solve i(u) = 0 for u.
1, 3/2
Factor 2/7*w**4 + 0*w + 166/7*w**3 + 0 - 24*w**2.
2*w**2*(w - 1)*(w + 84)/7
Let s(f) = f**2 - 12*f + 12. Let y be s(11). Let a(i) = 21*i**3 + i**2 - i + 1. Let m be a(y). Let m*t - 5*t**4 - 22*t + 5*t**2 = 0. Calculate t.
-1, 0, 1
Let r be 3/((-9)/(-2)) - (-12)/9. Solve -o**2 + 6*o**r - 4*o + 13*o**2 + 0*o - 14*o**3 = 0.
0, 2/7, 1
Let l(r) be the first derivative of r**4/6 - 4*r**3/3 - 3*r**2 + 28*r/3 - 2042. Determine t so that l(t) = 0.
-2, 1, 7
Suppose -21 = 17*q - 55. Let n = 130 + -82. Find d, given that 22*d**3 - 16 - 108*d**3 - 34*d**3 + n*d - 100*d**4 + 44*d**q = 0.
-1, 2/5
Let -250*r**3 + 2/3*r**4 - 754/3*r**2 + 752/3 + 250*r = 0. What is r?
-1, 1, 376
Let g(r) be the second derivative of 711*r**5/100 - 1571*r**4/60 + 148*r**3/15 + 2*r**2/5 + 6*r - 857. Factor g(w).
(w - 2)*(9*w - 2)*(79*w + 1)/5
Let v(a) be the second derivative of 3*a**5/100 + 73*a**4/2 + 1454*a**3/5 + 4356*a**2/5 - 6923*a. Suppose v(c) = 0. Calculate c.
-726, -2
Let f(u) be the first derivative of 1/3*u**2 + 10/27*u**3 + 7 + 1/18*u**4 - 2/45*u**5 + 0*u. Factor f(g).
-2*g*(g - 3)*(g + 1)**2/9
Let v(h) be the second derivative of -7*h**7/54 - 7*h**6/5 - 52*h**5/15 + 101*h**4/54 - 5*h**3/18 - 971*h + 2. Let v(y) = 0. What is y?
-5, -3, 0, 1/7
Suppose -5*y + 4*w = -60, -14*w = 5*y - 13*w - 10. Let 88/3*a - 16/3 - 12*a**2 - 98/3*a**y - 238/3*a**3 = 0. What is a?
-2, -1, 2/7
Suppose -16*v - 12 = -13*v, 4*g + v = 1016. Let i = 14 - 10. Suppose -g*t**2 - i*t**3 - 13 + 20*t + 0*t**3 + 243*t**2 + 4*t**4 + 5 = 0. Calculate t.
-2, 1
Let i = 15 + -75. Let n be (-14)/10*i/210. Factor -2/5*m**3 + 2/5*m**4 + 2/5*m - n*m**2 + 0.
2*m*(m - 1)**2*(m + 1)/5
Let r be (102/18 + -4)/((-25)/(-30)). Suppose 54 + 4 - 4 - 19*v**r + 21*v**2 + 24*v = 0. What is v?
-9, -3
Suppose 0*o + 3 = o. Suppose 5*t + f = 7, -o*f = 3*t - 0 + 3. Determine a so that -3*a**4 - 9*a**4 + 10*a**4 + t*a**2 = 0.
-1, 0, 1
Let g(p) be the third derivative of 3 + 1/8*p**6 - 29*p**2 + 7/60*p**5 + 2/105*p**7 - p**4 + 0*p - 10/3*p**3. What is v in g(v) = 0?
-2, -1, 5/4
Let w(t) = 3*t**3 + 93*t**2 + 251*t. Let x(a) = -a**3 - 23*a**2 - 63*a. Let c(s) = -6*w(s) - 22*x(s). Factor c(v).
4*v*(v - 15)*(v + 2)
Let i(p) be the second derivative of -3*p**5/40 - p**4/48 + 239*p**3/24 - 42*p**2 + 2391*p. Let i(l) = 0. Calculate l.
-7, 3/2, 16/3
Suppose 72*s - 13406 + 6610 + 6436 = 0. Find g such that 30/7*g + 2 + 4/7*g**2 - 2/7*g**s - 18/7*g**4 - 4*g**3 = 0.
-7, -1, 1
Let a = 20/2811 + 27970/19677. Factor 2/7*m**2 - a + 8/7*m.
2*(m - 1)*(m + 5)/7
Factor -55837*k + 12154 - 105245*k**4 + 17430 + 1028*k**3 - 62155*k + 105248*k**4 + 81317*k**2 + 6060*k**2.
(k - 1)*(k + 172)**2*(3*k - 1)
Let o(i) = -3*i**4 - i**2 - i - 2. Let j(m) = 25*m**4 - 25*m**3 + 151*m**2 + 177*m + 16. Let z(n) = 5*j(n) + 40*o(n). Factor z(u).
5*u*(u - 13)**2*(u + 1)
Let n(o) be the third derivative of 1/30*o**5 - 1/945*o**7 + 1/540*o**6 + 0*o - 1/12*o**4 + 0*o**3 + 0 - 102*o**2. Factor n(s).
-2*s*(s - 3)*(s - 1)*(s + 3)/9
Let j(z) be the first derivative of -5*z**4 - 586*z**3/3 + 213*z**2 + 180*z + 150. Factor j(d).
-2*(d - 1)*(d + 