*d + 28*d = 0?
-8, -2
Determine b so that -14154*b**2 + 5280*b - 56672*b**4 + 28340*b**4 + 28323*b**4 - 717*b**3 + 9600 = 0.
-40, -2/3, 1
Let j(d) be the first derivative of d**4/30 - 128*d**3/45 + 244*d**2/15 - 32*d + 174. Find v, given that j(v) = 0.
2, 60
Let f be (3 + (-114)/40)/((-192)/(-160)). Let p(d) be the third derivative of f*d**4 - 1/40*d**6 - 10*d**2 + 0 + 2*d**3 + 0*d - 1/5*d**5. Factor p(o).
-3*(o - 1)*(o + 1)*(o + 4)
Suppose -3*x - 539 = -4*o + 224, 3*o - 2*x - 572 = 0. Suppose 4*u = 2*k + 66 - o, 3*u = -3. Factor -6*w - 59*w**2 - 6*w + k*w**3 + 44*w**2 - 35*w**4 + 2*w.
-5*w*(w - 1)**2*(7*w + 2)
Suppose i + 60 - 301 = -4*g, 297 = 5*g - 3*i. Suppose -o + 11*o = g. Find v such that -17*v**3 - 2*v**4 + 10*v + o*v**4 + 7*v**3 + v**4 - 5*v**2 = 0.
-1, 0, 1, 2
Factor 72*m + 106 - 154*m - 5*m**2 - 446 - 23*m.
-5*(m + 4)*(m + 17)
Let v(b) be the first derivative of b**4/12 - 7*b**3/2 - 327*b + 52. Let a(w) be the first derivative of v(w). Factor a(f).
f*(f - 21)
Let u be (-3)/(-1)*(-506)/33. Let s be u/(-14) + 22/(-77). Suppose 19*m**2 - 25*m**4 + 5*m**5 + 7*m**2 + 0*m**2 - 5*m**s - m**2 = 0. What is m?
-1, 0, 1, 5
Suppose -637*w = 715*w + 1732*w - 7893 - 1359. Factor 5/8*d**2 - 5/8 - 1/8*d + 1/8*d**w.
(d - 1)*(d + 1)*(d + 5)/8
Let s = -76/5919 - -10548/1973. Determine p so that 14/3*p**5 + 44/3*p**3 + 0 - 278/9*p**4 - s*p + 152/9*p**2 = 0.
-2/3, 0, 2/7, 1, 6
Let n = 498 - 649. Let d = n - -151. Factor d + 2*t**2 + 1/2*t + 2*t**3.
t*(2*t + 1)**2/2
Let o = 794104/3 + -264698. Find j such that 128 - 736/3*j + 166/3*j**2 - o*j**3 = 0.
3/5, 8
Suppose -2*a - 5*u = 1, 2*a - 1 = 5*u - 8*u. Let 3*r - 75*r**a - r + 3*r = 0. Calculate r.
0, 1/15
Let a be (-8)/(-20) - (1708/(-20))/(-1). Let d be (-33)/(-15) + 17/a. Factor -105/2*p + 20*p**d - 5/2*p**3 + 45.
-5*(p - 3)**2*(p - 2)/2
Let p(j) be the second derivative of 7*j**5/10 + 65*j**4/6 - 7234*j**3/3 - 2072*j**2 + 123*j + 5. Factor p(z).
2*(z - 28)*(z + 37)*(7*z + 2)
Let o(l) = 18*l**4 + 36*l**3 - 576*l**2 + 517*l + 1134. Let z(v) = -3*v**4 - 6*v**3 + 96*v**2 - 86*v - 189. Let c(q) = 4*o(q) + 23*z(q). Factor c(x).
3*(x - 3)**2*(x + 1)*(x + 7)
Let r = 303458 - 303456. Let 31/3*u**r - 1/3*u**3 + 0*u + 0 = 0. Calculate u.
0, 31
Let g = -3383 + 3383. Let y(i) be the second derivative of g*i**2 - 1/120*i**5 + 0 - 10*i - 1/36*i**4 + 0*i**3. Factor y(k).
-k**2*(k + 2)/6
Let g(l) be the second derivative of 1/3*l**3 + 12*l - 1/180*l**6 - 6*l**2 + 1/90*l**5 + 5/36*l**4 + 0. Let i(k) be the first derivative of g(k). Factor i(m).
-2*(m - 3)*(m + 1)**2/3
Let h = -898 - -916. Let a be (-1)/(h/3 + -9). Factor 5/3*f + 4/3 + a*f**2.
(f + 1)*(f + 4)/3
Let u(a) be the second derivative of a**10/30240 - a**9/7560 + 21*a**4/4 + 109*a. Let d(v) be the third derivative of u(v). Let d(o) = 0. Calculate o.
0, 2
Let b(w) be the second derivative of w**4 + 1/14*w**7 - 1/10*w**6 - 3/5*w**5 + 0*w**2 + 11*w - 2 + 0*w**3. Factor b(f).
3*f**2*(f - 2)*(f - 1)*(f + 2)
Let k be 25 - (-36)/(-27)*3. Suppose -13*x = -k*x. What is a in 8/5*a**2 - 2/5 - 4/5*a**3 - 6/5*a**4 + x*a + 4/5*a**5 = 0?
-1, -1/2, 1
Suppose -5*c + 5*y - 4 + 19 = 0, y - 9 = -2*c. Let u(o) be the second derivative of -1/15*o**3 + 1/30*o**c - 3*o + 0 - 1/150*o**5 + 1/15*o**2. Factor u(h).
-2*(h - 1)**3/15
Let f(c) = 2*c + 2. Let t(d) be the first derivative of -d**3/3 + 7*d + 18. Let s be t(3). Let m(j) = j**2 - 6*j - 7. Let g(q) = s*m(q) - 7*f(q). Factor g(p).
-2*p*(p + 1)
Let f(l) be the second derivative of -1/15*l**6 - 4*l**2 + 2 - 3/10*l**5 - 53*l + l**3 + 5/6*l**4. Find y, given that f(y) = 0.
-4, -1, 1
Suppose -4*o + 247 = 135. Suppose -4*r + o = 5*w, -2*r + 4*w = -1 + 13. Find j, given that -2*j**3 - 2*j**3 + 836*j**r + j**4 - 833*j**2 = 0.
0, 1, 3
Suppose -25 + 21 = -2*p. Let k be (-18)/(-4) - 7/(-14). Determine g, given that 5*g - k*g**3 + 0 + 5/4*g**p - 5/4*g**4 = 0.
-4, -1, 0, 1
Let x(m) be the third derivative of m**7/525 + 56*m**6/15 + 157916*m**5/75 + 20832*m**4 + 415152*m**3/5 - 6000*m**2. Determine k so that x(k) = 0.
-558, -2
Suppose 2*h = 4*y - 32, -1834*h + 22 = -1832*h + 2*y. Factor 28/19*q + 48/19 + 2/19*q**h.
2*(q + 2)*(q + 12)/19
Let w(c) be the third derivative of -c**7/840 - c**6/24 - 5*c**5/8 + 19*c**4/4 + 52*c**2. Let j(b) be the second derivative of w(b). Factor j(k).
-3*(k + 5)**2
Let n(l) be the first derivative of 8*l**3/3 - 13*l**2 - 24*l - 37. Let h(k) = -k**2 + k + 1. Let g(a) = 10*h(a) + n(a). Factor g(i).
-2*(i + 1)*(i + 7)
Suppose 57 = 5*o - 208. Let l be 212/o*(2 - 3/2). Factor 1/2 - v + 1/2*v**l.
(v - 1)**2/2
Let y = 19 + -16. Let i be (-52)/78*-2*y. Factor -2/7*q**2 + 0 + 2/7*q**i + 2/7*q**5 - 2/7*q**3 + 0*q.
2*q**2*(q - 1)*(q + 1)**2/7
Let g(c) be the third derivative of -c**5/180 + 53*c**4/24 - 310*c**3/9 + 9588*c**2. Let g(o) = 0. Calculate o.
4, 155
Find b such that -326/3*b**2 + 4/3*b**5 - 10 - 76/3*b**4 + 87*b**3 + 167/3*b = 0.
1/2, 1, 2, 15
Let p(h) = -2*h**4 + 43*h**3 - 67*h**2 - 220*h + 357. Let g(s) = -s**4 + 4*s**3 - s**2 + 1. Let l(c) = 3*g(c) + p(c). Find t such that l(t) = 0.
-2, 2, 9
Suppose -485 = -7*r - 485. Suppose -m + 0*m + 3*x - 12 = r, -2*m + x - 4 = 0. Factor 1/5*d**4 + 1/5*d**3 - 1/5*d**2 + m - 1/5*d.
d*(d - 1)*(d + 1)**2/5
Let n(g) be the third derivative of 37/18*g**4 + 21*g**2 + 4 + 0*g - 4/3*g**3 - 5/6*g**5 - 91/120*g**6 + 7/90*g**7. Factor n(k).
(k - 6)*(k + 1)*(7*k - 2)**2/3
What is k in -172*k - 90*k**2 + 704965 - 2*k**3 - 704965 = 0?
-43, -2, 0
Let s(r) be the third derivative of r**6/960 + 3*r**5/160 - 11*r**4/96 + 4*r**2 + 95*r. Factor s(c).
c*(c - 2)*(c + 11)/8
Let q be (1089/77 - 14)*(385/20)/11. Solve -1/4*w - 7/4*w**2 + q*w**3 + 3/2 + 1/4*w**4 = 0.
-3, -1, 1, 2
Suppose 0 = 44*d + 179 - 707. Let w be d - 8 - (-36)/(-14). Let -12/7 - 2/7*m**2 - w*m = 0. Calculate m.
-3, -2
Let f = 18794/165 + -1250/11. Let w(p) be the third derivative of 0 + 1/30*p**4 - 1/150*p**6 + 0*p + 2/75*p**5 - f*p**3 - 14*p**2. Factor w(r).
-4*(r - 2)*(r - 1)*(r + 1)/5
Let -46/3*g - 31/2 + 47/3*g**2 + 46/3*g**3 - 1/6*g**4 = 0. What is g?
-1, 1, 93
Suppose 6*q - 5*q = 3. Let f(m) = -4*m**2 + 0*m**2 - 7*m + q*m**2 + 8*m. Let y(t) = 7*t**2 + 20*t + 21. Let w(n) = 4*f(n) + y(n). Factor w(o).
3*(o + 1)*(o + 7)
Let r(w) = w**2 - 20*w - 362. Let h be r(31). Let k be 6*28/h + 8. Factor -1/3*t + 1/3*t**2 + k.
t*(t - 1)/3
Let i be (4218/133 + -31)/(33/154). What is s in -14/3 + 26/3*s - i*s**2 - 2/3*s**3 = 0?
-7, 1
Let u = -20175/11 + 1837. Let t = u + -28/11. Factor -2/11 + t*r**2 - 2/11*r.
2*(r - 1)*(2*r + 1)/11
Let h(f) be the second derivative of 3*f**5/20 + 67*f**4/2 + 262*f**3 + 780*f**2 + 39*f + 18. Solve h(r) = 0.
-130, -2
Suppose 5*u - 11*d - 5 = -6*d, 0 = -4*d + 12. Suppose 5*k - 10 = -3*n, 4*n = k - 3*k + u. Factor -20/13*f + 50/13 + 2/13*f**k.
2*(f - 5)**2/13
Suppose -5*i + 22 = -18. Suppose -2*m - 2*f + 4*f = -i, 4*m = -3*f + 16. Suppose -m*k**3 + k + 2*k**3 - k**3 + 2*k + 3*k**2 - 3 = 0. What is k?
-1, 1
Let n be 101 + -9 - (-7 + 2 + 3). Suppose 5*v - 4*y - 23 = 0, -n*y - 8 = -4*v - 96*y. Suppose 0*i**2 + 0 + 0*i**4 - i**v + 1/2*i**5 + 1/2*i = 0. Calculate i.
-1, 0, 1
Let q(u) be the second derivative of 961*u**4/12 - 31*u**3 + 9*u**2/2 + 12303*u. Factor q(z).
(31*z - 3)**2
Suppose -3*n = 4*f - 12, 8 = -n + 3*n. Let q be ((-16)/20 - f)*-20. Factor -69*i**2 - 6 - 3*i**2 - q*i**3 + 34*i**2 - 28*i.
-2*(i + 1)**2*(8*i + 3)
Let s(l) be the second derivative of -1805*l**5/4 - 13585*l**4/3 - 1141*l**3/6 - 3*l**2 - 7481*l + 1. Determine y so that s(y) = 0.
-6, -1/95
Let a(r) = r**3 + 54*r**2 - 53*r + 118. Let x be a(-55). Let w(q) be the first derivative of 22 - 2*q**2 + x*q - 4/3*q**3. Let w(t) = 0. Calculate t.
-2, 1
Let c(w) = 103*w**3 + 103*w**2 - 104*w - 100. Let x(d) = d**4 + d**3 - d**2 - 3. Let r(i) = 4*c(i) + 4*x(i). Factor r(o).
4*(o - 1)*(o + 1)**2*(o + 103)
Let j = 1614 + -1610. Let k(l) be the second derivative of 13*l + 8*l**2 + 0 + 1/3*l**j + 10/3*l**3. Find b, given that k(b) = 0.
-4, -1
Let c = 10105 - 10100. Let l(g) be the third derivative of 0 + 1/144*g**4 - 1/720*g**6 - g**2 - 1/360*g**c + 1/36*g**3 + 0*g. Factor l(p).
-(p - 1)*(p + 1)**2/6
Let n be ((-2)/(-4))/(27577/(-2508) - -11). Suppose -n + 159 = 15*h. Let -24 - 9/2*r**2 - 18*r - 3/8*r**h = 0. Calculate r.
-4
Let w(a) be the first deri