427. Factor 2/7*v - m*v**4 - 2/7*v**5 + 4/7*v**2 + 0*v**3 + 0.
-2*v*(v - 1)*(v + 1)**3/7
Let s(c) = 3*c**3 + 3*c**2 - 3*c + 1. Suppose -2*o + 0*o + 22 = 0. Suppose -4*i = o + 5. Let m(k) = 1. Let g(r) = i*m(r) + s(r). Solve g(v) = 0.
-1, 1
Let j(n) be the second derivative of -n**4/4 + n**3 - 106*n. Factor j(a).
-3*a*(a - 2)
Suppose 0 = m - 2*f - 4, m + 1 + 0 = -3*f. Factor -l**m + 7*l - 2*l - 6*l.
-l*(l + 1)
Let b be (-8 + 3)/(0 + -1). Suppose -g = -0*g - b. What is h in -h**5 - 4*h**2 + 2*h**g + 0*h**5 + 2*h**2 - h + 2*h**4 = 0?
-1, 0, 1
Let c(a) be the second derivative of 16*a + 1/210*a**7 - 1/15*a**4 + 0 + 0*a**3 + 0*a**2 - 1/25*a**5 + 1/150*a**6. Factor c(y).
y**2*(y - 2)*(y + 1)*(y + 2)/5
Let 4*v**4 - 7*v + 241 - 41*v**2 - 9*v + 233*v**2 - 304*v - 48*v**3 - 49 = 0. Calculate v.
2, 6
Let r(c) be the first derivative of -4 + 16*c**2 - 7/6*c**4 + 8/3*c**3 - 4*c + 1/10*c**5. Let z(t) be the first derivative of r(t). What is b in z(b) = 0?
-1, 4
Let a be 630/130 - (-4)/26. What is k in 1/7*k**a + 2/7*k**4 - 4/7*k**2 + 2/7 - 2/7*k**3 + 1/7*k = 0?
-2, -1, 1
Find c such that -2/5*c**3 - 1/5*c**4 + 0*c**2 + 1/5 + 2/5*c = 0.
-1, 1
Let t be 3/(-2 - (-55)/20). Factor -2*o**3 + 37*o + 9*o**t + 3*o**5 - 61*o - 36*o**2 - 4*o**3 + 0*o**3.
3*o*(o - 2)*(o + 1)*(o + 2)**2
Let r(p) be the first derivative of 5*p**3/3 - 20*p - 106. Find n such that r(n) = 0.
-2, 2
Suppose -156*y**2 + 156 - y - 3295*y**3 - 2*y + 3298*y**3 = 0. What is y?
-1, 1, 52
Let i(o) = -10 + 15*o**2 + 6*o**2 + 15*o - 22*o**2. Let m(l) = -10*l**2 + 165*l - 110. Let k(f) = -45*i(f) + 4*m(f). Factor k(u).
5*(u - 2)*(u - 1)
What is k in 0*k**2 + 4/5*k**4 + 0 - 1/10*k**5 + 0*k - 7/10*k**3 = 0?
0, 1, 7
Suppose 14/9*h**2 - 4/9*h + 2*h**3 + 0 = 0. What is h?
-1, 0, 2/9
Let u(f) be the second derivative of -f**8/6720 - f**7/1120 - f**6/720 - 16*f**3/3 - 3*f. Let v(g) be the second derivative of u(g). Factor v(j).
-j**2*(j + 1)*(j + 2)/4
Determine u so that 12/7 - 4*u - 8/7*u**3 + 1/7*u**4 + 23/7*u**2 = 0.
1, 2, 3
Let n(h) be the second derivative of h**4/18 - 32*h**3 + 6912*h**2 - 449*h. Factor n(j).
2*(j - 144)**2/3
Let p = 3/22 + 0. Let n = 1/33 + p. Suppose 1/6*b**3 + n*b + 0 - 1/3*b**2 = 0. What is b?
0, 1
Let s(x) be the third derivative of -x**8/560 - 3*x**7/175 + 7*x**6/200 - 3*x**2 + 26*x. Determine j, given that s(j) = 0.
-7, 0, 1
Suppose 0*s - 1/2*s**2 - 1/2*s**5 + 0 + 1/2*s**4 + 1/2*s**3 = 0. Calculate s.
-1, 0, 1
Let a(k) = k**2 + 8*k + 9. Let h be a(-7). Suppose 2*f**h - 4*f**2 + 2 + 4*f**2 + 4*f = 0. What is f?
-1
Let t(b) be the first derivative of b**2/2 - 5*b + 53. Let k be t(7). Solve 1/4 - 5/8*v**3 - 9/8*v - 3/8*v**4 + 13/8*v**k + 1/4*v**5 = 0 for v.
-2, 1/2, 1
Let w(u) = u - 21. Let o be (-1 - -3) + (-189)/(-9). Let l be w(o). What is c in -12/11*c - 18/11 - 2/11*c**l = 0?
-3
Let a(z) be the second derivative of 7*z + 2/33*z**3 + 0 + 0*z**2 - 1/66*z**4 + 1/77*z**7 - 1/22*z**5 + 1/165*z**6. Let a(m) = 0. What is m?
-1, 0, 2/3, 1
Let r be 5/((-15)/48) - -1. Let t be -1 + (-4 - 85/r). Suppose -t*w - 2/9 - 2/3*w**2 - 2/9*w**3 = 0. What is w?
-1
Suppose -246*a = -286*a + 120. Factor -2/11*w**2 + 4/11*w - 2/11*w**a + 0.
-2*w*(w - 1)*(w + 2)/11
Let v(w) be the first derivative of w**5 + 10*w**3 - 10*w**2 - 11 + 25/4*w**4 - 40*w. Suppose v(h) = 0. Calculate h.
-2, 1
Let y be (1456/48 + -27)*(-6)/(-25). Factor 36/5 + y*t**2 + 24/5*t.
4*(t + 3)**2/5
Let d(v) be the second derivative of -4*v**7/273 - 17*v**6/195 - 12*v**5/65 - v**4/6 - 2*v**3/39 - 501*v. Suppose d(a) = 0. Calculate a.
-2, -1, -1/4, 0
Suppose 5*a = -4*f + 11, 3*f - 14 = -28*a + 30*a. Factor 4/5*d**5 + 2/5*d + 18/5*d**3 + 2*d**2 + 14/5*d**f + 0.
2*d*(d + 1)**3*(2*d + 1)/5
Suppose -23*v = -1382 + 1290. Factor -17/2*h**2 - v + 3/2*h**3 + 11*h.
(h - 4)*(h - 1)*(3*h - 2)/2
Suppose 0 = 3*s + u + 26 + 29, 3*u + 3 = 0. Let d be (-20)/s*(-12)/(-30). Solve 0 + 2/9*x**2 + 2/9*x**4 + 0*x + d*x**3 = 0.
-1, 0
Let j(h) = -12 + 2 + 14*h - 15*h. Let o be j(-16). Suppose 3*c**2 + 41 + o*c**3 - 41 + 3*c**4 = 0. Calculate c.
-1, 0
Let a be 9/(-45)*(-10)/2 + 4. Find l, given that 127*l**5 - 129*l**a + 2*l**2 - 6*l**2 + 4*l**4 + 0*l**2 + 2*l = 0.
-1, 0, 1
Let b be ((-85)/51)/(1/3). Let o be (-10)/12*9/b. Find c, given that -3/4*c**3 + 0 - o*c + 9/4*c**2 = 0.
0, 1, 2
Let w be (-4)/6*(-6)/4. Suppose -w = r - 5. Suppose h - 10*h**r + 3*h**3 + 12*h**4 + 2 - 4*h**2 - 4*h = 0. Calculate h.
-2, -1, 1/2, 1
Suppose 565*n = 579*n. Factor 3/2*m**3 + n - 9*m**2 + 27/2*m.
3*m*(m - 3)**2/2
What is j in 3/5*j**2 - 3/5*j - 6/5 = 0?
-1, 2
Let b(q) be the second derivative of q**5/4 - 65*q**4/3 + 172*q. Suppose b(i) = 0. Calculate i.
0, 52
Let 52*h**2 - 4*h**3 + 0*h**3 + 10*h**2 - 26*h**2 = 0. What is h?
0, 9
Let r be (-3 + 75)*1/2. Determine l, given that r*l**3 - 14 + 14 - 8*l**2 - 48*l**4 + 20*l**5 = 0.
0, 2/5, 1
Let v = 7 + -4. Solve 8*h**v + 2*h + 22*h**2 - 28*h**3 + 17 - 21 = 0 for h.
-2/5, 1/2, 1
Let b be (-32)/(-14) + (-4)/14. Let -2*p**b + 0*p**2 + 2*p**2 - 3*p**2 - 3*p**3 = 0. Calculate p.
-1, 0
Let i(u) be the first derivative of -3/20*u**5 + 11 - 15/16*u**4 + 0*u - 2*u**3 - 3/2*u**2. Solve i(o) = 0 for o.
-2, -1, 0
Let i be (-8)/14 + (-150)/(-42). Factor -6*r**2 - 28 + 19 + 4*r**3 - r**i - 15*r + 3*r**2.
3*(r - 3)*(r + 1)**2
Let s(g) = -3*g + 21. Let c be s(11). Let i be ((-9)/c)/((-2)/(-8)). Solve -8/5 - 16/5*j - 2/5*j**i - 2*j**2 = 0 for j.
-2, -1
Let n be (-23)/35 - (-356)/445. Determine j, given that -1/7*j + 2/7 - n*j**2 = 0.
-2, 1
Let q(d) be the second derivative of -d**9/7560 - d**8/1120 + d**6/90 - d**4 + 14*d. Let o(p) be the third derivative of q(p). Factor o(b).
-2*b*(b - 1)*(b + 2)**2
Factor -3/8*q**2 - 105/4*q - 3675/8.
-3*(q + 35)**2/8
Let 34848*x + 2/9*x**5 + 7334/9*x**3 + 206/9*x**4 + 10978*x**2 + 31944 = 0. Calculate x.
-33, -2
Factor -22/9*t**2 + 50/9*t - 26/9 - 2/9*t**3.
-2*(t - 1)**2*(t + 13)/9
Let k be (-1)/(-3) - 22/(-6). Let v(l) = 2*l**2 - 4. Let o be v(-2). Factor -50 + 50 + k*j - o*j**3.
-4*j*(j - 1)*(j + 1)
Let p(w) be the third derivative of -w**7/840 + w**6/960 + 5*w**4/24 + w**2. Let q(y) be the second derivative of p(y). Factor q(c).
-3*c*(4*c - 1)/4
Let b(g) be the first derivative of 14 + 1/10*g**6 - g**4 + 3/10*g**5 - 14*g + 9/2*g**2 - g**3. Let f(k) be the first derivative of b(k). Factor f(t).
3*(t - 1)**2*(t + 1)*(t + 3)
Suppose -4*k = 2*q - 20, 0 = 14*q - 2*k + k + 5. Find w such that q + 2/7*w + 2/7*w**2 = 0.
-1, 0
Let g(x) be the second derivative of 0 + 33*x + 1/2*x**4 + 1/6*x**5 + 1/45*x**6 + 2/3*x**2 + 7/9*x**3. Suppose g(y) = 0. Calculate y.
-2, -1
Suppose 36*j - 31*j = 4*p + 46, 0 = 2*j + 15*p + 131. Let t + 5/6 + 1/6*t**j = 0. What is t?
-5, -1
Let i(r) be the third derivative of 0 - 1/720*r**6 + 0*r + 1/72*r**5 - 41*r**2 - 5/36*r**3 + 1/144*r**4. Factor i(w).
-(w - 5)*(w - 1)*(w + 1)/6
Let d be ((-6)/(-3) - 3)*-8. Suppose 0 = 3*k - 4 - d. Factor -25*p**3 - 4*p - 21*p**3 + 38*p**3 - 10*p**2 - 2*p**k.
-2*p*(p + 1)**2*(p + 2)
Let p(v) be the first derivative of -3*v**4 - 3/5*v**5 + 12*v - 12 + 6*v**2 - 3*v**3. Solve p(a) = 0 for a.
-2, -1, 1
Let l(q) = -q**3 - 13*q**2 + 27*q - 45. Let n be l(-15). Let z(h) be the first derivative of 4/25*h**5 + n*h**2 + 4/15*h**3 - 1/2*h**4 + 0*h + 12. Factor z(m).
2*m**2*(m - 2)*(2*m - 1)/5
Let a = 271/1698 - -2/283. Let w = 243 - 1457/6. What is c in 0 + a*c**5 - w*c**4 + 1/3*c - 1/2*c**3 + 1/6*c**2 = 0?
-1, 0, 1, 2
Let t = -598 - -611. Let u(x) be the first derivative of -6/7*x**3 + 0*x + t - 1/2*x**4 - 2/7*x**2. Solve u(k) = 0 for k.
-1, -2/7, 0
Factor -33*m**3 - 42*m**2 - 12*m**4 - 6 - 3/2*m**5 - 51/2*m.
-3*(m + 1)**4*(m + 4)/2
Let v(k) be the first derivative of -k**6/3 - 2*k**5 + 33*k**4/2 + 54*k**3 - 432*k**2 + 648*k + 260. Determine c, given that v(c) = 0.
-6, 1, 3
Suppose 378/5*p**3 - 6/5*p**5 + 984/5*p + 288/5 + 996/5*p**2 + 33/5*p**4 = 0. What is p?
-2, -1/2, 12
Let j = 1951 - 1948. Factor 2/15*v**j - 2/15*v**2 + 0*v + 0.
2*v**2*(v - 1)/15
Let d(i) be the first derivative of 15/2*i**2 - 10*i - 5/4*i**4 + 0*i**3 - 25. Solve d(j) = 0.
-2, 1
Factor 160*i**2 - 15*i**3 - 145*i**2 - 5*i**3 - 5*i**3.
-5*i**2*(5*i - 3)
Let a(o) be the third derivative of -o**7/5880 - o**6/630 + o**5/280 + 3*o**4/28 - 10*o**3/3 + 15*o**2. Let q(y) be the first derivative of a(y)