lve d(b) = 0.
-2, 1
Let j(n) be the first derivative of -160*n**3 - 600*n**5 - 12 - 450*n**4 - 625/2*n**6 - 24*n**2 + 0*n. Let j(m) = 0. Calculate m.
-2/5, 0
Let l = 14 - 10. Suppose 0 = 2*c - 2*p - 14, -7 = c + l*p + 6. Let -m**2 + 0*m**2 + c*m**2 + 2*m**2 - 12*m = 0. What is m?
0, 3
Let g(v) be the third derivative of -v**6/30 + 2*v**5/15 + v**4/2 + 54*v**2. Factor g(m).
-4*m*(m - 3)*(m + 1)
Let x(h) be the second derivative of -3*h**5/20 + 8*h**4 - 285*h**3/2 + 675*h**2 + 231*h. Determine l so that x(l) = 0.
2, 15
Let h(f) = -f**3 + 31*f**2 - 146*f - 100. Let d be h(25). Let x(s) = -s - 6. Let l be x(-9). Suppose -3/5*v**l + d*v**2 + 0 + 0*v = 0. Calculate v.
0
Let i(v) be the third derivative of -v**10/50400 + v**8/6720 - v**5/60 - 11*v**2. Let u(z) be the third derivative of i(z). Solve u(s) = 0.
-1, 0, 1
Let n(a) be the second derivative of a**5/12 + 5*a**4/4 - 35*a**3/6 - 31*a**2/2 - 28*a. Let g(c) be the first derivative of n(c). Factor g(x).
5*(x - 1)*(x + 7)
Solve 86/9*o**3 - 32/9 - 146/9*o**2 + 112/9*o - 22/9*o**4 + 2/9*o**5 = 0.
1, 4
Let f be 3 - (-205)/(-65) - 82/(-26). Suppose -8*s = -21 - f. What is g in 8/3*g**3 - 1/3*g**4 - 22/3*g**2 - s + 8*g = 0?
1, 3
Let d(p) be the second derivative of -p**4/36 - p**3/9 + p**2/2 + 3*p + 2. Find v, given that d(v) = 0.
-3, 1
Suppose -2*a = -6 + 2. Let t(g) = 2*g**a - 12*g**2 - 1 - 3*g + 7 - 7*g. Let k(r) = 3*r**2 + 3*r - 2. Let m(n) = 7*k(n) + 2*t(n). Suppose m(w) = 0. What is w?
-2, 1
Let p(g) be the third derivative of g**8/294 - 13*g**7/735 + g**6/28 - g**5/30 + g**4/84 - 14*g**2 - 2*g. Factor p(o).
2*o*(o - 1)**3*(4*o - 1)/7
Factor -42434 - 36080 - 3*l**2 - 410*l + 7366 - 514*l.
-3*(l + 154)**2
Let q = 203/473 - -5/43. Let c(f) = -f**3 - 9*f**2 + 21*f - 8. Let j be c(-11). Factor 0*y + q*y**j + 0 - 4/11*y**2 + 0*y**4 - 2/11*y**5.
-2*y**2*(y - 1)**2*(y + 2)/11
Let w be (-10)/4 - 3/(-6). Let p be 6/9 + w/3. Let p - 2 + 3 - k**2 = 0. What is k?
-1, 1
Let u(k) be the first derivative of k**6/900 - k**4/180 - 21*k**2/2 + 18. Let q(r) be the second derivative of u(r). Find h, given that q(h) = 0.
-1, 0, 1
Factor -15/2 + 5/2*v**3 - 5/2*v + 15/2*v**2.
5*(v - 1)*(v + 1)*(v + 3)/2
Let m(i) be the second derivative of 5/6*i**4 + 3*i**2 - i + 0 + 1/10*i**5 + 7/3*i**3. Factor m(g).
2*(g + 1)**2*(g + 3)
Let c(j) be the first derivative of 25/4*j**4 - j**5 - 14 - 10*j - 15*j**3 + 35/2*j**2. Solve c(t) = 0.
1, 2
Let n(r) = 4*r**3 + 85*r**2 - 64*r + 45. Let g be n(-22). Factor -1/3*j**4 + 0*j**3 + 8/3*j + g + 2*j**2.
-(j - 3)*(j + 1)**3/3
Let h(w) be the first derivative of 1/5*w**2 - 15 + 0*w + 1/5*w**3 + 1/20*w**4. Determine b, given that h(b) = 0.
-2, -1, 0
Let p(d) be the third derivative of d**7/70 - d**6/40 - d**5/40 + 2*d**3 - 2*d**2. Let b(g) be the first derivative of p(g). Determine s so that b(s) = 0.
-1/4, 0, 1
Factor -113 + 3463*k - 3685*k - 106 - 3*k**2.
-3*(k + 1)*(k + 73)
Let n be (-14)/(-130) - 6/60. Let d(g) be the second derivative of 7*g - 2/39*g**3 + n*g**5 + 0*g**2 - 1/78*g**4 + 0. Factor d(o).
2*o*(o - 2)*(o + 1)/13
Let c(q) be the second derivative of -q**5/25 + 2*q**4 - 38*q**3/5 + 56*q**2/5 + 12*q. Factor c(k).
-4*(k - 28)*(k - 1)**2/5
Let m be 3458/399 - 2*4. Factor -1/2*w - m*w**4 - 7/6*w**3 + 7/3*w**2 + 0.
-w*(w - 1)*(w + 3)*(4*w - 1)/6
Let g(p) be the first derivative of p**4/3 - 4*p**3/9 + 86. Let g(c) = 0. What is c?
0, 1
Suppose 2*t + 82 = -4*c, -3*c = -4*c + 5*t - 15. Let v = -18 - c. Factor 4/3*l**3 - 2/3*l**4 + 0 + 2/3*l**v - 4/3*l.
-2*l*(l - 2)*(l - 1)*(l + 1)/3
Let t = 1467 + -1464. Find u such that -5/8*u + 1/4 - 1/8*u**t + 1/2*u**2 = 0.
1, 2
Let z(t) be the first derivative of 80/3*t**3 + 3 - 55/2*t**2 - 35/4*t**4 + 10*t. Solve z(n) = 0 for n.
2/7, 1
Factor -2/5*o**2 + 84/5*o - 882/5.
-2*(o - 21)**2/5
Factor 1/4*i**3 + 2*i + 0 - 9/4*i**2.
i*(i - 8)*(i - 1)/4
Suppose 3*s - 5 = -2*s. Let z(k) = 2*k**2 + 2*k - 2. Let f be z(s). Suppose 3*p**2 + f*p + 1/3 = 0. What is p?
-1/3
Suppose 0 = -5*s + 26 - 6. Suppose v - 4 + 0 = 0. Solve f - s*f - 3 + v*f + f**2 - 3*f = 0 for f.
-1, 3
Let g(q) = -12*q**2 - 24*q + 12. Let h(k) = -k**2 + 1. Let v = -29 - -28. Let b(s) = v*g(s) + 3*h(s). Factor b(a).
3*(a + 3)*(3*a - 1)
Let d(x) = x**3 + 4*x**2 - x - 2. Let w be d(-4). Suppose -w - 4 = -3*t. Factor -7*g**t - 3 + 0*g**3 - g**3 + 5*g + 4*g**3 + 2.
(g - 1)**2*(3*g - 1)
Let w = -4 - -1. Let t(x) = x**5 - x**4 - x**2 - x - 1. Let z(d) = 48*d**5 + 77*d**4 - 20*d**3 - 93*d**2 - 28*d + 7. Let j(k) = w*t(k) + z(k). Factor j(m).
5*(m - 1)*(m + 1)**3*(9*m - 2)
Let v(g) be the first derivative of 7*g**6/90 - 19*g**5/30 - g**4 + 31*g**3/3 + 9. Let i(m) be the third derivative of v(m). Find c, given that i(c) = 0.
-2/7, 3
Let c(o) = -o**3 + 6*o**2 + 11*o + 12. Let a be c(7). Suppose -48*m = -a*m - 24. Suppose 12/5*p**2 - 42/5*p + 9/5 + 18*p**m + 27/5*p**4 = 0. What is p?
-3, -1, 1/3
Suppose 0*t + 3*t**2 + 3*t**3 + 3/4*t**4 + 0 = 0. What is t?
-2, 0
Let v(g) be the first derivative of 1 - 40/3*g**3 - 2*g**2 + 32/5*g**5 + 10/3*g**6 + 8*g - 4*g**4. Factor v(d).
4*(d - 1)*(d + 1)**3*(5*d - 2)
Let v(b) = 15*b**2 + 29*b + 17. Let z(g) be the second derivative of 7*g**4/12 + 5*g**3/2 + 4*g**2 + 16*g. Let n(p) = 2*v(p) - 5*z(p). Factor n(r).
-(r + 3)*(5*r + 2)
Let z(x) be the third derivative of -x**8/1176 + 9*x**7/245 - 18*x**6/35 + 72*x**5/35 - 206*x**2. Find l such that z(l) = 0.
0, 3, 12
Let p be (0 - -1)/(-6) - (-36701)/588. Factor 130*q**3 + 1 + 13*q + 100*q**4 + p*q**2.
(4*q + 1)**2*(5*q + 2)**2/4
Let a(l) = 0*l - 3 + 3*l + 1 - 2*l. Let w be a(5). Factor -3/2*f**2 - w*f - 3/2.
-3*(f + 1)**2/2
Let d(f) be the third derivative of -f - 2*f**2 - 1/120*f**6 + 0*f**3 + 5/12*f**4 + 0 + 1/20*f**5. Factor d(o).
-o*(o - 5)*(o + 2)
Let k = -31 - -37. Let v be -1*3/3*k/(-4). Factor -3/2*u**2 + v*u + 1/2*u**3 - 1/2.
(u - 1)**3/2
Let y(c) be the first derivative of 3*c**2 + 1/10*c**4 + 18/5*c + 14/15*c**3 - 12. What is f in y(f) = 0?
-3, -1
Let y be (-1)/((-2)/2) + 3. Suppose -4*s - 10 = s, t - 11 = y*s. Factor t*z**2 + 4*z + z**2 + z**3 - 8*z**2 + 0*z.
z*(z - 2)**2
Let h be 45/(-75) + (-15)/(-25). Determine w, given that -9/4*w**4 + 3/4*w**5 + h + 0*w + 9/4*w**2 - 3/4*w**3 = 0.
-1, 0, 1, 3
Suppose 0*n - 3*n = -327. Let h be (-3)/18 + n/6. Factor 8*j**3 + 4*j**3 + j**4 + h*j**2 + j**4.
2*j**2*(j + 3)**2
Let b be (-8405)/(-1050) - 12 - (0 - 4). Let f(w) be the third derivative of -6*w**2 + b*w**5 + 1/21*w**3 + 0 - 1/42*w**4 + 0*w. Let f(i) = 0. Calculate i.
1
Let r(s) be the first derivative of s**4/6 - 20*s**3/9 + 32*s**2/3 - 64*s/3 + 17. Factor r(x).
2*(x - 4)**2*(x - 2)/3
Let n(h) = 6*h**4 + 8*h**3 - 16*h**2 - 30*h + 4. Let f(m) = 13*m**4 + 16*m**3 - 32*m**2 - 59*m + 10. Let u(r) = -2*f(r) + 5*n(r). Factor u(t).
4*t*(t - 2)*(t + 2)**2
Let l(b) be the third derivative of -40/3*b**3 + 0 + 12*b**2 - 1/12*b**5 + 0*b - 5/3*b**4. Let l(q) = 0. What is q?
-4
Let v(r) be the second derivative of 3/5*r**5 + 0 + 1/21*r**7 + 1/3*r**3 + 0*r**2 + 11*r + 2/3*r**4 + 4/15*r**6. Factor v(w).
2*w*(w + 1)**4
Let y = 43056541/195 - 220802. Let b = y - -1/39. Factor b - 8/5*h + 4/5*h**2.
4*(h - 1)**2/5
Let z(k) be the first derivative of -9 + 1/3*k**3 + 3*k**2 + 9*k. Factor z(a).
(a + 3)**2
Let k(i) be the first derivative of i**3/15 + 67*i**2/10 - 373. Factor k(x).
x*(x + 67)/5
Let v(u) = u**2 + 1 + 0 + 7*u**2 + u**2. Let m be v(1). Factor -24*y - 66*y**3 + 8*y**4 + 0*y**4 + m*y**4 + 84*y**2 - 3*y**4.
3*y*(y - 2)**2*(5*y - 2)
Let p(g) be the second derivative of -1/15*g**4 + 0 + 0*g**3 - 11*g + 0*g**2 + 1/50*g**5. Factor p(c).
2*c**2*(c - 2)/5
Let d(r) be the third derivative of 0 + 0*r**4 + 0*r**3 - 1/150*r**6 + 14*r**2 + 0*r - 1/525*r**7 - 1/150*r**5. Factor d(t).
-2*t**2*(t + 1)**2/5
Let r(v) be the second derivative of -3*v**5/50 - v**4/5 + 29*v**3/5 - 126*v**2/5 - 13*v - 2. Determine f, given that r(f) = 0.
-7, 2, 3
Suppose 928/5*g**3 + 14/5 - 58/5*g - 216/5*g**2 - 128/5*g**4 = 0. What is g?
-1/4, 1/4, 7
Let m be (-14)/(-10) + 4/(40/6). Solve 154 - 154 + 2*v**3 - 2*v**m = 0.
0, 1
Let v(r) = r**3 + 7*r**2 + 2*r + 16. Let w be v(-7). Suppose -w*a = 7*a - 27. What is b in 4/3*b**2 - 2/3 + b**a - 5/3*b = 0?
-2, -1/3, 1
Let c be 12*(-5)/(-10) + 4. Let b be 6 + 1020/(-175) + 4/c. What is f in 6/7*f**2 - b + 10/7*f = 0?
