he third derivative of -1/84*u**8 - 7*u**2 - 2/15*u**5 + 0*u + 8/105*u**7 - 2/15*u**6 + 5/6*u**4 + 0 - 4/3*u**3. Factor b(s).
-4*(s - 2)*(s - 1)**3*(s + 1)
Let n(m) = -m**2 + m - 1. Let f(u) be the second derivative of u**5/10 + u**4/3 + u**3 - u**2 + 14*u. Let a(p) = -2*f(p) + 4*n(p). Factor a(c).
-4*c*(c + 1)*(c + 2)
Let d(a) = -360*a**3 - a**2 + 1. Let p be d(-1). Determine i, given that 840*i**2 + 48*i**5 + 27 + 81*i + 180*i + 891*i**3 - 27*i**2 + p*i**4 = 0.
-3, -1, -1/4
Suppose 5/4*j**2 + 26*j - 1/4*j**3 + 0 = 0. Calculate j.
-8, 0, 13
Suppose 56*d - 752 = -132*d. Factor 2*o**2 + 0*o - 1/2*o**5 - 3/2*o**d + 0*o**3 + 0.
-o**2*(o - 1)*(o + 2)**2/2
Suppose -7*x - 30 = -30. Let u(n) be the second derivative of x*n**3 + 0 - 1/110*n**5 + 0*n**2 - 4*n - 1/165*n**6 + 1/231*n**7 + 1/66*n**4. Factor u(f).
2*f**2*(f - 1)**2*(f + 1)/11
Suppose 0 = 166*o - 100*o - 198. Find y such that 46*y**o - 4*y**4 - 225/4 + 345/2*y - 649/4*y**2 = 0.
3/4, 5
Suppose -145*a - 36 = -154*a. Factor 2/3*h**2 + 14/3*h + a.
2*(h + 1)*(h + 6)/3
Let a(x) be the second derivative of -x**5/3 + 35*x**4/24 + 5*x**3/3 + 12*x**2 - 29*x. Let f(j) be the first derivative of a(j). Factor f(u).
-5*(u - 2)*(4*u + 1)
Let j(u) be the third derivative of -u**7/280 - 3*u**6/32 - 158*u**2. What is c in j(c) = 0?
-15, 0
Let b(t) be the second derivative of t**9/1512 - t**8/840 - 7*t**3/6 - 14*t. Let i(f) be the second derivative of b(f). Factor i(q).
2*q**4*(q - 1)
Let d(o) = -o**2 + 11*o + 2. Let x be d(11). Suppose -5*z**2 - z**2 - z**x - 3*z = 0. What is z?
-3/7, 0
Let x(l) be the second derivative of -l**4/30 + 4*l**3/5 + 14*l - 3. Solve x(y) = 0.
0, 12
Suppose 2/9*r**4 - 2/9*r**2 + 8/9*r**3 - 8/9*r + 0 = 0. What is r?
-4, -1, 0, 1
Suppose -35 = -5*z - 2*l, -7*z + 35 = -3*z + 3*l. Determine t, given that -2/7*t**z - 32/7*t**3 + 32/7*t - 2*t**4 - 16/7*t**2 + 32/7 = 0.
-2, 1
Let p(v) = v**2 - 23*v + 48. Let n be p(21). Suppose 7*m + n - 20 = 0. Factor -1/2*b - 1/2*b**m - 1/6*b**3 - 1/6.
-(b + 1)**3/6
Let k(d) be the second derivative of d**4/8 + 3*d**3/4 - 21*d**2 - 133*d. Factor k(u).
3*(u - 4)*(u + 7)/2
Let w(i) be the second derivative of 0 + 1/95*i**5 - 5/57*i**3 + 1/114*i**4 + 2/19*i**2 + 26*i. What is b in w(b) = 0?
-2, 1/2, 1
Let p(w) be the second derivative of 0 - 30*w + 1/30*w**4 - 1/5*w**2 + 0*w**3. Find s, given that p(s) = 0.
-1, 1
What is f in -86*f + 4/3*f**2 + 128/3 = 0?
1/2, 64
Let z(n) be the first derivative of -5*n**6/39 - 76*n**5/65 + 33*n**4/13 + 40*n**3/39 - 61*n**2/13 + 36*n/13 + 167. Solve z(u) = 0.
-9, -1, 2/5, 1
Let h be -3*(1 + (-1)/((-4)/(-8))). Let s(x) be the first derivative of -1/21*x**h + 1/28*x**4 - 3/7*x - 9 - 5/14*x**2. Find d such that s(d) = 0.
-1, 3
Factor -369/2*o**3 + 0 - 75/2*o**4 + 15*o**2 + 0*o.
-3*o**2*(o + 5)*(25*o - 2)/2
Determine x so that 10*x**3 - 34/3*x**2 - 2/3*x**5 + 0 - 2*x**4 + 4*x = 0.
-6, 0, 1
What is h in -2/5*h**4 + 152/5*h**3 + 0 - 2888/5*h**2 + 0*h = 0?
0, 38
Let d = -1147/6 + 581/3. Let z(l) be the first derivative of 7/3*l**3 - 2*l - d*l**2 - 10. Factor z(b).
(b - 1)*(7*b + 2)
Determine h, given that 2*h - 48*h**3 + 10*h + 44*h**4 + 27*h**2 - 107*h**4 = 0.
-1, -1/3, 0, 4/7
Let p(u) be the second derivative of -u**5/50 + u**4/15 + u**3/3 - 6*u**2/5 - 271*u - 2. Factor p(q).
-2*(q - 3)*(q - 1)*(q + 2)/5
Let f be 15*1 + (-367 - -352). Determine i so that f*i + 4/5 - 4/5*i**2 = 0.
-1, 1
Solve -1/11*h**5 + 0 + 0*h**2 - 40/11*h**3 + 0*h - 14/11*h**4 = 0.
-10, -4, 0
Let j be (-1)/((-2)/(-18))*(-1)/3. Let a(l) be the first derivative of 7 - 1/9*l**j - 2/3*l**2 - l. Let a(z) = 0. What is z?
-3, -1
Let l(t) = 2*t**3 + 8*t**2 - 60*t - 3. Let u(g) = 15*g**3 + 55*g**2 - 420*g - 20. Let n(z) = 20*l(z) - 3*u(z). Factor n(r).
-5*r*(r - 3)*(r + 4)
Let n(v) = -7*v + 6. Let h(p) = -p. Let w(s) = 4*h(s) - n(s). Let r be w(6). Factor -3*u**2 - 28 - r*u + 43 - 27.
-3*(u + 2)**2
Let p(s) = -7*s**2 + 14*s**2 - 1 + s - 8*s**2. Let t(c) = -20*c**2 + 18*c - 16. Let z(j) = 36*p(j) - 2*t(j). Solve z(r) = 0 for r.
-1, 1
Let m(v) = -v. Let z be m(-1). Let a be 32 - z - (7 - 7). Factor 3*c**3 - 10*c - 35*c**2 + 4 + 7*c**3 + a*c**2.
2*(c - 1)*(c + 1)*(5*c - 2)
Suppose -203*z + 550*z - 1388 = 0. Solve 4/5*p - 16/15*p**z + 2/15 - 4/5*p**3 + 14/15*p**2 = 0.
-1, -1/2, -1/4, 1
Factor -39/2*w + 3/2*w**3 + 15/2*w**2 + 21/2.
3*(w - 1)**2*(w + 7)/2
Let p(o) = 3*o**4 - 147*o**3 + 423*o**2 - 418*o + 138. Let u(k) = -k. Let y(m) = p(m) - u(m). Let y(j) = 0. Calculate j.
1, 46
Let n(a) be the second derivative of a**4/6 - 4*a**3/3 + a**2 + a. Let t = -144 - -147. Let w(i) = i**2 - 7*i + 1. Let c(f) = t*n(f) - 4*w(f). Factor c(k).
2*(k + 1)**2
Let a(p) = -2*p**4 + p**2. Let w(d) = 15*d**4 + 6*d**3 - 45*d**2 + 30*d. Let i(g) = -6*a(g) - w(g). Factor i(u).
-3*u*(u - 2)*(u - 1)*(u + 5)
Suppose -10*j = -678 + 108. Suppose 65*n + n**3 - 3*n**3 + 2*n**2 - 8 - j*n = 0. What is n?
-2, 1, 2
Let i(w) = 2*w**2 - 2*w. Let n be i(2). Find y, given that 20*y**5 - 16*y**3 + 8 - 11*y**4 + 8*y**5 - 56*y**2 + 59*y**n - 12*y = 0.
-1, 2/7, 1
Let g(f) be the third derivative of f**6/720 - f**5/180 - f**4/36 + 2*f**3/9 - 4*f**2 + 2*f. Find p such that g(p) = 0.
-2, 2
Let f(m) = -16*m**5 + 20*m**4 - 4. Let u(a) = 15*a**5 - 19*a**4 + a**3 + 3. Let w(q) = 3*f(q) + 4*u(q). Let w(v) = 0. Calculate v.
0, 1/3, 1
Let g be (1 - 0 - 7)*1/(-6)*2. Factor 0 + 1/3*h**g + h.
h*(h + 3)/3
Factor 1095 + 66 - 282*z + 5466 + 3*z**2.
3*(z - 47)**2
Factor -78/7*w - 2/7*w**3 - 8 - 24/7*w**2.
-2*(w + 1)*(w + 4)*(w + 7)/7
Let x(a) be the first derivative of -1/3*a**3 - 2/3*a**6 - 12 + 13/4*a**4 - 9/2*a**2 - 2*a + 3/5*a**5. Solve x(k) = 0 for k.
-1, -1/4, 1, 2
Let w(l) be the third derivative of l**6/900 + l**5/150 + 17*l**3/6 + 7*l**2. Let u(a) be the first derivative of w(a). Find b, given that u(b) = 0.
-2, 0
Let j(d) = d**3 + 2*d**2 - 3*d. Let l(f) = -15*f**3 - 400*f**2 + 6165*f + 13690. Let r(a) = -20*j(a) - l(a). Factor r(k).
-5*(k - 37)**2*(k + 2)
Let z be (-3)/((-6)/10) + -27. Let c(b) = -b**2 - 23*b - 19. Let w be c(z). Find g, given that 6 + 14/3*g**2 - 10*g - 2/3*g**w = 0.
1, 3
Let j(l) be the first derivative of -l**6/10 + 27*l**5/20 + 10*l - 33. Let y(p) be the first derivative of j(p). Find b, given that y(b) = 0.
0, 9
Let v(f) be the second derivative of -f**7/1680 + f**5/240 - 7*f**3/6 + 4*f. Let y(h) be the second derivative of v(h). Factor y(a).
-a*(a - 1)*(a + 1)/2
Let z(w) be the third derivative of -w**8/2184 + 8*w**7/1365 + 14*w**2. Factor z(s).
-2*s**4*(s - 8)/13
Let c(v) = -5*v**2 + 68*v + 31. Let b be c(14). Solve 1/2*k**2 - 1/4*k**b - 1/4*k + 0 = 0 for k.
0, 1
Let g(z) be the first derivative of -2*z**3/39 + 10*z**2/13 + 22*z/13 - 186. Determine h, given that g(h) = 0.
-1, 11
Let t = 68 - 53. Suppose 2*d - t = -7. Factor -1/3*r + 1/3*r**3 - 1/3*r**2 + 1/3*r**d + 0.
r*(r - 1)*(r + 1)**2/3
Suppose -4*n - 126 = -2*r, 0*n = -3*n - r - 102. Let m = n + 36. Find z, given that 7*z - m*z + 3*z**2 - 10 + 2*z**2 + z = 0.
-2, 1
Let c = 11151 - 11148. Suppose 20/11*o**4 + 50/11*o**5 + 34/11*o + 40/11*o**2 + 4/11 - 148/11*o**c = 0. What is o?
-2, -1/5, 1
Suppose 6*u + 9 = m, -8*m + 3*m + 20 = -5*u. What is j in 2/3*j**2 + 1/3*j**5 - 4/3*j**4 + 2/3 - 5/3*j + 4/3*j**m = 0?
-1, 1, 2
Let y(b) be the second derivative of b**6/10 + 27*b**5/20 + 3*b**4/4 - 37*b**3/2 + 36*b**2 + 78*b + 2. What is u in y(u) = 0?
-8, -3, 1
Suppose -2*p = 6*p. Let i(o) be the third derivative of -5*o**2 + 1/330*o**5 + 0 + p*o - 1/66*o**4 + 1/44*o**6 + 0*o**3. Determine l, given that i(l) = 0.
-2/5, 0, 1/3
Let l(h) = h**3 - 5*h**2 + 7*h - 7. Let v be l(4). Let n = v - 2. Solve 2/3*r**2 - 1/3*r + r**n + 0 = 0.
-1, 0, 1/3
Let j(p) be the second derivative of -p**7/63 - 2*p**6/45 + 4*p**5/15 - 24*p + 2. Suppose j(k) = 0. What is k?
-4, 0, 2
Let t = 1346507 + -4051638991/3009. Let v = 8/177 + t. Let -14/17*m**3 + v*m**2 + 0 + 0*m = 0. What is m?
0, 2/7
Let x(g) = -3*g**2 + 4*g**2 - 1 + g + 5*g - 5*g. Let o(n) = 5*n**4 - 15*n**3 + 20*n**2 - 5. Let k(d) = o(d) - 5*x(d). Find l such that k(l) = 0.
0, 1
Let f be -3 + 1 + 8/(-3 - 1). Let i be 3 + (f - (3 + -4)). Suppose i - 4/5*y - 2/5*y**2 = 0. What is y?
-2, 0
Let a = 45 + -14. Suppose -a = -4*r - 23. Factor 2*o + o**2 - 6*o**2 - 2*o**3 - r + 7*o**2.
-2*(o - 1)**2*(o + 1)
Let a(t) be t