 + 16)*(2*h + 1)/3
Let m(k) = -k**4 - 12*k + 0*k**3 + 16 - 4*k**3 + 5*k**4 - 4*k**2. Let s(b) = -b + 1. Let d(p) = m(p) - 16*s(p). Find y such that d(y) = 0.
-1, 0, 1
Let w(z) be the second derivative of -16*z + 9/5*z**4 + 0*z**2 + 4/5*z**3 + 0 - 1/2*z**6 + 9/10*z**5. Find l such that w(l) = 0.
-2/5, 0, 2
Let y(t) be the second derivative of 5*t**7/42 - t**6/3 + 5*t**4/6 - 5*t**3/6 + 101*t. Suppose y(v) = 0. What is v?
-1, 0, 1
Let j(v) = 9*v**4 + 36*v**3 + 72*v**2 + 24*v + 3. Let w(q) = 17*q**4 + 73*q**3 + 142*q**2 + 48*q + 5. Let c(t) = -5*j(t) + 3*w(t). Factor c(s).
3*s*(s + 2)*(s + 4)*(2*s + 1)
Let k(q) be the third derivative of 2*q**2 + 7/24*q**4 - 7/120*q**6 + 1/42*q**7 - 1/20*q**5 + 0 - 1/3*q**3 + 0*q. Find d such that k(d) = 0.
-1, 2/5, 1
Let c(p) be the third derivative of 43*p**2 + 0*p - 1/450*p**5 + 0 - 1/90*p**4 + 0*p**3. Find y such that c(y) = 0.
-2, 0
Let t = 27 - 15. Let p = 17 - t. Factor 30*j - j**p - 30*j + j**3.
-j**3*(j - 1)*(j + 1)
Let z(y) be the second derivative of -y**6/840 - 3*y**5/280 - y**4/28 + 25*y**3/6 - 8*y. Let q(f) be the second derivative of z(f). Factor q(r).
-3*(r + 1)*(r + 2)/7
Let -10/9*i**3 + 4/9*i**2 + 0*i + 8/9*i**4 + 0 - 2/9*i**5 = 0. Calculate i.
0, 1, 2
Suppose -10*n = -12*n + 32. Find k, given that 68/5*k**4 + 0 - 24/5*k**3 - 4*k**5 - n*k**2 + 32/5*k = 0.
-1, 0, 2/5, 2
Let k(u) be the second derivative of 7*u - 8/3*u**2 - 2/3*u**3 + 1/9*u**4 + 0. Factor k(b).
4*(b - 4)*(b + 1)/3
Let g(c) be the third derivative of 243*c**6/140 - 1863*c**5/70 + 4761*c**4/28 - 12167*c**3/21 - 199*c**2. Determine l so that g(l) = 0.
23/9
Let x(k) be the first derivative of k**3/9 + 5*k**2/2 + 14*k/3 + 371. Factor x(v).
(v + 1)*(v + 14)/3
Let t be 816/780 - (-2)/13. Determine w, given that -6/5*w**3 + 0*w - 2/5*w**5 + 0 + 2/5*w**2 + t*w**4 = 0.
0, 1
Let d(s) = 7*s + 4. Let j be d(0). Let z(c) be the second derivative of 1/18*c**j - 1/9*c**3 + 5*c + 0 + 0*c**2. Factor z(w).
2*w*(w - 1)/3
Let 2/5*r**3 + 2/5*r**2 + 0 - 12/5*r = 0. Calculate r.
-3, 0, 2
Find f, given that 1/2*f**3 - 1/6*f**5 + 0 + 0*f - 1/3*f**2 + 0*f**4 = 0.
-2, 0, 1
Suppose 5*w - m = -3 + 25, -2*m + 1 = -w. Solve 3/5*r**4 - r**w + 27/5*r**3 + 0 + 5*r**2 + 6/5*r = 0 for r.
-1, -2/5, 0, 3
Let b(s) be the first derivative of s**4/2 + 158*s**3/3 - 80*s**2 - 131. What is q in b(q) = 0?
-80, 0, 1
Let h be 16/72*(-132)/(-80). Let x(r) be the third derivative of -8/105*r**7 - 2*r**2 - 1/6*r**4 + 0 - 3/5*r**5 + 0*r + 2/3*r**3 - h*r**6. Factor x(f).
-4*(f + 1)**3*(4*f - 1)
Let g(s) be the third derivative of s**7/1050 + s**6/360 - 7*s**5/600 - s**4/60 - s**3/6 - 11*s**2. Let f(q) be the first derivative of g(q). Factor f(r).
(r - 1)*(r + 2)*(4*r + 1)/5
Factor 63/4 + 15*y - 3/4*y**2.
-3*(y - 21)*(y + 1)/4
Factor 28/11 + 46/11*k + 2/11*k**3 + 20/11*k**2.
2*(k + 1)*(k + 2)*(k + 7)/11
Suppose 2*t + 32 = 8*k, -3*t + 42 - 5 = 5*k. Solve -58/5*j**2 - k*j**5 - 4/5*j + 8/5 + 29/5*j**3 + 10*j**4 = 0 for j.
-1, -2/5, 2/5, 1, 2
Let h(b) be the third derivative of b**7/4620 + b**6/495 + b**5/165 + b**4/8 + 12*b**2. Let m(s) be the second derivative of h(s). Factor m(y).
2*(y + 2)*(3*y + 2)/11
Suppose -106*v + 94*v + 48 = 0. Let a(h) be the second derivative of 0 + 0*h**3 - 4/5*h**6 - 2/5*h**5 + 1/3*h**7 + 0*h**v - 2*h + 0*h**2. Factor a(r).
2*r**3*(r - 2)*(7*r + 2)
Let c be (-8)/2*(-2)/4. Factor 4*l**c - 3*l**2 - 16*l**4 + 28*l**4 - 13*l**4.
-l**2*(l - 1)*(l + 1)
Let 9 + 4*t**2 - 3280*t - 39 + 3266*t = 0. Calculate t.
-3/2, 5
Let h(q) = 24*q**4 - 6*q**3 - 14*q**2 + 20*q + 4. Let l(b) = -4*b + 8 - 69*b**2 - 9 - 5*b**4 + b**3 + 72*b**2. Let i(w) = -3*h(w) - 14*l(w). Factor i(f).
-2*(f - 1)**3*(f + 1)
Let j(x) = -x**2 + 4*x + 8. Let g(w) be the third derivative of w**5/60 - w**4/6 - 7*w**3/6 + 11*w**2. Let z(l) = -6*g(l) - 4*j(l). Factor z(r).
-2*(r - 5)*(r + 1)
Suppose -2*i + 5*i + 14 = -5*r, 14 = 3*i - 2*r. Factor 2*z**4 - 4*z**5 + 6*z**i - 6*z**4 + 0*z**5 + 4*z**3 - 2*z**2.
-4*z**2*(z - 1)*(z + 1)**2
Let i(x) be the first derivative of -x**5/90 - x**4/9 - 4*x**3/9 - 8*x**2/9 - 5*x + 26. Let h(c) be the first derivative of i(c). Suppose h(w) = 0. Calculate w.
-2
Suppose -2*y - 3 = -7. Solve -12*f + y*f**2 + 2*f**2 + 8 + 0*f**2 = 0.
1, 2
Let u(q) be the first derivative of 3*q**4/10 + 16*q**3/15 + 4*q**2/5 + 55. Solve u(h) = 0.
-2, -2/3, 0
Let v = -1022/3 + 343. Let j(r) be the second derivative of -5/6*r**4 - 2*r**2 + v*r**3 + 0 - 2*r. Factor j(n).
-2*(n - 1)*(5*n - 2)
Determine x, given that -32/5*x + 28/5*x**4 + 8/5*x**3 + 0 - 112/5*x**2 = 0.
-2, -2/7, 0, 2
Suppose 165*b = 72*b - 130*b + 2899. Factor -1/2*q**4 + 1/2*q**5 - b*q**2 - 7*q**3 - 5/2 - 19/2*q.
(q - 5)*(q + 1)**4/2
Let u(p) be the second derivative of -4*p**2 + 0 - 8*p**4 - 26/5*p**5 - 12*p - 28/15*p**6 - 22/3*p**3 - 2/7*p**7. Factor u(a).
-4*(a + 1)**4*(3*a + 2)
Let y(j) = -j + 47. Let u be y(9). Suppose 0 = -6*x - 26 + u. Factor -2/9*q**3 + 0*q**x + 0 + 2/9*q.
-2*q*(q - 1)*(q + 1)/9
Let d(w) be the first derivative of -w**6/160 + 7*w**5/80 - 11*w**4/32 + 5*w**3/8 - 12*w**2 + 34. Let q(u) be the second derivative of d(u). Factor q(y).
-3*(y - 5)*(y - 1)**2/4
Let l = 1177/108 - -65/108. Factor 6 + 1/2*i**3 + 5*i**2 - l*i.
(i - 1)**2*(i + 12)/2
Factor -34 - 3*t**2 - 35*t - 107 - 102 - 19*t.
-3*(t + 9)**2
Let a be -4 - (-395)/90 - 18/81. Let q(k) be the third derivative of -1/20*k**5 - 2*k**2 - 1/8*k**4 - 1/120*k**6 + 0 + 0*k - a*k**3. Find c such that q(c) = 0.
-1
Determine v so that 10/9*v**2 + 8/9*v + 2/9*v**3 + 0 = 0.
-4, -1, 0
Let p be 5/2 + 29/(-58). Factor -2*q**p + q**3 + 4*q**3 + q**3 + 2*q - 6*q.
2*q*(q - 1)*(3*q + 2)
Solve -6*h**3 - 2/3 - 22/3*h - 38/3*h**2 = 0 for h.
-1, -1/9
Let d(r) be the second derivative of -5/12*r**4 + 0 - 5/2*r**2 + 9*r + 5/3*r**3. Let d(a) = 0. Calculate a.
1
Let k(g) = 9*g**2 - 3*g. Let p = -14 - -24. Suppose 0*y + 25 = 5*y + c, 2*y + 3*c - p = 0. Let t(v) = 8*v**2 - 2*v. Let a(i) = y*k(i) - 6*t(i). Factor a(u).
-3*u*(u + 1)
Let c(q) be the third derivative of 0*q + 0*q**3 + 0 + 3*q**2 - 3/40*q**5 + 1/80*q**6 + 1/8*q**4. Let c(s) = 0. Calculate s.
0, 1, 2
Suppose 24 = 3*j - 3*g, 0 = -j + 5*g - 0*g + 16. Factor -j*m - 3/2*m**2 + 0.
-3*m*(m + 4)/2
Let y(r) be the first derivative of 3*r**5/5 - 155*r**4/4 - 71*r**3 + 51*r**2/2 + 106*r + 310. Factor y(b).
(b - 53)*(b + 1)**2*(3*b - 2)
Suppose -13*d = -11*d. Let u(p) be the third derivative of 0*p**4 + d - 2*p**2 + 0*p + 1/42*p**3 - 1/420*p**5. Factor u(t).
-(t - 1)*(t + 1)/7
Let w be (-4)/10*-3*200/(-80). Let n be -15 + 19 + 1 + w. Factor -4/3*q - 2/3*q**n + 2.
-2*(q - 1)*(q + 3)/3
Let i(r) be the first derivative of 0*r + 2 + r**2 - 9/2*r**3 + 3/4*r**4 - 1/20*r**5. Let v(t) be the second derivative of i(t). Let v(m) = 0. Calculate m.
3
Let h = 21446 + -64337/3. Let s be (3/(-2))/((-3)/4). Factor 1/3*m + h*m**s - 2/3.
(m - 1)*(m + 2)/3
Find o, given that -1 + 145/2*o**3 + 93/4*o**2 + 161/4*o**4 - 10*o = 0.
-1, -2/23, 2/7
Suppose -2/9*d**2 - 16/3*d + 0 = 0. What is d?
-24, 0
Let l be (406/(-63) + 6 + 0)/(-2). Factor 8/9*g**3 + 4/3*g - 2*g**2 - l.
2*(g - 1)**2*(4*g - 1)/9
Let q be ((-507)/9)/(-13) + -4. Factor -2/3 + x - q*x**2.
-(x - 2)*(x - 1)/3
Let c(b) = b + 3. Let l be c(-1). Find v such that -5*v**2 + 8 - 1809*v + l + 1814*v = 0.
-1, 2
Let r(t) be the first derivative of 0*t**5 - 2/3*t**3 - t**4 - 2 + 3/2*t**2 + 1/6*t**6 + 2*t. What is s in r(s) = 0?
-1, 1, 2
Let f = 1058 + -1055. Factor -15/2*g - 19/2*g**2 - 1 - 3*g**f.
-(g + 1)*(g + 2)*(6*g + 1)/2
Let v = -6 - -6. Let f = 319 + -317. Factor -2 + v*o + 1/2*o**f.
(o - 2)*(o + 2)/2
Let f = 90 - 87. Suppose -3*z = f*v + 6, -3*z = -0*v + 2*v + 4. Factor 4/7*s - 2/7*s**2 + z.
-2*s*(s - 2)/7
Let c(t) be the first derivative of 1/21*t**3 - 1/28*t**4 + 4 + 0*t**2 - 4*t + 1/140*t**5. Let l(f) be the first derivative of c(f). Solve l(x) = 0.
0, 1, 2
Let 5/4*t**2 + 45/4 + 15/2*t = 0. Calculate t.
-3
Suppose -1194*p + 1183*p = -22. Let y(s) be the first derivative of 0*s + 1/4*s**p - 1/4*s**4 - 2 + 0*s**5 + 1/12*s**6 + 0*s**3. Factor y(f).
f*(f - 1)**2*(f + 1)**2/2
Factor 0 - 1/7*u**2 + 1/7*u - 5/7*u**3 - 3/7*u**4.
-u*(u + 1)**2*(3*u - 1)/7
Find d, given that -44/3*d**3 - 200/3 - 440/3*d - 94*d**2 - 2/3*d**4 = 0.
-10, -1
Let b(d) = -2*d**3 - 7*d**2 - 3*d - 3. Let n(t) = -2*t**3 - 8*t*