 + 10)/4
Let p(c) be the second derivative of -c**5/10 - c**4/6 - c + 53. Factor p(h).
-2*h**2*(h + 1)
Let f(w) be the second derivative of w**7/7560 + w**6/1080 + 7*w**4/2 - 40*w. Let k(i) be the third derivative of f(i). Suppose k(j) = 0. What is j?
-2, 0
Let n(y) be the third derivative of 1/20*y**5 + 1/40*y**6 + 10*y**2 + 0*y + 0 - 1/8*y**4 - 1/2*y**3. Let n(h) = 0. Calculate h.
-1, 1
Let s(l) = l + 4. Let t be s(-6). Let g be 1 + (7/t)/(-1). Factor 3/2*v**2 - g*v - 6.
3*(v - 4)*(v + 1)/2
Let 2/9*s**3 + 8/3*s - 4/3*s**2 - 16/9 = 0. Calculate s.
2
Let k(v) be the second derivative of -4*v**2 + 6/5*v**5 - 7/15*v**6 + 24*v + 11/6*v**4 - 4*v**3 + 0. What is c in k(c) = 0?
-1, -2/7, 1, 2
Let b = 3022/567 - -2/567. Suppose -4/3*w**3 - 4*w**2 + b + 0*w = 0. Calculate w.
-2, 1
Let a(x) = -6*x**2 - 126*x + 2. Let t be a(-21). What is w in -1/5*w - 1/5*w**t + 2/5 = 0?
-2, 1
Let n(p) be the third derivative of 0 + 1/180*p**6 + 0*p**3 + 4*p**2 + 1/36*p**4 + 0*p + 1/45*p**5. Factor n(q).
2*q*(q + 1)**2/3
Let b be 16/(-190) + -5 + (-108)/(-20). Determine r so that b*r - 4/19 + 0*r**2 - 2/19*r**3 = 0.
-2, 1
Let f(q) be the second derivative of q**6/10 - q**5/2 + 3*q**4/4 - q**3/3 + 132*q. Find o, given that f(o) = 0.
0, 1/3, 1, 2
Let m = -48 - -93. Suppose 3*g + 39 = m. Factor -2/7*z**g + 6/7*z - 4/7.
-2*(z - 2)*(z - 1)/7
What is w in 0*w + 2/5*w**2 - 2/5*w**3 + 0 = 0?
0, 1
Let h be (1032/430)/((-1)/(15/(-8))). Let 3/4*t**2 - 33/4*t**4 - h*t + 12*t**3 + 0 = 0. Calculate t.
-6/11, 0, 1
Suppose -4 + 12 = 4*f. Factor r**4 - 2 - 3*r**f + 0*r**3 + 5*r + 10*r**3 - 6*r**3 - 5*r**3.
(r - 1)**3*(r + 2)
Let q be (-6)/5 + 4181/3330. Let m(i) be the first derivative of 0*i - q*i**6 + 1/6*i**4 + 0*i**3 - 5 + 0*i**5 - 1/6*i**2. Factor m(v).
-v*(v - 1)**2*(v + 1)**2/3
Factor 72/7 - 246/7*c - 3*c**2.
-3*(c + 12)*(7*c - 2)/7
Find p such that -3/5*p + 1/5*p**2 - 4/5 = 0.
-1, 4
Let a(p) be the third derivative of 14*p**2 + 1/15*p**5 + 0*p + 4/3*p**3 + 1/60*p**6 + 0 - 7/12*p**4. Factor a(z).
2*(z - 1)**2*(z + 4)
Factor 4/3*m**2 - 4/3*m**3 - 2/3*m**4 + 2/3*m**5 - 2/3 + 2/3*m.
2*(m - 1)**3*(m + 1)**2/3
Let b(l) = -15*l**4 + 115*l**3 + 275*l**2 + 140*l + 10. Let j(f) = -8*f**4 + 57*f**3 + 138*f**2 + 70*f + 6. Let m(g) = 3*b(g) - 5*j(g). Factor m(o).
-5*o*(o - 14)*(o + 1)**2
Let l(k) be the first derivative of -14/5*k**5 + 11 - 1/3*k**6 - 6*k - 9*k**4 - 13*k**2 - 44/3*k**3. Factor l(v).
-2*(v + 1)**4*(v + 3)
Let m = 916 - 615. Factor -d + m*d**2 - 301*d**2 + d**3.
d*(d - 1)*(d + 1)
Factor -3 - 25*i - 5*i - 42*i**4 + 7 + 36*i**3 - 158*i**3 - 114*i**2.
-2*(i + 1)**3*(21*i - 2)
Let u(f) be the first derivative of -1/28*f**4 + 0*f**5 + 6 + 0*f**2 + 0*f**3 + 0*f + 1/42*f**6. Determine n, given that u(n) = 0.
-1, 0, 1
Suppose 9*o - 23*o = -56. Let i be (6/120*-18)/((-3)/o). Determine x, given that 0*x**3 - 3/5*x**4 + 0 + 9/5*x**2 - i*x = 0.
-2, 0, 1
Let k(w) be the second derivative of -w**4/3 - 20*w**3/3 - 50*w**2 - 130*w. Factor k(r).
-4*(r + 5)**2
Let p(o) be the first derivative of 3*o**4/8 + o**3 + 3*o**2/4 - 76. Find s such that p(s) = 0.
-1, 0
Suppose 40 - 5/2*r**4 - 40*r + 0*r**2 + 10*r**3 = 0. Calculate r.
-2, 2
Factor 2/11*l**4 + 10/11*l**3 + 0*l + 0 + 12/11*l**2.
2*l**2*(l + 2)*(l + 3)/11
Suppose -216 = -67*m - 5*m. Determine s, given that 5/4*s**m + 9/4*s + 3/4*s**4 - 1/2 - 13/4*s**2 - 1/2*s**5 = 0.
-2, 1/2, 1
Let r = -119000/3 + 39668. Factor 14/3*b**2 - 2*b + 0 - r*b**3.
-2*b*(b - 3)*(2*b - 1)/3
Let d(b) be the third derivative of -b**8/1176 + 82*b**7/735 - 1837*b**6/420 + 1066*b**5/35 - 507*b**4/7 - b**2 + 5. Suppose d(z) = 0. Calculate z.
0, 2, 39
Let z(f) = -f**4 - 2*f**2 - 2*f. Let g(o) = -3*o**5 - 27*o**4 - 36*o**3 + 36*o**2 + 180*o + 144. Let b(r) = -g(r) + 6*z(r). Factor b(d).
3*(d - 2)*(d + 2)**3*(d + 3)
Let b(y) = -6*y**3 + 4*y**2 + 34*y - 2. Let q(h) = -7*h**3 + 2*h**2 + 35*h - 3. Let r(c) = 3*b(c) - 2*q(c). Let r(j) = 0. What is j?
-2, 0, 4
Let y(g) be the first derivative of -17 - 8/27*g**3 - 4/9*g**4 + 2/15*g**5 + 1/3*g**6 + 0*g + 0*g**2. Determine l so that y(l) = 0.
-2/3, 0, 1
Let c be (272 - 268)/(-2*1/(-2)). Let y(o) be the second derivative of 0 + 8/27*o**3 - 2*o + 16/9*o**2 + 1/54*o**c. Factor y(z).
2*(z + 4)**2/9
Let v(t) be the third derivative of 4/9*t**4 - 1/315*t**7 - 7/180*t**6 + 0*t**3 + 0*t + 15*t**2 - 4/45*t**5 + 0. Factor v(s).
-2*s*(s - 1)*(s + 4)**2/3
Let b(f) be the first derivative of -2*f**5/95 + 37*f**4/38 - 70*f**3/19 + 103*f**2/19 - 68*f/19 - 250. Factor b(g).
-2*(g - 34)*(g - 1)**3/19
Suppose -4*q + 34 = -246. Let l be ((-12)/q)/((-15)/(-200)*-2). What is w in l*w**4 - 6/7*w**3 + 0 - 8/7*w**2 - 2/7*w**5 + 8/7*w = 0?
-1, 0, 1, 2
Let b(w) be the first derivative of w**4/8 + 31*w**3/6 + 92. Factor b(d).
d**2*(d + 31)/2
Suppose -12 + 68 = 16*f + 24. Factor 10 - 4*l + 2/5*l**f.
2*(l - 5)**2/5
Let m be ((-12)/15)/((-296)/444 + (-104)/15). Factor 2/19*k - m*k**2 + 12/19.
-2*(k - 3)*(k + 2)/19
Let n be 2/(-15) + -7*3/(-90). Let u(z) be the third derivative of 1/75*z**6 - z**2 + 1/5*z**4 + 0 + 0*z + 4/15*z**3 - n*z**5. Let u(y) = 0. What is y?
-1/4, 2
Suppose -88*x - 4*h - 18 = -90*x, 0 = -3*h - 6. Factor -6/5*q**4 + 0*q**3 + 6/5*q**2 + 3/5*q**x - 3/5*q + 0.
3*q*(q - 1)**3*(q + 1)/5
Let m(s) be the third derivative of -1/40*s**6 + 1/210*s**7 + 1/336*s**8 + 0*s**3 + 0*s - 1/12*s**5 - 4*s**2 - 1/12*s**4 + 0. Factor m(p).
p*(p - 2)*(p + 1)**3
Let p(b) = -10*b**3 + 355*b**2 + 505*b. Let g(d) = d**3 - 39*d**2 - 56*d. Let z(s) = 35*g(s) + 4*p(s). Determine u so that z(u) = 0.
-1, 0, 12
Let q(r) = -r**5 - r**4 - r**3 - r**2. Let k(f) = 2*f**5 + 2*f**4 + 10*f**3 + 4*f**2 - 6*f. Let o(y) = 2*k(y) + 6*q(y). Solve o(n) = 0.
-3, -1, 0, 1, 2
Let y(x) be the first derivative of x**3/3 + 3*x**2 - 7*x - 13. Let f(b) = b - 1. Let v(t) = -21*f(t) + 3*y(t). Solve v(h) = 0.
0, 1
Determine f so that -8/5 + 48/5*f + 42/5*f**3 - 74/5*f**2 - 8/5*f**4 = 0.
1/4, 1, 2
Let t(s) = -2*s + 6. Let m be t(2). Solve -6*b + b**5 - 4*b**5 + 160*b**4 + 21*b**m - 27*b**3 - 145*b**4 = 0 for b.
0, 1, 2
Let b be (8/48*0)/3. Let g(l) be the third derivative of -2*l**2 + 8/3*l**3 + b - 1/10*l**5 + 0*l - 5/6*l**4. Factor g(z).
-2*(z + 4)*(3*z - 2)
Let v(x) be the second derivative of x**6/120 - 57*x**5/80 + 781*x**4/48 + 319*x**3/8 - 841*x**2/4 + 119*x - 2. Factor v(i).
(i - 29)**2*(i - 1)*(i + 2)/4
Suppose 23 = 5*v - 12. Factor 4*x**4 + x**3 + x**3 - 5*x**5 + v*x**5.
2*x**3*(x + 1)**2
Let s = -16 - -22. Let b(d) = -17*d**3 + 18*d**3 - 8*d**3 + 8 - 3*d + 6*d**2. Let t(x) = x**3 - x**2 + x - 1. Let f(m) = s*t(m) + b(m). Factor f(y).
-(y - 2)*(y + 1)**2
Let s(j) = -10*j**2 - 6877*j + 988461. Let l(t) = 4*t**2 + 2292*t - 329488. Let c(g) = 11*l(g) + 4*s(g). Factor c(h).
4*(h - 287)**2
Let r(g) be the second derivative of -16/3*g**3 + 77/12*g**4 + 2*g**2 - 49/20*g**5 - 21*g + 0. Factor r(m).
-(m - 1)*(7*m - 2)**2
Let t(v) be the second derivative of -v**6/45 + v**5/6 - 7*v**4/18 + v**3/3 - 2*v - 66. Factor t(n).
-2*n*(n - 3)*(n - 1)**2/3
Let c = 9442/11 + -858. Find t such that -8/11*t**2 + 8/11*t**4 - c*t**3 + 6/11*t - 2/11*t**5 + 0 = 0.
-1, 0, 1, 3
Suppose 5*x - 3*x = r + 4, x - 2 = 2*r. Let 0 + 2/5*j - j**x + 4/5*j**3 - 1/5*j**4 = 0. What is j?
0, 1, 2
Suppose -15/2*s**4 - 171/4*s - 3/4*s**5 - 51*s**2 - 57/2*s**3 - 27/2 = 0. Calculate s.
-3, -2, -1
Factor -33/7*f**2 + 9/7*f**4 + 3/7*f**5 - 3/7*f**3 - 12/7 - 36/7*f.
3*(f - 2)*(f + 1)**3*(f + 2)/7
Let x be -4 + (-84)/(-81)*114. Let n = x - 114. Factor 2/9*t**5 + 2/9*t - 4/9*t**2 + n + 2/9*t**4 - 4/9*t**3.
2*(t - 1)**2*(t + 1)**3/9
Let g = -11748/7 - -1680. Determine z so that -9/7*z**3 + g*z**5 + 15/7*z**2 - 3/7*z + 0 - 15/7*z**4 = 0.
-1, 0, 1/4, 1
Suppose -5*u - 5 + 15 = 0. Let t be -2*(-21)/(-28) - -2. Factor u + t*m**2 - 2*m.
(m - 2)**2/2
Let i(l) be the second derivative of 0 + 20*l + 0*l**2 + 5/36*l**3 + 1/24*l**5 + 5/36*l**4. Find h such that i(h) = 0.
-1, 0
Let m(f) be the first derivative of -3*f**4/8 - f**3 + 6*f**2 - 90. Solve m(x) = 0.
-4, 0, 2
Let x(r) be the first derivative of 1/4*r**4 + 3/10*r**5 + 0*r**2 + 2*r + 4 - r**3 - 1/10*r**6. Let o(q) be the first derivative of x(q). Factor o(d).
-3*d*(d - 2)*(d - 1)*(d + 1)
Let q be 19 - ((-11)/1 + 5 + 1). Let b(m) be the first derivative of -11 - 63*m**4 + q*m + 147/10*m**5