k + 3)
Let d(k) be the first derivative of -2*k**3/33 - 2*k**2/11 + 16*k/11 - 73. Let d(t) = 0. Calculate t.
-4, 2
Let v(y) be the second derivative of y**4/8 - 17*y**3/4 + 12*y**2 + 57*y. Suppose v(k) = 0. What is k?
1, 16
Let b(p) be the second derivative of -5*p + 0 - 8/5*p**3 + 16/5*p**2 - 1/25*p**5 + 2/5*p**4. Factor b(c).
-4*(c - 2)**3/5
Let d(c) be the second derivative of c**5/30 - 41*c**4/9 + 161*c**3/9 - 80*c**2/3 + 158*c. Determine m, given that d(m) = 0.
1, 80
Suppose -56*l + 11*l = 40 - 130. Suppose -s**l + 1 - 1/2*s**3 + 1/2*s = 0. Calculate s.
-2, -1, 1
Let w(s) be the third derivative of -s**8/672 - s**7/28 + 17*s**6/120 - s**5/60 - 11*s**4/16 + 17*s**3/12 + 253*s**2. Factor w(x).
-(x - 1)**3*(x + 1)*(x + 17)/2
Let m(i) be the second derivative of i**7/189 + 2*i**6/135 - 2*i**5/15 + 7*i**4/27 - 5*i**3/27 - 36*i. Determine z so that m(z) = 0.
-5, 0, 1
Find d such that -8/3 - 40/9*d - 2/9*d**3 - 2*d**2 = 0.
-6, -2, -1
Let w(t) be the first derivative of t**6/360 - t**5/90 + t**4/72 + 29*t**2/2 + 17. Let s(y) be the second derivative of w(y). Suppose s(a) = 0. Calculate a.
0, 1
Let h(n) be the third derivative of 2/35*n**7 - 2/15*n**5 + 1/84*n**8 - 2/3*n**3 + 0 + 0*n + 1/15*n**6 + 8*n**2 - 1/2*n**4. Factor h(k).
4*(k - 1)*(k + 1)**4
Let d be (-20171)/759 + 26 - (-1 - (-1)/3). Let 1/11*c - 2/11*c**2 + d = 0. Calculate c.
-1/2, 1
Let z be 6/18 + (-1185)/180 + 7. Factor 1/2 - 2*c**2 - z*c - 3/4*c**3.
-(c + 1)*(c + 2)*(3*c - 1)/4
Suppose 5*u - 49 = 3*d + 213, 0 = -u + 5*d + 48. Let f = u - 211/4. Factor 0*k - f + 1/4*k**2.
(k - 1)*(k + 1)/4
Let b(r) be the third derivative of -r**7/420 + r**6/20 + r**5/120 - r**4/4 - 83*r**2 + r. Determine a so that b(a) = 0.
-1, 0, 1, 12
Let m = 5/1794 - -271/1794. What is r in 0 + m*r**3 - 2/13*r**2 + 0*r = 0?
0, 1
Let q(u) be the first derivative of 0*u - 1/3*u**3 + 34 + 3/2*u**2 + 1/5*u**5 - 3/4*u**4. Determine g, given that q(g) = 0.
-1, 0, 1, 3
Find l such that 12/17 - 2/17*l**2 - 2/17*l = 0.
-3, 2
Find n, given that 8/17*n - 8/17 + 2/17*n**5 + 10/17*n**2 - 10/17*n**3 - 2/17*n**4 = 0.
-2, -1, 1, 2
Let y(f) be the third derivative of f**10/7560 - f**9/1890 - f**8/1680 + f**7/315 - 19*f**4/24 - 5*f**2. Let v(j) be the second derivative of y(j). Factor v(o).
4*o**2*(o - 2)*(o - 1)*(o + 1)
Suppose -32*v - 4 = 33*v - 66*v. Factor 3/5*u**v + 399/5*u**2 + 147*u + 61/5*u**3 - 686/5.
(u + 7)**3*(3*u - 2)/5
Let x = -28/39 + 18/13. Let o(c) be the first derivative of -5/6*c**2 + 1/12*c**4 - x*c + 2 + 1/15*c**5 - 1/3*c**3. Factor o(j).
(j - 2)*(j + 1)**3/3
Determine j, given that 12*j**3 - 2*j**4 + 96 + 80*j**2 - 1/2*j**5 + 152*j = 0.
-4, -2, 6
Let m = 16 + -2. Let b = m - 12. Solve -4*n + n - 3*n**b + n = 0 for n.
-2/3, 0
Let p(z) = -z**3 - 34*z**2 - 50*z + 450. Let i be p(-32). Factor 2/5 - 6/5*n**i - 4/5*n**4 - 2/5*n + 2*n**3.
-2*(n - 1)**3*(2*n + 1)/5
Let d(l) be the first derivative of 12 + 1/3*l**3 - 2*l - 1/2*l**2. Factor d(m).
(m - 2)*(m + 1)
Let a be (-4)/(-22) - (-66)/(-363). Let p(c) be the third derivative of 0*c**5 - 1/120*c**6 + 0 + 3*c**2 + a*c**4 - 1/210*c**7 + 0*c + 0*c**3. Factor p(l).
-l**3*(l + 1)
Suppose -2*s - 5*v + 7 = -4*v, 2*s - 5*v - 25 = 0. Let q be (-191)/(-45) - 4 - (-1)/s. Factor 2/9*z**3 + 4/9 - 2/9*z - q*z**2.
2*(z - 2)*(z - 1)*(z + 1)/9
Let j(y) be the second derivative of 2*y**6/15 - 24*y**5/5 + 65*y**4/3 - 28*y**3 - 2*y + 21. Let j(p) = 0. Calculate p.
0, 1, 2, 21
Let i(z) be the third derivative of 0 + 1/90*z**5 - 2/3*z**3 + 0*z + z**2 - 1/36*z**4. Determine h so that i(h) = 0.
-2, 3
Factor -1156/9 - 1/9*n**2 + 68/9*n.
-(n - 34)**2/9
Let r(j) = -28*j**3 - j - 1. Let a be r(-1). What is s in -1 - 37*s + a*s**2 - 1 + 17*s - 6 = 0?
-2/7, 1
Solve 7*k**2 + 1156*k + 6*k**3 + 2*k**2 - 1108*k + 36 - 9*k**3 = 0.
-2, -1, 6
Let x(a) be the second derivative of 0*a**2 + 1/3*a**4 + 8*a + 1/90*a**6 + 1/10*a**5 + 4/9*a**3 + 0. Suppose x(j) = 0. What is j?
-2, 0
What is f in 72 - 10*f + 0*f**2 - 18*f + 10*f + 3*f**2 - 15*f = 0?
3, 8
Let l(b) = b**2 - 21*b + 56. Let m(x) = -17*x**3 + 2*x**2 + x. Let t be m(-1). Let k be l(t). Factor 0 + 2/7*u**k + 4/7*u.
2*u*(u + 2)/7
Suppose -4*c - 9 = 7, o - 5*c - 10 = 0. Let b be (12/o)/(4/(-10)). Factor -b - 4*d + d + d**2 + 3 + 2.
(d - 2)*(d - 1)
Suppose 2*v = 4*s, -6*v + v = 4*s. Suppose a + 11 = 3*n, 3*n = -2*a - 2 - 2. Factor -1/3 + 0*l**3 + s*l + 2/3*l**n - 1/3*l**4.
-(l - 1)**2*(l + 1)**2/3
Let c(k) be the second derivative of 1/100*k**5 + 4*k + 0*k**2 - 1/60*k**4 + 0*k**3 + 0. Factor c(j).
j**2*(j - 1)/5
Let i(r) be the third derivative of 7*r**2 + 0*r + 0 + 0*r**3 - 1/42*r**4 + 1/210*r**5. Suppose i(v) = 0. What is v?
0, 2
Let p = -13672/7 + 1954. Suppose -p*s**4 + 4/7*s**3 + 0 - 4/7*s + 6/7*s**2 = 0. Calculate s.
-1, 0, 2/3, 1
What is p in 0 + 5/2*p**3 + 0*p + 200*p**2 = 0?
-80, 0
Find x such that -3/4 + 1/4*x**4 + 1/2*x**2 - x**3 + x = 0.
-1, 1, 3
Let z(s) be the first derivative of -s**4/2 + 10*s**3/3 + 8*s**2 - 5*s - 14. Let d(a) be the first derivative of z(a). What is i in d(i) = 0?
-2/3, 4
Factor -1569 - 10*i + i**2 + 5925 - 91*i - 31*i.
(i - 66)**2
Let w(v) be the third derivative of -v**7/11340 - v**6/1620 - v**5/540 - 3*v**4/8 - 10*v**2. Let o(g) be the second derivative of w(g). Factor o(l).
-2*(l + 1)**2/9
Let t = -6 - 9. Let m be t/(-10) - 3/(-6). Factor 4/9*c + 2/9 + 2/9*c**m.
2*(c + 1)**2/9
Let t be (-24881)/156 - 1*(-6)/9. Let y = -631/4 - t. Suppose 18/13*j - y*j**2 - 4/13 = 0. Calculate j.
2/7, 1
Suppose 11*j + 12 = 14*j. Let x = 9 + -5. Factor -16*w + 6*w - j + x*w + 10*w - w**2.
-(w - 2)**2
Let w(t) = 4*t**2 + 3*t - 2. Let g be w(-8). Let c = -230 + g. Factor c + 1/3*k + 1/3*k**2.
k*(k + 1)/3
Suppose 0 = -3*o + 4*v + 6, 3*o + o - 8 = 5*v. Let -2*p**o - 3*p**5 + 6*p**3 - 11*p**3 + 8*p**3 + 5*p**2 - 3*p**4 = 0. What is p?
-1, 0, 1
Factor 3/4*s**3 - 15*s**2 + 351/4*s - 243/2.
3*(s - 9)**2*(s - 2)/4
Let m be (12/8)/(9/18). Factor -8 + 13*n**2 - m*n**2 - 7*n**2 - 10*n.
(n - 4)*(3*n + 2)
Factor 7930/7*h**3 + 8450/7*h**4 + 8/7*h - 512/7*h**2 + 0.
2*h*(h + 1)*(65*h - 2)**2/7
Let i(b) be the second derivative of -3*b**5/140 - b**4/28 + b**3/14 + 3*b**2/14 - 570*b. Factor i(x).
-3*(x - 1)*(x + 1)**2/7
Let q(b) be the second derivative of 0*b**3 + 1/100*b**5 - 1/60*b**4 + 0*b**2 + 3*b + 0. Suppose q(m) = 0. Calculate m.
0, 1
Let p = 451/3 - 443/3. Solve p*i - 4/3*i**3 + 0 - 4/3*i**2 = 0 for i.
-2, 0, 1
Let c be (-1*(41 - -6))/7 - -7. Let 8/7*l**3 + 10/7*l**2 + 4/7*l + 0 + c*l**4 = 0. Calculate l.
-2, -1, 0
Let p(n) be the third derivative of n**8/1120 + n**7/140 + n**6/48 + n**5/40 - 3*n**3/2 + 5*n**2. Let r(o) be the first derivative of p(o). Factor r(g).
3*g*(g + 1)**2*(g + 2)/2
Find s such that 3/2*s**4 + 0*s**2 + 0*s - 2*s**3 + 0 = 0.
0, 4/3
Let i(v) be the first derivative of -v**4/4 + 137*v**3/12 - 595*v**2/4 + 289*v/4 + 113. Factor i(s).
-(s - 17)**2*(4*s - 1)/4
Let x(v) = 5*v**3 - 5*v**2 + 20*v. Let f(b) be the third derivative of -b**4/24 - 2*b**2 - 17. Let k(l) = -30*f(l) - x(l). Factor k(q).
-5*q*(q - 2)*(q + 1)
Determine v, given that 14*v - 2*v**5 + 40*v**2 - 4*v**4 - 2*v + 3*v + v + 14*v**3 + 8*v = 0.
-2, -1, 0, 3
Let f be 336/15 - (-2)/(-5). Let t = -20 + f. Factor 3/2*z**2 + t + 5*z - 9/4*z**3.
-(z - 2)*(3*z + 2)**2/4
Factor -42/17*w**2 + 0 + 36/17*w - 2/17*w**4 + 16/17*w**3.
-2*w*(w - 3)**2*(w - 2)/17
Let o = -59 + 44. Let v be -8 + 9 - 3/o. Solve 3/5*a**4 - v - 9/5*a + 3/5*a**2 + 9/5*a**3 = 0.
-2, -1, 1
Let w(l) be the first derivative of l**4/16 - l**3/2 + 3*l**2/8 + 5*l/2 + 49. Determine r, given that w(r) = 0.
-1, 2, 5
Let k(q) = -4*q**3 + 16*q**2 + 26*q - 102. Let d(y) = -y**3 + y**2 - y - 3. Let w(r) = -2*d(r) + k(r). Determine t so that w(t) = 0.
-3, 2, 8
Let x be (-51)/6*(-1096)/4658. Factor -2/5 - 2/5*r**3 + 2/5*r + 2/5*r**x.
-2*(r - 1)**2*(r + 1)/5
Let v(l) be the second derivative of -l**4/16 - 11*l**3/8 - 45*l**2/4 - l + 12. Factor v(r).
-3*(r + 5)*(r + 6)/4
Let b(t) be the second derivative of -t**4/3 - 28*t**3/3 + 30*t**2 + 102*t. Let b(a) = 0. Calculate a.
-15, 1
Let r(y) be the first derivative of -y**6/240 + 7*y**5/80 - 5*y**4/8 - 35*y**3/3 - 28. Let f(b) be the third derivative of r(b). Let f(w) = 0. Calculate w.
2, 5
Factor 0*t + 0 + 10*t**3 + 1/3*t**4 - 31/3*t**2.
t**2*(t - 1)*(t + 31)/3
Suppo