 such that -1/2*s**3 - 16*s + 16 + 5*s**2 = 0.
2, 4
Let g(k) = 4*k**2 - 18*k - 132. Let a be g(-7). Let m = -569/3 + a. Factor -1/3*f**2 + 2/3 + m*f.
-(f - 2)*(f + 1)/3
Let j(o) = -1859 - 1903 - 15*o**2 + 879 - 5*o**2 + 169*o. Let z(h) = -7*h**2 + 56*h - 961. Let r(x) = -6*j(x) + 17*z(x). Suppose r(p) = 0. Calculate p.
31
Let k(m) be the first derivative of 3 + 3*m + 1/3*m**4 - 2*m**2 - 1/10*m**5 + 1/3*m**3. Let r(h) be the first derivative of k(h). Let r(v) = 0. What is v?
-1, 1, 2
Let w(r) be the second derivative of -r**7/2520 + r**6/120 + 7*r**5/120 + 41*r**4/12 + 72*r. Let p(i) be the third derivative of w(i). Factor p(n).
-(n - 7)*(n + 1)
Factor 150 - 150*r**2 + 3/2*r - 3/2*r**3.
-3*(r - 1)*(r + 1)*(r + 100)/2
Suppose p + 4*c = -4, -2*p - 3*c = -0*c - 17. Solve 5*r**4 - p*r**3 - 23*r**3 + 43*r**3 + 100*r - 80 - 29*r**3 = 0 for r.
-2, 1, 2, 4
Suppose -10*l + 20 = -5*l - d, -2*l - 14 = 4*d. Let t be (-40)/(-16)*6/35. Let -18/7*a**2 - t - l*a = 0. Calculate a.
-1, -1/6
What is d in -2/13*d**3 - 70/13*d**2 + 1768 + 32*d = 0?
-26, 17
Let v be ((-2)/(-27))/((-6292)/(-8712))*6. What is n in 0 - 20/13*n - 14/13*n**2 + v*n**3 + 2/13*n**4 = 0?
-5, -1, 0, 2
Let n(a) be the third derivative of -1/6*a**6 + 0 + 35/24*a**4 + 0*a - 5/12*a**5 + 5/3*a**3 + 62*a**2. Factor n(c).
-5*(c - 1)*(c + 2)*(4*c + 1)
Let v(a) be the second derivative of -a**5/100 + a**4/40 + a**3/5 - 95*a**2/2 + a - 2. Let t(p) be the first derivative of v(p). Determine c so that t(c) = 0.
-1, 2
Let x(y) be the second derivative of y**6/15 + 81*y**5/10 + 6721*y**4/24 + 540*y**3 + 400*y**2 - 1146*y. Let x(k) = 0. What is k?
-40, -1/2
Let l = -1030 + 1105. Suppose l = -19*z + 132. Factor 24/5*a - 16/5 - 4/5*a**2 - 6/5*a**z + 2/5*a**4.
2*(a - 2)**2*(a - 1)*(a + 2)/5
Let y be (-4)/(-12) + (-13)/39. Let a(b) be the second derivative of y - 8*b**4 - 4*b**2 + 9/5*b**5 - 34*b + 26/3*b**3. Factor a(j).
4*(j - 2)*(3*j - 1)**2
Determine r so that 1/2*r**4 + 9*r**3 - 1/2*r**2 + 0 - 9*r = 0.
-18, -1, 0, 1
Suppose 18*o - 35*o + 51 = 0. Determine p so that -15*p**5 + 16*p - p**o - 8*p**3 - 32 - 40*p**4 + 72*p**2 + 3*p**5 + 5*p**3 = 0.
-2, -1, 2/3, 1
Let l = 833386/71621 - -2/6511. What is c in 224/11*c - 28/11*c**3 + 6*c**2 + l + 2/11*c**4 = 0?
-1, 8
Let k(c) be the second derivative of c**5/40 - 2*c**4/3 - 77*c**3/12 - 15*c**2 + 101*c + 6. Factor k(v).
(v - 20)*(v + 1)*(v + 3)/2
Let d = 4/407 + 9748/2035. Let r = -3473/20 - -709/4. Determine n so that 3/5*n**3 + 36/5*n + r*n**2 + d = 0.
-2
Let b(t) be the third derivative of t**6/40 - 29*t**5/20 - 85*t**4/4 - 6276*t**2. Factor b(a).
3*a*(a - 34)*(a + 5)
Let t(s) be the second derivative of -23*s - 1/72*s**4 + 0 - 12*s**2 - 1/72*s**6 + 1/40*s**5 + 0*s**3. Let r(m) be the first derivative of t(m). Factor r(p).
-p*(2*p - 1)*(5*p - 2)/6
Let i(h) be the third derivative of h**6/120 + h**5/10 + 2*h**4/3 + 16*h**3/3 + 217*h**2. Let p be i(-4). Factor -2/21*w**3 + p - 4/21*w + 2/7*w**2.
-2*w*(w - 2)*(w - 1)/21
Determine t, given that 99*t**3 + 56*t**4 + 19*t**3 - 2*t**5 - 26840*t**2 + 26900*t**2 = 0.
-1, 0, 30
Let t(s) = 4*s**2 + 1. Let i(z) = z**3 + 14*z**2 - 16*z - 16. Let q be i(-15). Let f be t(q). Factor 90*x + 60 - f*x**2 - 389 - 76.
-5*(x - 9)**2
Let a be (2 - (-18642)/(-2070)) + 7. Let c = 1414/5865 + a. Find t such that 2/17*t**3 - c*t**2 + 0 + 2/17*t = 0.
0, 1
Let m be (-1479)/(-406) + 150/(-70). Let 0 + m*f**3 - 3/2*f - 1/2*f**4 + 1/2*f**2 = 0. Calculate f.
-1, 0, 1, 3
Let s = 2813 + -2809. Let h(j) be the second derivative of 2/9*j**3 + 0 - 1/36*j**s - 5*j - 2/3*j**2. Factor h(y).
-(y - 2)**2/3
Suppose -14*q - 21 = -4*r - 13*q, -3*r - 13 = 5*q. Let n(k) be the second derivative of 0 + 2*k**2 - 2/3*k**r + 11*k + 2/3*k**3. Let n(a) = 0. Calculate a.
-1/2, 1
Factor 96*z**2 - 54*z**2 + 567*z + 270*z**2 + 0*z**3 - 3*z**3 + 252*z**2.
-3*z*(z - 189)*(z + 1)
Factor -504*r + 0 - 1508/3*r**2 + 4/3*r**3.
4*r*(r - 378)*(r + 1)/3
Suppose -1235 = -372*x + 125*x. Find o, given that 11/5*o**4 + 4*o**x + 32/5*o - 88/5*o**3 - 43/5*o**2 - 4/5 = 0.
-2, -1, 1/5, 1/4, 2
Let z(d) = -d + 3. Let g be z(1). Suppose 95 + 61 = 39*c. Determine i, given that 3*i - 3*i**4 - 8*i**3 - i**c + 4*i**g + 5*i = 0.
-2, -1, 0, 1
Let f(m) = m**2 + 10*m + 34. Let a(c) = -c**2 + 1. Let q(s) = -2*s**3 - 29*s**2 - 12*s + 22. Let p be q(-14). Let y(i) = p*a(i) - f(i). Factor y(l).
5*(l - 4)*(l + 2)
Let s(u) be the first derivative of -6*u**5/5 - 11*u**4/3 + 4*u**3/3 - 27*u - 92. Let d(k) be the first derivative of s(k). Let d(l) = 0. Calculate l.
-2, 0, 1/6
Suppose 6*f + 3*f = 144. Let i = f + -14. Find t, given that 2 - 2*t**i - 579*t + 579*t = 0.
-1, 1
Let f(u) = 2*u**4 - 49*u**3 + 25*u**2 - 10. Let v(k) = -k**4 + 25*k**3 - 10*k**2 + 4. Let p(b) = 4*f(b) + 10*v(b). Solve p(z) = 0 for z.
0, 27
Let w(m) be the second derivative of 1/10*m**5 - 170*m + 56*m**3 + 25/6*m**4 + 0 + 144*m**2. Find a, given that w(a) = 0.
-12, -1
Let q(g) be the third derivative of 961*g**7/140 + 527*g**6/20 + 671*g**5/20 + 51*g**4/4 + 9*g**3/4 + 135*g**2. Factor q(b).
3*(b + 1)**2*(31*b + 3)**2/2
Factor -3/2*j**4 + 0 - 432*j**3 + 0*j + 867/2*j**2.
-3*j**2*(j - 1)*(j + 289)/2
Let r(l) = -l**4 + l**3 - l + 1. Let a(x) = 6*x**5 - 9*x**5 - 11*x + 14*x**3 + 69 - 67 - 2*x**4. Let m(z) = -a(z) + 4*r(z). Determine p, given that m(p) = 0.
-1, -1/3, 1, 2
Let r(z) = -z**5 + 5*z**4 + 2*z**3 + 24*z**2 - 4. Let a(t) = t**5 - 3*t**4 - 4*t**3 - 24*t**2 + 3. Let y(m) = 4*a(m) + 3*r(m). Factor y(u).
u**2*(u - 3)*(u + 2)*(u + 4)
Suppose 2*g - 3*a = a - 8, 0 = -3*a + 9. Determine v, given that -185 + 2*v**g + 155 - 2*v**2 - 5*v**2 + 35*v = 0.
1, 6
Let i(p) = 3*p - 42. Let b be i(13). Let k(d) = -d**2 - 8*d - 12. Let t be k(b). Find n such that -12 + 0*n**2 - 2*n + 3*n**3 + 12*n**2 + 0*n - n**t = 0.
-6, -1, 1
Solve 11*s - 23/2 + 12*s**2 - 1/2*s**4 - 11*s**3 = 0 for s.
-23, -1, 1
Let j(y) be the second derivative of y**3/3 - 11*y**2/2 - 28*y. Let f be j(8). Factor 6*m**4 + 21*m + 5 + 3*m**f + 9 - 4 + 6*m**2 - 22 - 24*m**3.
3*(m - 1)**3*(m + 1)*(m + 4)
Suppose -4170 - 14849 = 77*k. Let i = k - -247. What is l in i + 0*l**3 - 2/7*l**5 + 32/7*l + 8/7*l**4 - 32/7*l**2 = 0?
-2, 0, 2
Let m = 1312 + -1312. Let p be 3 - -1*3/6*m. Factor 26/3*n - 2/3*n**p + 10/3*n**2 + 14/3.
-2*(n - 7)*(n + 1)**2/3
Let g(v) = 9*v**2 - 4*v + 10. Let y(p) = 2*p**2 - p + 2. Let s(k) = g(k) - 5*y(k). Let x(w) = 2*w**2 + 13*w + 21. Let b(d) = 5*s(d) + x(d). Factor b(o).
-3*(o - 7)*(o + 1)
Let p(u) be the second derivative of 230*u - 100/9*u**2 + 0 - 1/54*u**4 + 20/27*u**3. Determine n so that p(n) = 0.
10
Suppose 84*l - 87*l - 9 = 3*y, 3*y - 3*l = 9. Let z(n) be the second derivative of 0*n**2 + 0*n**3 - 1/60*n**5 - 23*n + y - 1/18*n**4. Factor z(v).
-v**2*(v + 2)/3
Suppose 566*q + 3736 - 5434 = 0. Suppose 2/17 + 0*w + 32/17*w**4 - 2*w**2 + 0*w**q = 0. What is w?
-1, -1/4, 1/4, 1
Let z(b) be the second derivative of -b**4/48 - 17*b**3/12 - 273*b**2/8 - 2964*b + 2. Factor z(a).
-(a + 13)*(a + 21)/4
Let p(b) be the first derivative of -48*b**2 + 1152*b + 2/3*b**3 + 77. Let p(w) = 0. Calculate w.
24
Let r(i) be the first derivative of i**4/26 + 70*i**3/39 + 274*i**2/13 + 480*i/13 + 3880. Solve r(f) = 0.
-24, -10, -1
Let x be -3 + (1 - (-10 + 4)). Factor -15 + 9*k**2 - 3*k**x + 25 + 60*k - 18*k**3 + 26.
-3*(k - 2)*(k + 1)**2*(k + 6)
Let y(o) be the first derivative of o**6/60 - 3*o**5/50 - o**4/40 + o**3/10 - 4276. Determine d, given that y(d) = 0.
-1, 0, 1, 3
Factor -760/3*b - 2/3*b**2 - 72200/3.
-2*(b + 190)**2/3
Let o(x) be the second derivative of 5*x**2 - x + 1/12*x**4 + 41 - 7/6*x**3. Solve o(t) = 0 for t.
2, 5
Suppose 9*b - 906 = 201. Factor 12 + 202*r**2 - 124*r**3 + 17*r**3 - b*r**3 + 121*r + 50*r**4 - 11*r.
2*(r - 3)*(r - 2)*(5*r + 1)**2
Let l = 24628/187225 - 386/7489. Let a = -1000833/25 + 40043. Let l*s**2 + 44/25*s + a = 0. Calculate s.
-11
Factor -7134*k**3 - 7129*k**3 + 14264*k**3 + 787*k**2.
k**2*(k + 787)
Let l(v) be the first derivative of 2*v**5/55 + 17*v**4/11 + 746*v**3/33 + 1428*v**2/11 + 3528*v/11 + 482. Solve l(p) = 0.
-14, -3
Let d(t) = -651*t + 55988. Let m be d(86). Determine a, given that 1/5*a**3 + 0*a + 0 - 1/5*a**4 + 0*a**m = 0.
0, 1
Let m be (4 - -2 - 2)*(-9)/(-9). Factor -7*w**2 - w**3 - 418*w**4 - 11*w + 419*w**m - 2*w**2 - 4.
