, given that p + 7/2*a + 1/4*a**2 = 0.
-7
Let p(z) be the first derivative of -z**6/18 - 7*z**5/15 - 3*z**4/2 - 22*z**3/9 - 13*z**2/6 - z + 121. Solve p(g) = 0.
-3, -1
Let c(t) = t + 9. Let g be c(3). Let v = -10 + g. Factor 50 - 30 - k**2 + 6*k**v + 20*k.
5*(k + 2)**2
Let o(b) be the first derivative of 3 - b - 1/42*b**4 + 0*b**3 + 1/7*b**2. Let h(a) be the first derivative of o(a). Determine s so that h(s) = 0.
-1, 1
Let a(w) be the second derivative of -5*w**4/48 + 275*w**3/12 - 68*w. Factor a(i).
-5*i*(i - 110)/4
Determine h, given that 52/3*h**2 - 32/3*h**3 - 16/3*h + 5/3*h**4 + 0 = 0.
0, 2/5, 2, 4
Let w(s) be the third derivative of -s**5/150 - s**4/30 + 14*s**2. Let w(x) = 0. Calculate x.
-2, 0
Let h = -2 + 6. Suppose -13 = -h*i + 7. Factor -4*k**3 + 3*k**4 - 3*k**5 + 5*k**3 + i*k**3.
-3*k**3*(k - 2)*(k + 1)
Let l(q) be the first derivative of 5*q**4/18 + 8*q**3/9 + q**2 + 4*q/9 - 98. Solve l(j) = 0 for j.
-1, -2/5
Let p(b) = -b**3 + 9*b**2 - 8*b + 3. Suppose 10 = -2*f + 26. Let j be p(f). What is t in 7/5*t**j + 17/5*t**2 + 9/5*t**5 - 21/5*t**4 + 4/5 - 16/5*t = 0?
-1, 2/3, 1
Suppose 16 - 132/5*m**2 - 88/5*m - 6/5*m**5 + 52/5*m**4 + 94/5*m**3 = 0. What is m?
-2, -1, 2/3, 1, 10
Let w(y) be the second derivative of -y**6/10 + 273*y**5/20 - 506*y**4 - 1058*y**3 - 78*y - 1. Factor w(v).
-3*v*(v - 46)**2*(v + 1)
Let k(w) = 2*w**3 - 4*w**2 + 4*w - 3. Let i be k(2). Let b be (-4 - 584/(-112)) + 4/14. Factor b*y**4 + 0 + i*y**3 + 14/3*y**2 + 4/3*y.
y*(y + 2)*(3*y + 2)**2/6
Let c(s) be the third derivative of 0*s + 0*s**7 - 16*s**2 + 0*s**4 + 1/504*s**8 + 1/45*s**5 + 0*s**3 + 0 - 1/60*s**6. Factor c(r).
2*r**2*(r - 1)**2*(r + 2)/3
Determine u, given that -365*u**2 + 87*u**2 - 40*u + 89*u**2 + 93*u**2 + 42 + 94*u**2 = 0.
-21, 1
Let a(o) be the third derivative of o**6/120 + o**5/15 - 5*o**4/24 - 248*o**2. Solve a(h) = 0.
-5, 0, 1
Let -2/5*f**5 + 2/5*f**3 + 0*f - 18/5*f**2 + 0 + 18/5*f**4 = 0. What is f?
-1, 0, 1, 9
Let j(t) = -t**3 - 24*t**2 + 10*t + 5. Let w(h) = h**3 + 36*h**2 - 16*h - 7. Let n(o) = -7*j(o) - 5*w(o). Determine c so that n(c) = 0.
0, 1, 5
Let k(a) be the second derivative of 0 + 0*a**3 - 1/60*a**6 - 2/45*a**5 + 1/9*a**4 - 5/2*a**2 + a. Let u(i) be the first derivative of k(i). Factor u(q).
-2*q*(q + 2)*(3*q - 2)/3
Find i such that 2*i - 12*i**4 - 22*i**5 - 68*i**2 + 4*i**5 + 80*i**2 + 16*i**3 = 0.
-1, -1/3, 0, 1
Let u be (-24)/(-15)*((-270)/12)/(-9). Let k(f) be the second derivative of -1/80*f**5 + 0*f**3 + 1/120*f**6 - 8*f + 0 + 0*f**2 - 1/24*f**u. Solve k(i) = 0.
-1, 0, 2
Let q = 1041/698 + 3/349. Factor -q*a**3 - 3 + 3*a**2 + 3/2*a.
-3*(a - 2)*(a - 1)*(a + 1)/2
Let z(u) be the third derivative of -u**6/960 + 7*u**5/480 - 5*u**4/96 + 4*u**2 + 5. Determine l so that z(l) = 0.
0, 2, 5
Let f(v) be the first derivative of -13 - 1/6*v**2 - 2/9*v**3 + 0*v - 1/12*v**4. Suppose f(a) = 0. Calculate a.
-1, 0
Let m be -1*(2163/(-3780) + 8/14). Let s(d) be the third derivative of 1/630*d**5 - 1/63*d**4 + 0*d - 4/63*d**3 + 0 + 2*d**2 + m*d**6. Factor s(v).
2*(v - 2)*(v + 1)*(v + 2)/21
Let x(p) be the third derivative of -1/1050*p**7 + 0*p + 7/5*p**4 + 0 - 73/300*p**5 - 24/5*p**3 - 15*p**2 + 7/300*p**6. Determine o so that x(o) = 0.
3, 4
Let x(t) be the third derivative of 2*t**7/105 + 2*t**6/5 + 3*t**5 + 25*t**4/3 - 2*t**2 + 20*t. Factor x(b).
4*b*(b + 2)*(b + 5)**2
Let r be (-738)/36 + (-6)/4. Let o(l) = 19*l**3 + 24*l**2 - 11*l. Let z(f) = 5*f**3 + 6*f**2 - 3*f. Let i(j) = r*z(j) + 6*o(j). Factor i(t).
4*t**2*(t + 3)
Let s(f) be the third derivative of f**8/2240 - 19*f**4/24 + 3*f**2. Let l(j) be the second derivative of s(j). Factor l(c).
3*c**3
Suppose -l = -6*l + 5400. Find q such that 90*q**2 + 14*q**3 - 35*q**3 + l - 540*q + 16*q**3 = 0.
6
Let r(t) be the third derivative of -30*t**2 - 1/300*t**6 + 0*t + 0 - 4/15*t**3 + 2/75*t**5 + 1/60*t**4. Determine l, given that r(l) = 0.
-1, 1, 4
Let v(z) be the first derivative of 5*z**6/6 - 7*z**5 + 45*z**4/2 - 110*z**3/3 + 65*z**2/2 - 15*z + 53. Suppose v(w) = 0. Calculate w.
1, 3
Suppose 0 + 2/7*t**2 - 1/7*t**3 + 3/7*t = 0. Calculate t.
-1, 0, 3
Let x(y) be the first derivative of -4/5*y + 1/10*y**4 - 1/5*y**2 + 13 + 4/15*y**3. Factor x(c).
2*(c - 1)*(c + 1)*(c + 2)/5
Let a = -590/53 + 1233/106. Factor 1/4*c**2 - a - 1/4*c.
(c - 2)*(c + 1)/4
Let p = 3465/292 + 28/73. Let t be 646/85 + ((-15)/50)/((-6)/8). Let -t*q**2 - p*q**4 + 77/4*q**3 + 0 + q = 0. What is q?
0, 2/7, 1
Suppose 2*j - h = 9, 27 = j + 4*j - 4*h. Suppose 0 = -4*u + 75 - 40 - 19. Solve j*n**u - 9/2*n**2 - 3*n + 9/2*n**3 + 0 = 0.
-2, -1/2, 0, 1
Let i(k) be the third derivative of -27*k**6/40 + 39*k**5/20 - 5*k**4/3 + 2*k**3/3 - k**2 - 21. Suppose i(a) = 0. What is a?
2/9, 1
Find w, given that 20/19*w**2 + 46/19*w + 24/19 - 2/19*w**3 = 0.
-1, 12
Let a(k) be the first derivative of -k**5/2 + 5*k**4/8 + 5*k**3/2 - 5*k**2/4 - 5*k + 77. What is n in a(n) = 0?
-1, 1, 2
Let j(t) be the second derivative of -t**6/30 + 17*t**5/20 + 19*t**4/6 - 389*t. What is w in j(w) = 0?
-2, 0, 19
Factor j**2 + 3569*j - 34*j**2 - 24 - 3431*j.
-3*(j - 4)*(11*j - 2)
Factor -386*b - 5*b**2 + 195*b + 216*b.
-5*b*(b - 5)
Let a(q) be the second derivative of 10*q - 8/3*q**3 - 16/5*q**2 - 2/75*q**6 - 7/25*q**5 - 6/5*q**4 + 0. Suppose a(v) = 0. Calculate v.
-2, -1
Let u(c) be the second derivative of 0 + 1/110*c**5 + 1/33*c**3 - 1/33*c**4 - 11*c + 0*c**2. Factor u(f).
2*f*(f - 1)**2/11
Let i(y) be the first derivative of 3/20*y**4 + 0*y - 7/10*y**6 + 2/15*y**3 + 7 + 0*y**2 - 4/5*y**5. Suppose i(h) = 0. Calculate h.
-1, -2/7, 0, 1/3
Let x(z) be the first derivative of -z**6/105 - 3*z**5/70 - z**4/14 - z**3/21 - 14*z - 16. Let l(k) be the first derivative of x(k). Solve l(s) = 0 for s.
-1, 0
Let c(g) = -g + 7. Let m be c(4). Suppose -z**4 + 4*z + m*z**5 + 10*z + 9*z**2 - 2*z - 15*z**3 - 8*z**4 = 0. What is z?
-1, 0, 1, 4
Factor 0 + 1/3*a**3 + 8/3*a**2 - 4*a - 1/3*a**4.
-a*(a - 2)**2*(a + 3)/3
Solve 5*q + 14/5*q**2 + 1/5*q**3 + 12/5 = 0.
-12, -1
Let c(x) = 7*x**4 - 64*x**3 + 111*x**2 - 75*x + 16. Let o(v) = -4*v**4 + 32*v**3 - 56*v**2 + 38*v - 8. Let n(i) = 2*c(i) + 5*o(i). Solve n(b) = 0.
1/3, 1, 2
Let z(w) be the second derivative of -5*w**8/84 + 2*w**7/35 + w**6/15 + 7*w**2/2 - 12*w. Let o(b) be the first derivative of z(b). Let o(a) = 0. What is a?
-2/5, 0, 1
Let b(v) be the second derivative of -v**7/280 + v**6/120 + v**5/20 + v**3/2 - 7*v. Let c(a) be the second derivative of b(a). Factor c(t).
-3*t*(t - 2)*(t + 1)
Let l(b) be the first derivative of 54*b - 1/16*b**4 + 3/2*b**3 + 1 - 27/2*b**2. Factor l(i).
-(i - 6)**3/4
Let t = -38 + 41. Let p be 297/(-121) + (t - 0). Factor 8/11 - 4/11*d**3 + 8/11*d + 2/11*d**4 - p*d**2.
2*(d - 2)**2*(d + 1)**2/11
Find f, given that -328 + 280 - 12*f + 0*f**2 - 6*f + 3*f**2 = 0.
-2, 8
Let x be (-63)/18 - (-14 - -3). Factor x*y**2 - 6*y + 0 - 3/2*y**3.
-3*y*(y - 4)*(y - 1)/2
Suppose 32*c = -2*c - 7*c. Let k(n) be the third derivative of 0 - 5*n**2 + 0*n**3 + 0*n**4 + 1/30*n**5 + c*n. Factor k(t).
2*t**2
Let w = 4561 - 4559. Factor 0 + 1/2*s**w - 1/2*s.
s*(s - 1)/2
Let s(c) be the second derivative of 13/6*c**3 + 37/80*c**5 + 1/12*c**6 + 0 - 32*c + 1/168*c**7 + 2*c**2 + 4/3*c**4. Find b such that s(b) = 0.
-4, -2, -1
Let 552/5 - 284/5*q + 4/5*q**2 = 0. Calculate q.
2, 69
Let o = 14 - 7. Let 3*b**2 + b + 5*b**3 - 5 + o*b**2 - 6*b - 5*b**2 = 0. What is b?
-1, 1
Factor 235*c**3 - 79*c**3 + 15*c**2 - 73*c**3 - 73*c**3 - 5*c**4.
-5*c**2*(c - 3)*(c + 1)
Let r(x) be the third derivative of 20/3*x**4 + 32/3*x**3 + 0 + 0*x - 28*x**2 + 2/21*x**7 + 8/3*x**5 + 2/3*x**6 + 1/168*x**8. Suppose r(c) = 0. What is c?
-2
Let i(k) = -5*k**2 - 84*k + 19. Let z be i(-17). Let a(o) be the third derivative of 0*o - 1/240*o**5 + 0*o**4 + 0*o**3 - 5*o**z + 0. Solve a(j) = 0.
0
Let j(s) be the first derivative of -25*s**6/6 + 7*s**5 + 29*s**4/4 - 47*s**3/3 - 4*s**2 + 16*s - 153. Factor j(g).
-(g - 1)**3*(5*g + 4)**2
Let m(x) be the first derivative of 3*x**5/5 + 9*x**4/4 + 2*x**3 + 304. Determine q so that m(q) = 0.
-2, -1, 0
Let w(t) = t - 10. Let v be w(13). Suppose v*y - 21 + 3 = 0. Factor -3*r**4 - r**3 - 2*r**3 + 12*r**2 - y*r**2.
-3*r**2*(r - 1)*(r + 2)
Suppose 8*m + 2 = -14. Let j be m + 21/(-9) + 5. Suppose -11/3*u**2 - j*u - 7/3*u**4 