d s such that t(s) = 0.
1, 4
Let d(x) be the third derivative of x**5/240 + 17*x**4/48 - 35*x**3/24 + 138*x**2. Solve d(z) = 0.
-35, 1
Let p(b) be the second derivative of -10*b - 1/15*b**3 - 1/150*b**6 + 1/50*b**5 + 0*b**4 + 1/10*b**2 + 0. Find m, given that p(m) = 0.
-1, 1
Let o = 327 + -324. Let p(s) be the third derivative of 0 + 0*s**4 - 1/180*s**5 + 0*s + 3*s**2 + 0*s**o. Solve p(a) = 0.
0
Suppose 0*r + 21 = -2*o + 5*r, -5*o + r = -5. Find a such that o*a**3 + 6*a + 5*a**2 - 2*a**2 - 5*a**3 - 6*a**2 = 0.
-2, 0, 1
Let a(y) = 36*y - 504. Let k be a(14). Solve k + 1/3*o + 1/3*o**2 = 0 for o.
-1, 0
Let w(n) be the third derivative of n**7/21 - 11*n**6/24 + 19*n**5/12 - 65*n**4/24 + 5*n**3/2 + 233*n**2 - 2. Find r, given that w(r) = 0.
1/2, 1, 3
Let w be (5/(-50)*-4)/((-2)/(-10)). Find c such that 2*c**2 + 86*c**3 + 4*c**4 - 101*c**3 - 6*c**w = 0.
-1/4, 0, 4
Let m(r) be the first derivative of -8*r**3/3 + 5*r**2 + 12*r + 46. Factor m(o).
-2*(o - 2)*(4*o + 3)
Let s(p) be the first derivative of -2*p**5/5 - 7*p**4/4 + 26*p**3/3 - 23*p**2/2 + 6*p - 590. Let s(k) = 0. Calculate k.
-6, 1/2, 1
Let m(g) = g**4 - 2*g**3 + 2*g**2 - 1. Let b(k) = k**4 - 2*k**3 + k**2 + k - 1. Let r(j) = 10*b(j) - 5*m(j). Factor r(s).
5*(s - 1)**3*(s + 1)
Factor -3/8*k**2 + 135/4 - 81/8*k.
-3*(k - 3)*(k + 30)/8
Suppose s = -4*r + 26 - 6, -3*s + 20 = 2*r. Let b(w) be the first derivative of w**2 - 1/3*w**3 + 0*w - 1/4*w**r - 8. Factor b(j).
-j*(j - 1)*(j + 2)
Let d(v) = -5*v**3 - 38*v**2 - 37*v - 28. Let b(q) = -5*q**3 - 37*q**2 - 38*q - 27. Let l(p) = 8*b(p) - 7*d(p). Factor l(c).
-5*(c + 1)**2*(c + 4)
Let z(r) be the first derivative of r**4/22 - 2*r**3/11 - 24*r**2/11 - 56*r/11 - 14. Determine i so that z(i) = 0.
-2, 7
Let d(h) be the first derivative of 0*h**2 + 0*h**3 + 1/18*h**4 - 1/45*h**5 + 0*h + 3. Factor d(c).
-c**3*(c - 2)/9
Let q(z) = 472*z + 1888. Let d be q(-4). Factor 0*w - 80/7*w**3 + d - 8/7*w**2 - 162/7*w**5 - 234/7*w**4.
-2*w**2*(w + 1)*(9*w + 2)**2/7
Let n(t) be the second derivative of t**7/14 - 43*t**6/10 - 3*t**5/10 + 43*t**4/2 + t**3/2 - 129*t**2/2 - 267*t + 3. Determine m, given that n(m) = 0.
-1, 1, 43
Suppose 0 = 24*a - 25*a + 4. Let i(y) = -y**3 + 15*y**2 - 11*y + 9. Let s(w) = 2*w**3 - 15*w**2 + 12*w - 8. Let b(p) = a*s(p) + 3*i(p). Solve b(f) = 0.
1
Let x(v) = -2*v**3 - 60*v**2 + 300*v - 506. Let q(d) = -3*d**3 + 137 - 394 + 600*d - 120*d**2 - 754. Let s(j) = -6*q(j) + 11*x(j). What is f in s(f) = 0?
5
Factor 13 - z + 2*z**2 + 15 + 3*z + 0 - 20*z.
2*(z - 7)*(z - 2)
Suppose 0 = 5*o - 42*o + 74. Let l(c) be the second derivative of 0 + c**4 - 7/3*c**3 + 2/5*c**5 + 1/7*c**7 + o*c**2 - 8/15*c**6 - 6*c. Let l(w) = 0. What is w?
-1, 2/3, 1
Suppose 0 = -0*u + 4*u - 3*u. Let j(q) be the first derivative of 0*q**2 + 1/14*q**4 + 2/21*q**3 + u*q - 4. Suppose j(p) = 0. Calculate p.
-1, 0
Let b be (10/(-18))/((1295/42)/(-37)). Let k(r) be the first derivative of -7 + b*r**3 + 4*r - 3*r**2. Suppose k(a) = 0. What is a?
1, 2
Let n be (5/5)/((-223)/(-2)). Let h = n - -428/2007. Solve 0 + 2/9*j**2 + h*j = 0 for j.
-1, 0
Let m(t) be the second derivative of -2*t**6/15 + 2*t**5/5 + 4*t**4/3 - 4*t**3/3 - 6*t**2 + 162*t. Factor m(o).
-4*(o - 3)*(o - 1)*(o + 1)**2
Let z(w) be the first derivative of -w**4/4 + 2*w - 3. Let o be z(0). Determine t so that -2 + t**o - 1 - t + 1 = 0.
-1, 2
Let h(i) be the first derivative of -i**5/5 - i**4/2 + i**3/3 + i**2 - 60. Determine t, given that h(t) = 0.
-2, -1, 0, 1
Let x(w) = 1 + 4*w - 2*w**3 + 0*w + 3. Let j(n) = n + 1. Let p(u) = -6*u - 6. Let t(l) = 11*j(l) + 2*p(l). Let r(s) = 4*t(s) + x(s). Factor r(g).
-2*g**3
Suppose -c + 41 = 39. Suppose c*o + 3 = 3*o. Factor 0*i - 3/4*i**o + 0 - 1/4*i**5 - 3/4*i**4 - 1/4*i**2.
-i**2*(i + 1)**3/4
Let o(y) be the second derivative of y**7/210 - y**5/10 - y**4/3 + 7*y**3/2 + 12*y. Let h(n) be the second derivative of o(n). Factor h(a).
4*(a - 2)*(a + 1)**2
Let i = 147/17 + -1051/153. Let s(u) be the first derivative of -1 + 0*u + 25/9*u**6 + i*u**3 + 28/3*u**5 + 22/3*u**4 + 0*u**2. Let s(p) = 0. What is p?
-2, -2/5, 0
Let t be (-8 + -247 - 3) + (-4)/(-2). Let q = -256 - t. Let 0*p**2 + 8/15*p**4 + q + 0*p - 2/15*p**3 = 0. What is p?
0, 1/4
Let o(d) be the third derivative of -d**6/120 - 2*d**5/15 - 2*d**4/3 + 6*d**2 - 2. Find t such that o(t) = 0.
-4, 0
Find f, given that 3/4*f**3 + 192 + 168*f - 93/4*f**2 = 0.
-1, 16
Let d(p) = 15*p**2 + 13*p - 19. Let j(r) = -8*r**2 - 6*r + 10. Let w(o) = 6*d(o) + 11*j(o). Let b be w(-8). What is u in 6 - 8/3*u**3 + 50/3*u**2 - b*u = 0?
1/4, 3
Let d(p) be the second derivative of -16*p**2 + 52/3*p**3 + 18*p + 0 + 7/3*p**4. Find n, given that d(n) = 0.
-4, 2/7
Let a = 63 + -35. Let o = 22 + -15. Solve -2*u**2 + o*u**3 - a*u**3 + 12*u + 9*u**4 + 2*u**2 = 0.
-2/3, 0, 1, 2
Let s(u) = -u**3 - 58*u**2 - 57*u. Let z be s(-57). Factor 3/4*j + z - 1/4*j**2.
-j*(j - 3)/4
Let g = 3/167 + 313/1169. Solve 2*m**3 - 8/7 - 16/7*m - g*m**2 + 10/7*m**4 + 2/7*m**5 = 0.
-2, -1, 1
Suppose -3*m + 12 = 67*w - 70*w, -3*m = -w - 10. Let k(r) be the first derivative of -9/2*r**2 - 1/12*r**4 - r**m - 9*r + 6. Determine t, given that k(t) = 0.
-3
Let i be 9/15 - (28/5)/(-4). Factor -11*j + 173*j**3 - j - 169*j**3 + 10*j**i - 2*j**4.
-2*j*(j - 3)*(j - 1)*(j + 2)
Let j(p) = 3*p**3 + 2*p**2 + 3*p. Let s(n) = -10*n**3 - 7*n**2 - 10*n. Let d(c) = 7*j(c) + 2*s(c). Let f(k) = 3*k**3 + k. Let t(v) = -d(v) + f(v). Factor t(x).
2*x**3
Let u(m) be the third derivative of m**5/30 - 11*m**4/12 + 10*m**3/3 - 335*m**2. Factor u(s).
2*(s - 10)*(s - 1)
Let -5041/2 - 1/2*y**2 - 71*y = 0. What is y?
-71
Let s(m) be the third derivative of m**8/672 - m**7/140 - m**6/80 + 11*m**5/120 - m**4/8 - 62*m**2 - 1. Factor s(b).
b*(b - 3)*(b - 1)**2*(b + 2)/2
Let y(p) be the first derivative of 2*p**5/55 + p**4/11 - 18*p**3/11 + 52*p**2/11 - 56*p/11 + 284. Determine m so that y(m) = 0.
-7, 1, 2
Find b such that 18/5*b**3 - 1/5*b**5 - 6/5 - 32/5*b**2 - 2/5*b**4 + 23/5*b = 0.
-6, 1
Let a(i) = -13*i**2 - 23*i - 102. Let y(o) = -5*o**2 - 12*o - 51. Let p(w) = 2*a(w) - 5*y(w). Factor p(v).
-(v - 17)*(v + 3)
Suppose -3*i - 1 = -o, -14*i - 6 = -10*i - 2*o. Solve -5/2 + 5/2*m + 5/2*m**i - 5/2*m**3 = 0.
-1, 1
Let t(m) = -m**3 - m**2 + m + 2. Let s be t(-1). Let b(u) be the first derivative of -4*u**2 - 8*u - 2/3*u**3 + s. Let b(r) = 0. Calculate r.
-2
What is f in 48*f + 418*f - 3*f**2 - 118*f + f**2 - 10092 - f**2 = 0?
58
Let s = -34 + 44. Factor -s*x**3 + 698*x**2 - 55*x**3 - 763*x**2 - 15*x - 15*x**4.
-5*x*(x + 1)*(x + 3)*(3*x + 1)
Let y(t) = t**2 - 6*t + 3. Let n be y(6). Suppose 2*j - 15 = -n*j. Suppose -3*s**2 + 100*s**5 + 60*s**3 + s**2 - 2*s**2 - 140*s**4 - 16*s**j = 0. Calculate s.
0, 1/5, 1
Let o be (-2 + 3 - (-416)/(-480))/((-6)/(-20)). Let -o*a**2 + 40/9*a - 4 = 0. Calculate a.
1, 9
Suppose 0 = b - 10*b. Let i(d) be the first derivative of 0*d**2 - 4 + 0*d - 1/22*d**4 + 1/33*d**6 + 0*d**5 + b*d**3. Suppose i(j) = 0. What is j?
-1, 0, 1
Let l(f) be the first derivative of f**3/9 - 10*f**2/3 + 100*f/3 + 15. Factor l(m).
(m - 10)**2/3
Suppose -g + 56 = 3*g. Factor -40 + 25*k - g*k + 15*k**2 + 39*k.
5*(k + 4)*(3*k - 2)
Let f(j) = j - 6. Let m be f(16). Suppose -2*w + m = 4*v, -4*w = 3*v - 4 - 11. Find h such that -3*h**5 + 2 + h**5 - 5*h**4 - 4*h**w + 6*h - h**4 + 4*h**2 = 0.
-1, 1
Let a = 69/20 - 13/4. Let p(o) be the first derivative of 4/15*o**3 - 3 + 1/10*o**4 - 4/5*o - a*o**2. Suppose p(t) = 0. What is t?
-2, -1, 1
Let v(f) be the first derivative of -2*f**3/9 - f**2 + 10. Suppose v(i) = 0. What is i?
-3, 0
Let q(m) be the second derivative of -m**6/90 + m**5/6 + 2*m**4/3 + 153*m. Factor q(s).
-s**2*(s - 12)*(s + 2)/3
Let -8/11*f - 8/11 - 2/11*f**2 = 0. What is f?
-2
Factor -60/7 - 2/7*q + 2/7*q**2.
2*(q - 6)*(q + 5)/7
Suppose -100*a + 167 = 35 - 168. Determine c so that 14 + 128*c + 49*c**4 + 791/2*c**a + 771/2*c**2 = 0.
-7, -1/2, -2/7
Let b(l) be the third derivative of 0 + 5/3*l**4 + 0*l + 1/42*l**7 + 0*l**6 - 21*l**2 - 1/2*l**5 - 5/2*l**3. Factor b(k).
5*(k - 1)**3*(k + 3)
Suppose 0*f**2 + 24/7*f**3 + 0*f - 2/7*f**4 + 0 = 0. Calculate f.
0, 12
Let t(h) be the second derivative of -3/2*h**2 + h + 5/72*h**4 + 1/9*h**3 + 0 + 1/45*h**5 + 1/360*h**6. Let a(m) be the first derivative of t(m). Factor