1. Let i(s) = s**4 + 14*s**3 + 23*s**2 + 13*s + 3. Let y(m) = 22*i(m) - 6*t(m). Find k, given that y(k) = 0.
-8, -2, -1, 0
Suppose -112/5 + 2/5*h**2 + 22*h = 0. Calculate h.
-56, 1
Let w = 24 - 26. Let g be (-324)/42 + 5 - (w + -1). Solve 0*c - g*c**2 - 2/7*c**3 + 0 = 0 for c.
-1, 0
Suppose -3 = -0*p + 3*p. Let f(c) = -c**3 + c**2 - c + 1. Let y(a) = -4*a**4 - 6*a**3 - 3*a**2 + 2*a - 1. Let z(d) = p*y(d) - f(d). Solve z(n) = 0 for n.
-1, 0, 1/4
Factor 23*r**2 + 2 + 51*r - 689*r**3 + r**2 + 692*r**3 + 28.
3*(r + 1)*(r + 2)*(r + 5)
Let t = 79 - 76. Let s(p) = p**5 + p**3 + p**2 + p - 1. Let g(v) = 3*v**5 + 2*v**4 - v**3 - 6*v**2 - 2*v - 2. Let h(l) = t*g(l) - 6*s(l). Factor h(c).
3*c*(c - 2)*(c + 1)**2*(c + 2)
Let z(n) = -2*n - 5*n - 11*n**2 - 7*n**3 + n**2. Let h(p) = -p**3 - p**2 - p. Suppose -12*q + 3*q - 9 = 0. Let s(w) = q*z(w) + 4*h(w). Factor s(j).
3*j*(j + 1)**2
Suppose -3*p + 73 = 67. Let d(s) be the first derivative of -1/12*s**3 + 0*s - 3 + 1/8*s**p. What is k in d(k) = 0?
0, 1
Let t(f) be the first derivative of f**5/30 - f**4/18 - f**3/9 + f**2/3 - 2*f - 15. Let h(o) be the first derivative of t(o). Determine r so that h(r) = 0.
-1, 1
Suppose -8*c + 20 = -4. Let m(n) be the second derivative of 1/63*n**7 - 1/9*n**4 + 2/45*n**6 - 1/9*n**c + 0*n**2 + 0*n**5 + 0 - 7*n. Factor m(b).
2*b*(b - 1)*(b + 1)**3/3
Suppose 25*j = 11*j. Find n such that 1/2*n**3 + 0*n - 1/4*n**4 + j - 1/4*n**2 = 0.
0, 1
Let b(n) be the third derivative of -n**6/24 - 11*n**5/12 - 155*n**4/24 - 35*n**3/2 - 302*n**2. Solve b(j) = 0 for j.
-7, -3, -1
Let p(z) be the second derivative of -z**7/126 + 2*z**6/45 + 123*z. What is u in p(u) = 0?
0, 4
Determine t so that 0 + 0*t - 1/3*t**4 + 10/3*t**3 + 11/3*t**2 = 0.
-1, 0, 11
Suppose -231*x**2 + 7*x**5 + 4*x - 228*x**2 - 21*x**3 + 451*x**2 + 0*x**5 - 2*x**4 = 0. Calculate x.
-1, 0, 2/7, 2
Let n = 5 - 6. Let o = n + 7. What is p in -17*p**2 + 6*p**2 + 8*p**2 + o*p = 0?
0, 2
Let n(o) = 2*o**2 - 16*o - 1. Let v be n(8). Let l(y) = -y**4 - y**2 + y - 1. Let w(d) = -10*d**3 - 5*d + 5. Let p(k) = v*w(k) - 5*l(k). Solve p(g) = 0.
-1, 0
Let d = 222 + -222. Let k be (d + 42/15)*(-38)/(-133). Let -14/5*l**3 + 4/5*l**4 + 0 - k*l + 14/5*l**2 = 0. What is l?
0, 1/2, 1, 2
Solve 100/3*r**3 + 60*r - 60*r**5 + 305*r**4 - 305*r**2 + 100/3 = 0.
-1, -1/4, 2/3, 5
Let g = 962 - 31742/33. Let v(h) be the third derivative of 1/330*h**5 + g*h**3 - 1/33*h**4 + 3*h**2 + 0*h + 0. Factor v(s).
2*(s - 2)**2/11
Find u such that 656*u**3 - 2539*u**4 + 1814*u**4 - 500*u**2 + 125*u**5 + 364*u**3 + 80*u = 0.
0, 2/5, 1, 4
Let o(u) be the second derivative of 46*u - 4/11*u**3 + 9/11*u**2 + 1/22*u**4 + 0. Find a such that o(a) = 0.
1, 3
Let q(s) be the third derivative of 20*s**2 + 3/8*s**6 + 1/20*s**5 + 0*s**4 + 45/56*s**7 + 0*s + 0*s**3 + 0. What is p in q(p) = 0?
-2/15, 0
Let 0 - 6*g**3 - 1/9*g - 55/9*g**2 = 0. Calculate g.
-1, -1/54, 0
Let p be 5 + 2/(-3)*-3. Let i(c) be the third derivative of -1/210*c**p + 0*c + 0*c**3 + 1/72*c**4 + 7/360*c**6 - 1/36*c**5 + 0 - 3*c**2. Factor i(l).
-l*(l - 1)**2*(3*l - 1)/3
Let g(b) be the first derivative of 5 - 10*b**5 - 112/5*b**2 - 10*b**4 + 32/5*b + 32*b**3. Let g(i) = 0. Calculate i.
-2, 2/5
Suppose -17*c + 384 = 31*c. Factor 6 + 2/3*m**4 - 4/3*m**2 - c*m + 8/3*m**3.
2*(m - 1)**2*(m + 3)**2/3
Factor -5/3*j**3 + 0 - 1/3*j**4 + 14/3*j**2 + 0*j.
-j**2*(j - 2)*(j + 7)/3
Let u(d) be the first derivative of d**4/4 + 7*d**3/3 + 11*d**2/2 + 5*d + 98. Factor u(g).
(g + 1)**2*(g + 5)
Suppose 70*b**2 + 142*b + 123*b - 106*b**3 + 111*b**3 + 200 = 0. Calculate b.
-8, -5, -1
Let x be (-1 - (-9)/6)/(0 + (-80)/(-32)). Factor -2/5*j**2 + x*j**5 + 0 + j**3 + 0*j - 4/5*j**4.
j**2*(j - 2)*(j - 1)**2/5
Factor 63*u - 15*u + 4*u**4 - 12*u**3 + 113 - 8*u**2 - 73 - 72.
4*(u - 2)**2*(u - 1)*(u + 2)
Let i(w) be the second derivative of -w**6/60 + 3*w**5/10 - 5*w**4/4 - 25*w**3/3 + 375*w**2/4 + 50*w. Factor i(j).
-(j - 5)**3*(j + 3)/2
Let a(i) be the first derivative of i**3/9 - 242*i**2/3 + 58564*i/3 - 201. Factor a(m).
(m - 242)**2/3
Factor 5/6*m + 0 - 1/6*m**3 + 2/3*m**2.
-m*(m - 5)*(m + 1)/6
Let u(t) be the first derivative of t**4/6 - 20*t**3/9 + 32*t**2/3 - 64*t/3 - 99. Factor u(r).
2*(r - 4)**2*(r - 2)/3
Let f(m) be the third derivative of -m**6/30 + m**5/30 - m**4/72 + 11*m**3/6 - 16*m**2. Let p(j) be the first derivative of f(j). Factor p(b).
-(6*b - 1)**2/3
Let p = -751 + 753. Let b(j) be the first derivative of 0*j - 2*j**p + 4/3*j**3 + 5. Suppose b(k) = 0. Calculate k.
0, 1
Suppose -f + 4*u = -11, -f - 2 = 3*u + 1. Factor 1 + 2*a + 2 - 6*a**2 - 2*a + f*a**4.
3*(a - 1)**2*(a + 1)**2
Suppose -t = 4*p + 20, 5*t + p + 15 = -2*p. Let a(q) be the third derivative of 0*q**5 + t*q + 0 - 1/96*q**4 + 0*q**3 - 5*q**2 + 1/480*q**6. Factor a(o).
o*(o - 1)*(o + 1)/4
Let c = 770 + -770. Let x(l) be the first derivative of c*l**2 + 0*l + 8 - 2/51*l**3 + 2/17*l**4. Factor x(j).
2*j**2*(4*j - 1)/17
Suppose -2*z = -w - 52 + 58, w + 7 = -11*z. Factor -5/6*s**3 - 5/3*s**2 + 0 + 5/6*s**w + 0*s.
5*s**2*(s - 2)*(s + 1)/6
Suppose -9*k - 5*m = -122 + 99, m = 4*k - 36. Factor -3/2*w**2 - 19/2*w + k.
-(w + 7)*(3*w - 2)/2
Let u(d) be the second derivative of d**5/15 + 15*d**2/2 + 7*d. Let c(l) be the first derivative of u(l). Suppose c(b) = 0. What is b?
0
Suppose 121 = 3*s - 128. Solve -s - 16*a**2 - 84 - 48*a**3 + 36*a**4 + 167 + 28*a**5 = 0 for a.
-2, -2/7, 0, 1
Let w(l) be the third derivative of l**6/30 - 44*l**5/15 + 82*l**4/3 - 320*l**3/3 - 9*l**2 - 43*l. Solve w(h) = 0.
2, 40
Let o(k) = 6*k - 2. Let b be o(1). Let w(c) = -6*c**2 + 81*c + 24. Let t = 24 - 45. Let d(i) = -i**2 + 16*i + 5. Let u(x) = b*w(x) + t*d(x). Factor u(n).
-3*(n + 1)*(n + 3)
Suppose -32/13 - 112/13*q - 98/13*q**2 = 0. What is q?
-4/7
Let o(c) be the third derivative of c**6/40 - 117*c**5/20 + 4563*c**4/8 - 59319*c**3/2 + 128*c**2. Suppose o(q) = 0. What is q?
39
Let z(q) be the second derivative of -1/3*q**4 - 13*q - 5*q**3 - 7*q**2 + 0. Factor z(i).
-2*(i + 7)*(2*i + 1)
Let i = -30 - -16. Let j be ((-4)/i)/((-1)/(-7)). Factor -9*m**2 + 1 + 15*m**j + 0 + m**4 - 4*m - 4*m**3.
(m - 1)**4
Let o(z) be the third derivative of -z**6/360 + 13*z**5/180 - 23*z**4/72 + 11*z**3/18 - z**2 + 3*z. Determine q, given that o(q) = 0.
1, 11
Let j(c) = c + 5. Let y = -25 + 29. Let l be j(y). Let m(w) = -w**2 + 10*w + 11. Let a(v) = -5*v - 5. Let t(s) = l*a(s) + 4*m(s). What is b in t(b) = 0?
-1, -1/4
Let b = -30017/3 - -10006. Let -1/6*t**2 + 1/6*t + b = 0. Calculate t.
-1, 2
Let t(u) be the second derivative of u**4/8 - 2*u**3 - 15*u**2 + 716*u. Factor t(n).
3*(n - 10)*(n + 2)/2
Let t(a) be the third derivative of 5/336*a**8 + 0 - 2*a**2 + 5/3*a**3 - 2/21*a**7 + 1/6*a**6 - 33*a - 25/24*a**4 + 1/6*a**5. Factor t(y).
5*(y - 2)*(y - 1)**3*(y + 1)
Factor -3/7*m**4 + 2/7*m**3 + 0*m + 1/7*m**5 + 0 + 0*m**2.
m**3*(m - 2)*(m - 1)/7
Suppose 281 = 4*i - 39. Let 5*d**4 + 12 + 80*d + i*d**2 + 40*d**3 + 5*d**4 + 20 - 3*d**5 + 4*d**5 = 0. What is d?
-2
Find y, given that 0*y**4 + 15*y**4 - y**4 - 19*y**4 + 100 + 160*y - 50*y**3 + 15*y**2 = 0.
-10, -1, 2
Let d(p) be the first derivative of -4*p**3/3 + 84*p**2 - 1764*p + 89. Let d(n) = 0. What is n?
21
Let m(f) = -4*f - 4. Let u be 8 + 2 + -5 + 0. Let a(c) = -c**2 + 4*c + 5. Let h(i) = u*m(i) + 4*a(i). Factor h(z).
-4*z*(z + 1)
Let t = -86/11 + 441/55. Let s(p) be the second derivative of -t*p**2 + 1/30*p**4 - 1/50*p**5 + 1/15*p**3 + 0 + 2*p. Factor s(j).
-2*(j - 1)**2*(j + 1)/5
Suppose -2*y - 3 = y, 5*c - 33 = 3*y. Suppose 13 = -3*f - 5*n + 89, -f - n = -26. Factor 23*r**2 - c*r**2 - f*r**3 + 48*r - 6*r**2 - 12 + 22*r**2.
-3*(r - 2)*(r + 1)*(9*r - 2)
Let m(d) = d**2 - 150*d + 6237. Let j(h) = -2*h + 1. Let w(g) = 4*j(g) + m(g). Factor w(r).
(r - 79)**2
Find h such that -67*h**3 - 20*h**2 - 262*h + 71*h**3 + 286*h = 0.
0, 2, 3
Let t(i) be the first derivative of -i**6/1620 + i**5/180 - i**4/54 - 7*i**3/3 + 2. Let p(j) be the third derivative of t(j). Factor p(h).
-2*(h - 2)*(h - 1)/9
Let p(y) be the third derivative of y**5/480 + 89*y**4/96 + 7921*y**3/48 - 292*y**2 - 2. Factor p(z).
(z + 89)**2/8
Suppose -25/2*q**4 - 2*q + 6*q**2 + 0 + 45/2*q**3 = 0. Calculate q.
-2/5, 0, 1/5, 2
Let -225 + 59*u**2 + 30*u**2 + 5*u**3 - 57*u**2 + 455*u - 136*u**2 - 131*u**2 