 1)
Determine c so that 15 + 5/3*c**3 + 5*c - 25/3*c**2 = 0.
-1, 3
Let n(m) = m**2 - 1. Let o(z) = -3*z**3 + 12*z**2 - 6. Let v = 14 - 8. Let q(f) = v*n(f) - o(f). Determine x, given that q(x) = 0.
0, 2
Let q(h) be the first derivative of -25/2*h**4 - 24*h**2 - 8*h + 6 - 30*h**3. Find r such that q(r) = 0.
-1, -2/5
Let r be ((-6)/80)/((-279)/31). Let f(b) be the third derivative of 0*b - r*b**5 + 0 + 1/16*b**4 + 2*b**2 - 1/6*b**3. Find q, given that f(q) = 0.
1, 2
Let m be 4*(2 - 30/20). Suppose 2/9*q**m + 0*q + 0 + 2/9*q**3 = 0. Calculate q.
-1, 0
Let r be (-9)/15 + (-36)/(-10). Factor -r*u - 3 + 9 - 9*u**2 + u**3 + 3*u**4 + 2*u**3.
3*(u - 1)**2*(u + 1)*(u + 2)
Factor -12/7 - 3/7*w**2 - 15/7*w.
-3*(w + 1)*(w + 4)/7
Let l(z) = z**2 + 7*z + 9. Let s be l(-6). Let s*a + 7*a**4 - 5*a**2 + a**5 - 2*a**5 + 3*a**3 - a - 6*a**4 = 0. What is a?
-2, 0, 1
Solve 2/17 + 0*a - 2/17*a**2 = 0 for a.
-1, 1
Let m(r) be the third derivative of 0 + 0*r**3 + 0*r + 0*r**5 + 1/300*r**6 + 0*r**4 - 4*r**2. Determine o, given that m(o) = 0.
0
Let t be ((-4)/(-10))/((-4)/40). Let s(b) = b**3 + 9*b + 6. Let d(q) = -2*q**3 + q**2 - 19*q - 13. Let f(o) = t*d(o) - 9*s(o). Factor f(r).
-(r + 1)**2*(r + 2)
Let b(g) be the second derivative of 2*g**6/105 - g**5/140 - g**4/21 + g**3/42 + 12*g. Determine i so that b(i) = 0.
-1, 0, 1/4, 1
Let t(i) be the third derivative of 1/120*i**6 - 6*i**2 + 0*i + 0*i**5 + 0*i**3 - 1/24*i**4 + 0. Factor t(k).
k*(k - 1)*(k + 1)
Let l(d) be the second derivative of 0 - 1/12*d**4 + 1/6*d**3 + d + 1/60*d**5 - 1/2*d**2. Let m(h) be the first derivative of l(h). Factor m(j).
(j - 1)**2
Let n be 2/25*(-6)/(-36). Let r(a) be the second derivative of 0*a**2 + a - 1/30*a**4 + 0 + n*a**6 - 1/50*a**5 + 1/15*a**3. Determine x, given that r(x) = 0.
-1, 0, 1
Let h be ((-1130)/(-210))/((-146)/(-8)). Let a = h - 2/219. Factor -a*s**3 - 2/7*s + 0 - 4/7*s**2.
-2*s*(s + 1)**2/7
Let n(p) be the second derivative of p**5/60 - p**4/36 - p**3/18 + p**2/6 + 5*p. Factor n(q).
(q - 1)**2*(q + 1)/3
Factor -2/3*v**2 + 8/3*v - 8/3.
-2*(v - 2)**2/3
Let v(l) be the second derivative of -3*l - 1/2*l**2 + 0 - 1/3*l**3 - 1/12*l**4. Find c such that v(c) = 0.
-1
Let u(s) be the second derivative of s**4/12 + 14*s**3/3 + 98*s**2 + 6*s + 3. Factor u(v).
(v + 14)**2
Suppose -4*l**3 - 18/5*l**4 + 24/5*l + 8/5 - 4/5*l**5 + 2*l**2 = 0. What is l?
-2, -1, -1/2, 1
Find p such that -3/4*p**4 - p**3 + 0 + 0*p - 1/4*p**2 = 0.
-1, -1/3, 0
Factor 18/7 + 18/7*n**2 + 3/7*n**3 + 33/7*n.
3*(n + 1)*(n + 2)*(n + 3)/7
Let p be 2/(-7) - 1472/(-1232). Suppose 18/11*g**4 - 18/11*g**2 + 0 - 14/11*g**5 + 4/11*g + p*g**3 = 0. Calculate g.
-1, 0, 2/7, 1
Let g be ((-4)/(-3))/(2/7). Let h(d) be the first derivative of -2*d**2 + 14/5*d**5 + 0*d - g*d**3 - 2 + 5/3*d**6 - 3/2*d**4. Determine m, given that h(m) = 0.
-1, -2/5, 0, 1
Let w(p) be the second derivative of p**4/6 + 4*p**3/3 + 3*p**2 + 2*p. Factor w(n).
2*(n + 1)*(n + 3)
Let t(f) be the third derivative of -f**8/90720 - f**7/11340 - f**5/20 + 3*f**2. Let i(p) be the third derivative of t(p). Factor i(c).
-2*c*(c + 2)/9
Let u(k) = 6*k**5 + k**4 - 17*k**3 - 41*k**2 - 17. Let g(d) = -2*d**5 + 6*d**3 + 14*d**2 + 6. Let v = 2 - 19. Let t(w) = v*g(w) - 6*u(w). Factor t(f).
-2*f**2*(f - 1)*(f + 2)**2
Let j(b) be the second derivative of -2*b**6/15 - b**5/5 + b**4/3 + 2*b**3/3 - 4*b. Factor j(s).
-4*s*(s - 1)*(s + 1)**2
Let j(x) be the first derivative of -2*x**3/33 + 2*x/11 + 23. What is o in j(o) = 0?
-1, 1
Let x = 5 - 5. Let g = x - -2. Factor 2/11*k**g + 0 - 4/11*k.
2*k*(k - 2)/11
Let k be (-1)/3 + 95/(-75) + 2. Suppose -k*z - 2/5*z**2 + 2/5 + 2/5*z**3 = 0. Calculate z.
-1, 1
Let z(y) be the third derivative of y**9/30240 - y**5/30 + y**2. Let p(c) be the third derivative of z(c). Let p(h) = 0. What is h?
0
Let z(w) be the second derivative of w**8/2240 + w**7/280 + w**6/80 + w**5/40 - 5*w**4/12 + 3*w. Let k(v) be the third derivative of z(v). Factor k(s).
3*(s + 1)**3
Let o be 7/(-2)*16/(-14). Factor -i - 30*i**4 + 26*i**o + 4*i**2 + i.
-4*i**2*(i - 1)*(i + 1)
Let v = 25 - 49/2. Let l be (-30)/(-36)*15/25. Solve -v*o**3 + 0 - 1/2*o**4 + 1/2*o**2 + l*o = 0.
-1, 0, 1
Suppose -2*k + b = 1, -5*k + b = 6*b - 5. Factor -2*n**4 - n**3 + 0*n**3 - n**5 + k*n**3.
-n**3*(n + 1)**2
Let h be 15/(-12)*(-2 + -2). Let a be (20/15)/(h/3). Factor 0 + a*b + 2/5*b**2.
2*b*(b + 2)/5
Let v(j) be the first derivative of -1/8*j**2 - 4 + 1/16*j**4 - 1/12*j**3 + 1/4*j. Factor v(l).
(l - 1)**2*(l + 1)/4
Factor 4*i**3 - 5 + 12*i + 4 + 5 + 12*i**2.
4*(i + 1)**3
Let 14/3*l**3 + 0*l + 0 + 2*l**2 + 2/3*l**5 + 10/3*l**4 = 0. Calculate l.
-3, -1, 0
Suppose -15 = o - 6*o. Factor 5*s**o + 51*s - 6 + 23*s**2 - 140*s**2 + 2*s**3 + 17*s**3 + 48*s**4.
3*(s - 1)*(s + 2)*(4*s - 1)**2
Let q be 715/(-18) - 38/(-171). Let d = -38 - q. Determine b so that 1 + d*b + 1/2*b**2 = 0.
-2, -1
Let s(m) = -2*m**3 - 14*m**2 - 4*m + 2. Let a(i) = -i**3 - i**2 - 1. Let z(w) = 6*a(w) - s(w). Find x such that z(x) = 0.
-1, 1, 2
Let l(r) be the first derivative of -r**4/4 - 5*r**3/3 - r**2/2 - 5*r + 2. Let g be l(-5). What is n in n**3 + g*n**3 + n - 2*n = 0?
-1, 0, 1
Let r(n) = 3*n**3 - 26*n**2 + 22*n - 44. Let c be r(8). Find g, given that -22/3*g**2 - 8/3*g - 4/3*g**5 + 8/3 + 10/3*g**c + 8/3*g**3 = 0.
-1, 1/2, 2
Let o(u) be the first derivative of -2*u - u**4 + 7/2*u**2 + 4 - 4/3*u**3. Let o(r) = 0. Calculate r.
-2, 1/2
Let z = -700 - -33601/48. Let p(q) be the third derivative of -q**2 + 0*q - z*q**4 + 0 - 1/240*q**5 - 1/24*q**3. Let p(x) = 0. What is x?
-1
Let h(r) = -10*r**2 + 11*r + 8. Let f(m) = m**2 - 2. Let o be f(2). Let j(z) = -z**2 + z + 1. Let a(g) = o*h(g) - 18*j(g). Suppose a(p) = 0. What is p?
1
Let y(t) be the second derivative of 3*t**5/20 + 3*t**4/4 - 6*t**2 + 2*t. Let y(c) = 0. What is c?
-2, 1
Suppose 2*o - 10 = -3*o. Suppose n = 2*l, -l - 36 = -4*n - 5*l. Suppose 1 + o*x**2 + 5 - n = 0. Calculate x.
0
Let a be -2 + (3 - (-3)/6). Let m = a - 5/6. Let 2*l**2 - m*l**3 - 4/3*l + 0 = 0. Calculate l.
0, 1, 2
Let r(a) be the second derivative of -a + 0 + 0*a**2 - 1/6*a**4 - 1/6*a**3 - 1/20*a**5. Factor r(j).
-j*(j + 1)**2
Let j(r) be the third derivative of r**6/1440 + r**5/480 + r**3/6 - r**2. Let u(w) be the first derivative of j(w). Factor u(g).
g*(g + 1)/4
Suppose 2*k**5 + 12*k**3 - 12*k**4 + 68 + k**5 + 6*k**2 - 15*k - 62 = 0. Calculate k.
-1, 1, 2
Let n(k) be the second derivative of -k**4/66 + 4*k**3/33 - 4*k**2/11 - 3*k. Solve n(r) = 0 for r.
2
Suppose r = -15 + 17. Find d, given that 0*d + 0 - 2/3*d**r - 1/3*d**3 = 0.
-2, 0
Let w(f) be the third derivative of -f**5/180 - f**4/12 - 5*f**3/18 + 14*f**2. Let w(s) = 0. What is s?
-5, -1
Let i(w) be the third derivative of w**8/80640 - w**7/20160 + w**5/60 - 5*w**2. Let z(y) be the third derivative of i(y). Factor z(t).
t*(t - 1)/4
Let i(f) be the third derivative of -f**5/80 + 7*f**4/16 - 49*f**3/8 - 20*f**2. Factor i(z).
-3*(z - 7)**2/4
Let r be 7/98 + (-12)/(-28). Solve 3/4*h**3 + 0 - r*h - 1/4*h**2 = 0 for h.
-2/3, 0, 1
Let x(s) = s - 5. Let y be x(7). Solve -31*c**3 + c**y + c + 30*c**3 - 4*c**4 + 3*c**2 = 0.
-1, -1/4, 0, 1
Let l(u) = -2*u**3 - 24*u**2 - 22*u - 24. Let a(k) = -k**2 - 1. Let c(f) = 12*a(f) - l(f). Factor c(m).
2*(m + 1)*(m + 2)*(m + 3)
Let q(y) = -3*y**2 - y**3 - 3*y**2 + 4 + 11*y - 1 - 16*y. Let p be q(-5). Factor -2/3*g - 4/3*g**2 + 0 + 4/3*g**4 + 0*g**p + 2/3*g**5.
2*g*(g - 1)*(g + 1)**3/3
Let f = -2/359 - -740/3949. Factor 0 + 2/11*s**3 - f*s + 0*s**2.
2*s*(s - 1)*(s + 1)/11
Let a(o) be the first derivative of 21*o**5/25 - 3*o**4/4 - 2*o**3/5 + 3. Factor a(i).
3*i**2*(i - 1)*(7*i + 2)/5
Factor 243/5 + 54/5*d + 3/5*d**2.
3*(d + 9)**2/5
Let c = -7 + 10. Suppose i + c*o + 5 = -2*o, 0 = -3*i - o - 1. Factor i - 2/3*d**2 + 2/3*d**4 + 1/3*d - 1/3*d**3.
d*(d - 1)*(d + 1)*(2*d - 1)/3
Let l(r) be the first derivative of -1 + r**3 - 4*r + 0*r**2 - 1/4*r**4. Suppose l(w) = 0. Calculate w.
-1, 2
What is f in 3*f**3 - 13*f**3 - 40*f**2 + 50*f**4 + 8*f**2 + 0*f**4 - 8*f = 0?
-2/5, 0, 1
Let v(z) be the second derivative of z**7/2016 - z**6/1440 - z**4/3 + 2*z. Let o(c) be the third derivative of v(c). Find a such that o(a) = 0.
0, 2/5
Let r(n) = -47*n - 796. Let k be r(-17). Determine w so that 2*w + 1/2 + 2*w**k + 3*w**2 + 1/2