- 10*c**5 + 4*c**4 + t*c**5 = 0. What is c?
-1, 0, 1
Let z(y) be the second derivative of y**5/10 + y**4/6 - 4*y**3 - 149*y - 1. Determine i so that z(i) = 0.
-4, 0, 3
What is v in 27/5*v**3 - 72/5*v**2 - 1/5*v**4 + 96/5 - 4/5*v = 0?
-1, 2, 24
Let p(v) = 4*v**2 - 2. Let f be p(1). Determine g so that -385*g**4 - 6*g**f + 4*g + 379*g**4 + 16*g**3 - 8*g**2 = 0.
0, 2/3, 1
Factor -11*s**2 - 4*s**4 - 4848*s**3 + 64*s + 4832*s**3 + 27*s**2.
-4*s*(s - 2)*(s + 2)*(s + 4)
Let j(i) be the first derivative of -i**6/120 - i**5/30 - i**4/24 - 5*i**3/3 + 6. Let q(v) be the third derivative of j(v). Factor q(r).
-(r + 1)*(3*r + 1)
Let n(o) be the first derivative of 33 + 0*o - 4/5*o**3 + 9/5*o**2 + 1/10*o**4. Factor n(s).
2*s*(s - 3)**2/5
Let d be (-9)/(-21) + (-442)/(-14). Let c = -26 + d. Let -126*q - 1323/2*q**2 - c = 0. What is q?
-2/21
Let d = 40871 - 40869. Let b be -3*2*(-2)/26. Factor -b*m**d + 4/13*m + 2/13.
-2*(m - 1)*(3*m + 1)/13
Let p(l) be the third derivative of l**8/448 - l**7/210 - 7*l**6/480 + 18*l**2 - 1. Factor p(m).
m**3*(m + 1)*(3*m - 7)/4
Let x(q) be the first derivative of 0*q + 4/3*q**3 + 0*q**2 - 10. Let x(d) = 0. What is d?
0
Let q be (60/(-150))/((-5)/(-25)*11 + -3). Factor 1/4*d**3 - 1/4*d**4 + 3/4*d**2 - 1/4*d - q.
-(d - 2)*(d - 1)*(d + 1)**2/4
Let h(c) be the third derivative of c**6/30 - 14*c**5/15 - 35*c**4/6 + 32*c**3 + 2*c**2 + 32*c. Suppose h(p) = 0. Calculate p.
-3, 1, 16
Let v(y) be the third derivative of 0*y + 5/112*y**8 + 5/12*y**4 - 5/24*y**6 + 0 - 5/42*y**7 + 0*y**3 + 5/12*y**5 + 9*y**2. Suppose v(d) = 0. Calculate d.
-1, -1/3, 0, 1, 2
Let o = 1110 + -4437/4. Determine w so that 1/4 + 1/4*w**3 + o*w + 3/4*w**2 = 0.
-1
Let r(x) be the third derivative of -19*x**2 - 1/45*x**5 + 0 + 1/45*x**6 - 1/504*x**8 + 0*x**7 - 1/12*x**4 + 2/9*x**3 + 0*x. What is k in r(k) = 0?
-2, -1, 1
Find k, given that -141 - 36061*k**2 - 309 + 36058*k**2 + 453*k = 0.
1, 150
Let n(h) be the first derivative of 9*h**5/100 - h**4/20 - h**3/6 - h**2/10 - 5*h + 8. Let f(b) be the first derivative of n(b). What is a in f(a) = 0?
-1/3, 1
Let y(x) = x - 33. Let w be y(-19). Let i be (2 + -3)/7 - w/28. Factor -2/7*a**2 + i*a - 18/7.
-2*(a - 3)**2/7
Find b such that -1/4*b**5 - 84*b + 70*b**2 + 36 + 17/4*b**4 - 26*b**3 = 0.
1, 2, 6
Let j(r) be the first derivative of 0*r + 0*r**2 + 3 + 1/2*r**4 + 4/27*r**3. Solve j(i) = 0.
-2/9, 0
Factor -1/2*w**2 - 8 + 65/4*w.
-(w - 32)*(2*w - 1)/4
Suppose 3*p + x = 8, -4*x = p - 5*p. Let n(g) be the first derivative of 0*g + 2/3*g**p - 2/9*g**3 - 5. Factor n(v).
-2*v*(v - 2)/3
Let j(w) be the second derivative of -55*w**4/48 - 65*w**3/24 - 5*w**2/4 + 268*w. Factor j(d).
-5*(d + 1)*(11*d + 2)/4
Let v(h) be the second derivative of -3*h**5/160 + 51*h**4/32 - 675*h**3/16 + 1875*h**2/16 + 155*h. Factor v(s).
-3*(s - 25)**2*(s - 1)/8
Suppose 2 = v - h + 5*h, -5*v + 5*h - 40 = 0. Let l be (-4)/v + (65/15 - 5). What is n in -32/3*n**3 + 16/3*n**2 + 20/3*n**4 - 4/3*n**5 + l + 0*n = 0?
0, 1, 2
Suppose -95 + 53 = -6*m. Let p(i) be the second derivative of -3/14*i**4 + 0 - 1/7*i**2 - m*i + 2/7*i**3 + 2/35*i**5. Suppose p(v) = 0. What is v?
1/4, 1
Solve -1/2*h**5 + 5*h**3 + 26*h**2 + 16 + 36*h - 3/2*h**4 = 0.
-2, -1, 4
Let n(v) be the second derivative of -11*v + 1/3*v**4 + 0*v**3 + 0 - 18*v**2. Factor n(y).
4*(y - 3)*(y + 3)
Let z = -2345/2 + 1173. Factor 0*o + o**3 - z + 3/2*o**2.
(o + 1)**2*(2*o - 1)/2
Let t be (3 + 1)/8*50. Suppose g + n = -2*n + 9, 5*g - t = -5*n. Let -3*k**4 + k - 8*k**3 - k + 5*k**g = 0. What is k?
-1, 0
Suppose 5/2*g**3 + 1/2*g**4 - 2 + 3/2*g**2 - 5/2*g = 0. Calculate g.
-4, -1, 1
Let j(n) be the third derivative of -n**7/840 - n**6/30 - 2*n**5/5 - 8*n**4/3 - 32*n**3/3 + 161*n**2. Suppose j(u) = 0. What is u?
-4
Let s(x) be the third derivative of -x**6/140 + 9*x**5/35 - 24*x**4/7 + 128*x**3/7 - 157*x**2. Factor s(w).
-6*(w - 8)**2*(w - 2)/7
Suppose -5*h = 2*w - 49 + 12, 3*w - 18 = 0. Factor 0*s + 0*s**2 + 0*s**3 + 0 - 1/2*s**h - s**4.
-s**4*(s + 2)/2
Let d(a) be the first derivative of 2*a**3/9 + a**2 - 57. Suppose d(c) = 0. What is c?
-3, 0
Let r = 47 + -95. Let c = -95/2 - r. Determine x so that 0*x + 0 - c*x**2 = 0.
0
Let y(k) be the third derivative of k**8/84 + 32*k**7/105 + 17*k**6/10 + 32*k**5/15 - 26*k**4/3 - 32*k**3 + 15*k**2. Suppose y(f) = 0. What is f?
-12, -2, -1, 1
Suppose 22/7*g + 2/7*g**2 + 0 = 0. Calculate g.
-11, 0
Let v(d) be the first derivative of d**4 - d**4 - 16 + 6*d**4 - 7*d**4. Factor v(h).
-4*h**3
Let z(d) be the first derivative of -d**5/5 + 4*d**4/3 - 8*d**3/3 + 8*d - 31. Let p(c) be the first derivative of z(c). Factor p(l).
-4*l*(l - 2)**2
Let w(h) be the second derivative of -h**4/20 - 6*h**3/5 - 81*h**2/10 + 131*h. Factor w(q).
-3*(q + 3)*(q + 9)/5
Let p(f) be the second derivative of f**6/900 + f**5/300 - 3*f**3/2 + 19*f. Let c(r) be the second derivative of p(r). Find x such that c(x) = 0.
-1, 0
Let q(j) be the first derivative of -4*j**5/5 - 3*j**4/2 + 8*j**3/3 + 3*j**2 - 4*j - 775. Find c, given that q(c) = 0.
-2, -1, 1/2, 1
Suppose 16/3*w - 2/3*w**2 - 14/3 = 0. What is w?
1, 7
Find s, given that 82/17*s - 2/17*s**3 - 14/17*s**2 - 66/17 = 0.
-11, 1, 3
Let r(v) be the third derivative of -8*v**2 - 1/30*v**4 - 1/60*v**6 + 0*v**3 + 0*v + 0 + 7/150*v**5. Factor r(k).
-2*k*(k - 1)*(5*k - 2)/5
Factor 5*k**2 - 782*k - 376*k + 72000 - 42*k.
5*(k - 120)**2
Let y(o) be the second derivative of -o**4/8 - 3*o**3/8 + 3*o**2/4 - 16*o + 1. Factor y(r).
-3*(r + 2)*(2*r - 1)/4
Factor 88/3 + 2/3*y**2 + 30*y.
2*(y + 1)*(y + 44)/3
Let f(d) be the third derivative of 3/200*d**6 - 7/100*d**5 + 0 - 17*d**2 + 0*d**3 + 1/20*d**4 + 0*d. Factor f(r).
3*r*(r - 2)*(3*r - 1)/5
Let t = 14546/5 + -2908. Factor -14/15*v + t*v**2 + 4/15 + 2/15*v**4 - 2/3*v**3.
2*(v - 2)*(v - 1)**3/15
Suppose 0 = -a + s + 3 + 2, 4*a = -4*s - 4. Factor 2/7*p**4 - 2/7*p + 0 + 6/7*p**a - 6/7*p**3.
2*p*(p - 1)**3/7
Let b = 4597/5 - 36731/40. Let -b*z**2 - 3/8*z**3 - 9/8*z - 3/8 = 0. Calculate z.
-1
Let g(b) be the second derivative of -5/18*b**4 + 1/45*b**6 + 0*b**2 + 0 + 1/30*b**5 + 36*b + 1/3*b**3. Find m such that g(m) = 0.
-3, 0, 1
Let y(i) be the first derivative of -i**7/2520 - i**6/360 - i**5/180 - 4*i**3/3 - 10. Let n(z) be the third derivative of y(z). Let n(a) = 0. Calculate a.
-2, -1, 0
Let k be -5*((-60)/20 + 57/20). Let b = 105/4 + -26. Factor 1/4*v**3 + k*v - 3/4*v**2 - b.
(v - 1)**3/4
Let y = 713073/101 - 4510421247/638825. Let u = -2/575 - y. Let 0 + 2/11*a**3 + u*a - 6/11*a**2 = 0. Calculate a.
0, 1, 2
Let f(y) be the first derivative of -5*y**3/3 + 25*y**2/2 + 551. Solve f(n) = 0.
0, 5
Let t(p) be the second derivative of 0 + 0*p**2 + 30*p - 1/3*p**4 - 1/5*p**5 + 4/3*p**3. Solve t(o) = 0 for o.
-2, 0, 1
Let m(q) = 2*q**4 + 6*q**3 - q + 3. Let l(v) = v**4 + 3*v**3 - v**2 - v + 2. Let f(a) = -5*l(a) + 2*m(a). Factor f(k).
-(k - 1)**2*(k + 1)*(k + 4)
Let g(k) = 4*k**2 + 23*k - 22. Let l be g(1). Let a(t) be the third derivative of -7*t**2 + 0*t + 0 + 0*t**4 - 1/240*t**l + 0*t**3 - 1/480*t**6. Factor a(n).
-n**2*(n + 1)/4
Let i(y) = y**2 + 2*y + 3. Let v be i(-2). Let a(s) be the first derivative of 0*s**2 + 0*s - 1/6*s**v - 2 + 1/24*s**6 - 3/16*s**4 + 0*s**5. Factor a(p).
p**2*(p - 2)*(p + 1)**2/4
Let g = 9697/53774 + -15/2338. Determine r, given that 4/23*r + 2/23 - 2/23*r**2 - g*r**3 = 0.
-1, -1/2, 1
Let x(m) = -9*m - 60. Let r(t) = 20*t + 122. Let a(z) = -6*r(z) - 13*x(z). Let g be a(15). Factor 0 - 8/9*l**2 + 2/9*l**4 - 4/9*l + 1/9*l**5 - 1/3*l**g.
l*(l - 2)*(l + 1)**2*(l + 2)/9
Suppose -137 = -5*d - 2*t, -3*d + 101 - 21 = -t. Factor 704*n**5 - 152*n**4 - 19*n**3 + d*n**3 - 32*n**4 + 354*n**5.
2*n**3*(23*n - 2)**2
Let j = -1018 + 1023. Let f(y) be the second derivative of 1/15*y**2 + 0 + 1/15*y**3 - y + 1/30*y**4 + 1/150*y**j. Suppose f(w) = 0. What is w?
-1
Let d(r) be the first derivative of -3*r**7/35 + r**6/5 + 4*r**5/25 - 2*r**4/15 + 16*r + 25. Let c(a) be the first derivative of d(a). What is v in c(v) = 0?
-2/3, 0, 1/3, 2
Let m be 49/(-210) - 3/6. Let p = -2/5 - m. Factor 1/3*w**2 - p*w - 1/9*w**3 + 1/9.
-(w - 1)**3/9
Let w(y) be the second derivative of y**7/42 + y**6/30 - 29*y**5/20 - 29*y**4/12 + 68*y**3/3 - 40*y**2 - 2*y - 57. Find d such that w(d) = 0.
-4, 1, 5
Suppose -3*s = 5*z - 82, 3