k**t - 6*k**5 + 3*k**4 = 0. Calculate k.
-2, 0, 1
Let k(b) be the first derivative of -1/33*b**3 + 1/22*b**2 - 1/44*b**4 - 39 + 1/11*b. Find z, given that k(z) = 0.
-1, 1
Suppose 22*c + 328 - 372 = 0. Let o(h) be the third derivative of 1/60*h**4 + 0*h**3 + 1/300*h**5 + 3*h**c + 0*h + 0. What is b in o(b) = 0?
-2, 0
Let s be 13/10 + (-8 + 10)/10. Factor -1/2*c**3 - s*c**2 + 0*c + 2.
-(c - 1)*(c + 2)**2/2
Let z(h) = 87*h - 5391. Let f be z(62). Let 2 + 7/3*k**f - 5/3*k**2 - 7/3*k - 1/3*k**4 = 0. What is k?
-1, 1, 6
Suppose -5*r - 7 = -0*r + 4*c, 4*r - 2*c = -16. Let i be ((-3)/9)/(r/27). Find q, given that -1/5*q**i - 1/5*q**4 + 2/5*q**2 + 0 + 0*q = 0.
-2, 0, 1
Let z(k) be the first derivative of -k**6/900 + 13*k**3/3 + 27. Let g(n) be the third derivative of z(n). Find d such that g(d) = 0.
0
Factor 38/5*m**4 + 1/5*m**5 + 684/5*m**2 + 397/5*m**3 + 0 + 324/5*m.
m*(m + 1)**2*(m + 18)**2/5
Let z = -720 + 724. Let h(r) be the first derivative of -r**4 + 0*r**2 + 0*r + 2/5*r**5 + z + 2/3*r**3. Factor h(w).
2*w**2*(w - 1)**2
Let k(b) be the third derivative of b**5/60 + b**4/24 - b**3 - 6*b**2 + 18. Determine z so that k(z) = 0.
-3, 2
Let j = 15009 - 60035/4. Factor -1/4*d**3 + 0 + d**2 - j*d**4 + d.
-d*(d - 2)*(d + 1)*(d + 2)/4
Factor 0 - 10/11*d**4 + 16/11*d**3 + 0*d + 2/11*d**5 - 8/11*d**2.
2*d**2*(d - 2)**2*(d - 1)/11
Let x(k) be the third derivative of k**6/160 + 15*k**5/16 + 171*k**4/4 - 361*k**3/2 - 41*k**2 - 1. Solve x(v) = 0.
-38, 1
Let c(o) be the second derivative of 1/120*o**6 - 7*o + 0*o**4 + 0 + 0*o**3 - 1/60*o**5 + 11/2*o**2. Let a(g) be the first derivative of c(g). Factor a(w).
w**2*(w - 1)
Suppose -4*q = 3*w - 6 - 3, w - 3 = 2*q. Suppose -s + q = -3. Factor -2/7*n**s + 0 + 6/7*n**4 + 0*n**2 + 0*n.
2*n**3*(3*n - 1)/7
Let f(u) = 8*u**5 - 2*u**4 + 4*u**3 - 6*u**2 + 3*u - 2. Let x(c) = -7*c**5 + c**4 - 2*c**3 + 6*c**2 - 3*c + 1. Let d(j) = -4*f(j) - 5*x(j). Factor d(r).
3*(r - 1)**2*(r + 1)**3
Let y(b) be the third derivative of -1/12*b**5 - 125/6*b**3 + 14*b**2 + 0 + 0*b - 25/12*b**4. Let y(n) = 0. What is n?
-5
Let d(s) be the first derivative of -s**6/10 + 9*s**5/20 - s**4/2 - 20*s + 14. Let z(a) be the first derivative of d(a). Find o such that z(o) = 0.
0, 1, 2
Let l(k) = -12*k**4 - 27*k**3 + 72*k**2 - 3. Let v(a) = 3*a**4 - a**3 + 1. Let w(b) = l(b) + 3*v(b). Factor w(t).
-3*t**2*(t - 2)*(t + 12)
Let l(r) be the first derivative of -2 + 1/80*r**5 + 6*r + 0*r**3 + 0*r**2 + 0*r**4 - 1/120*r**6. Let i(c) be the first derivative of l(c). Factor i(s).
-s**3*(s - 1)/4
Suppose -20 = -4*r - 2*m, -4*r + 384 - 406 = -5*m. Factor 2/3*j**2 + r*j + 4/3.
2*(j + 1)*(j + 2)/3
Let j(b) be the third derivative of -b**5/60 - b**4/4 - 4*b**3/3 + 71*b**2. Let j(f) = 0. What is f?
-4, -2
Factor 4/5*q - 2/5 - 2/5*q**2.
-2*(q - 1)**2/5
Let o(x) be the second derivative of -x**6/270 + x**5/18 - 2*x**4/9 + 4*x**3 - 12*x. Let j(s) be the second derivative of o(s). Solve j(u) = 0.
1, 4
Let y(x) be the second derivative of x**5/40 - 5*x**4/24 + 7*x**3/12 - 3*x**2/4 + 2*x - 37. Determine d so that y(d) = 0.
1, 3
Let y be (-1 + 13 - 1) + -2. Let r = 11 - y. Factor 4*x + 2*x**2 - 8*x**2 - 5*x**3 - r*x**2.
-x*(x + 2)*(5*x - 2)
Suppose -79*n + 97*n = 72. Suppose 8/5*t**3 + 0 + 0*t + 0*t**2 + 4/5*t**n = 0. Calculate t.
-2, 0
Let i(n) be the third derivative of -n**6/48 + n**5/2 + 5*n**2. Suppose i(t) = 0. Calculate t.
0, 12
Let f(r) be the first derivative of -r**6/120 + r**5/60 + r**4/12 + 3*r**2 - 14. Let l(o) be the second derivative of f(o). Let l(q) = 0. What is q?
-1, 0, 2
Let z(l) be the second derivative of -3*l**7/98 - 11*l**6/70 + 57*l**5/140 - 5*l**4/28 + 454*l. Solve z(g) = 0.
-5, 0, 1/3, 1
Suppose 1080*j + 5*j**3 + 800 + 2120*j - 318*j**2 - 80*j + 3*j**3 = 0. Calculate j.
-1/4, 20
Let u = -2995/9 - -333. Factor u*z**2 + 2/3 + 8/9*z.
2*(z + 1)*(z + 3)/9
Let a be (-28)/(-72)*(126/49 + 14/(-7)). Factor 0*y**4 - 2/9*y**2 + 4/9*y**3 + a - 1/3*y - 1/9*y**5.
-(y - 1)**3*(y + 1)*(y + 2)/9
Let m(s) be the first derivative of -s**4/8 - s**3 + 7*s**2/4 - 233. Suppose m(a) = 0. What is a?
-7, 0, 1
Let f(g) = 3*g**2 - 1. Let d be f(1). Find a such that -2*a**2 + 4*a**d + 0*a**2 + a**2 - 12 = 0.
-2, 2
Factor 15*y + 0*y**4 + 2 + 3*y**2 - 10*y - y**4 + 25*y**3 - 26*y**3.
-(y - 2)*(y + 1)**3
Let j(u) = 5*u**2 - 5*u - 2. Let a = 81 + -26. Let v(s) = -a*s**2 + 4*s**2 + 6 + 9 + 6 + 51*s. Let o(y) = 21*j(y) + 2*v(y). Factor o(n).
3*n*(n - 1)
Let y(z) be the first derivative of -2*z**5/45 + 4*z**4/9 - 10*z**3/27 - 14*z**2/9 + 14. Factor y(b).
-2*b*(b - 7)*(b - 2)*(b + 1)/9
Find r such that 185/2*r**2 + 5/2*r**3 + 195/2 - 385/2*r = 0.
-39, 1
Factor -961 + 31*i - 1/4*i**2.
-(i - 62)**2/4
Let c(x) be the second derivative of x**7/15120 + x**6/1440 - x**5/180 - x**4/6 + 3*x. Let o(g) be the third derivative of c(g). Factor o(l).
(l - 1)*(l + 4)/6
Let b be 23/6 - ((-1275)/(-50) + -23). Find k such that -4/3*k + 2*k**2 + 1/3*k**4 + 1/3 - b*k**3 = 0.
1
Let q = -589 - -592. Let t(u) be the second derivative of -1/42*u**4 + 7*u + 0*u**2 + 1/21*u**q + 0. Factor t(x).
-2*x*(x - 1)/7
Suppose 23/3*m + 26 - 1/3*m**2 = 0. What is m?
-3, 26
What is l in -4*l + 16/11 + 18/11*l**2 = 0?
4/9, 2
Let h(a) be the first derivative of a**4/4 - a**3/3 - a**2 - 84. Factor h(c).
c*(c - 2)*(c + 1)
Factor -12/19*x**3 + 0 - 2/19*x + 8/19*x**4 - 2/19*x**5 + 8/19*x**2.
-2*x*(x - 1)**4/19
Let g(j) = -43*j - 342. Let b be g(-8). Factor 0*l - 16/21*l**b + 24/7*l**3 - 20/7*l**4 + 0 + 2/3*l**5.
2*l**2*(l - 2)**2*(7*l - 2)/21
Let r(q) be the third derivative of q**7/70 + 7*q**6/60 + 13*q**5/45 + 11*q**4/36 + q**3/6 - 201*q**2. Factor r(o).
(o + 1)*(o + 3)*(3*o + 1)**2/3
Let c(o) be the third derivative of o**6/210 - 4*o**5/105 + o**4/42 + 4*o**3/7 + 57*o**2. Factor c(m).
4*(m - 3)*(m - 2)*(m + 1)/7
Let a(s) be the third derivative of -s**5/150 + 7*s**4/10 - 147*s**3/5 - 2*s**2 + 1. Factor a(j).
-2*(j - 21)**2/5
Let n(q) be the third derivative of q**6/600 + q**5/10 + 83*q**4/120 + 9*q**3/5 - 29*q**2 - 4. Suppose n(j) = 0. Calculate j.
-27, -2, -1
Let q(g) be the first derivative of 2*g**5/85 - 3*g**4/17 + 8*g**3/51 + 6*g**2/17 - 10*g/17 - 25. Suppose q(h) = 0. What is h?
-1, 1, 5
Suppose 217 = -19*n + 4454. Let p = 2009/9 - n. Factor 4/3*j**3 + 2/9*j**5 + 0 + p*j - 8/9*j**2 - 8/9*j**4.
2*j*(j - 1)**4/9
Let r(n) = -36*n**4 - 240*n**3 - 136*n**2 - 36*n. Let y(o) = -o**2 + o. Let j(g) = r(g) + 12*y(g). Let j(l) = 0. What is l?
-6, -1/3, 0
Let w = 126590/19 + -6662. Determine h so that -8/19*h**2 + w + 10/19*h = 0.
-3/4, 2
Let g(i) be the third derivative of -8/9*i**3 - 1/630*i**7 + 0 + 4/9*i**4 + 1/45*i**6 + i**2 - 2/15*i**5 + 0*i. Factor g(j).
-(j - 2)**4/3
Let i be 111/21 + (-10)/35. Factor -2*c + 7*c + 2*c - 16*c**3 + 8*c**2 + 4*c**5 - 8 + i*c.
4*(c - 1)**3*(c + 1)*(c + 2)
Let i be 11/33*(15 - 0). Solve 6*n**3 - n**5 + 2*n - 2*n - 8*n**4 + 3*n**i = 0.
0, 1, 3
Let u(c) be the second derivative of -c**7/63 - c**6/9 + 244*c. Solve u(v) = 0.
-5, 0
Let v(u) = u**2 + 4*u + 2. Let h(y) = 1 - 10 + 3*y**2 - 4*y**2 - 4*y + 8. Let o(i) = 2*h(i) + 3*v(i). Let o(r) = 0. Calculate r.
-2
Let v(c) be the first derivative of 1/3*c**3 + 0*c + 1/5*c**2 + 12 - 7/20*c**4. Suppose v(r) = 0. Calculate r.
-2/7, 0, 1
Let y(u) be the first derivative of 128*u**3/15 + 16*u**2/5 + 2*u/5 - 119. Factor y(z).
2*(8*z + 1)**2/5
Let u(w) be the third derivative of -w**8/96 - w**7/210 + 7*w**6/80 + w**5/6 + w**4/12 + 24*w**2 - 2. Suppose u(m) = 0. What is m?
-1, -2/7, 0, 2
Let s(k) = -k**3 + 6*k**2 - 4*k. Let j be s(5). Let p = j - 2. Factor -a + 4 - a**2 + 9*a**2 - 2*a**p + 4*a**3 + 11*a.
2*(a + 1)**2*(a + 2)
Suppose -352/19*c - 28/19*c**4 - 2/19*c**5 - 344/19*c**2 - 128/19 - 146/19*c**3 = 0. Calculate c.
-4, -1
Suppose -h + 3 = s, 2*s + s - 5 = -2*h. Suppose -6*m + 10 = -11*m + h*a, 0 = -4*m - 3*a + 23. Factor -1/4*f**3 + 1/8*f**4 - 1/8*f**m + 0 + 1/4*f.
f*(f - 2)*(f - 1)*(f + 1)/8
Let t(p) be the third derivative of -p**9/60480 + p**8/10080 - p**7/5040 - 3*p**5/20 - 10*p**2. Let f(a) be the third derivative of t(a). Factor f(x).
-x*(x - 1)**2
Find q, given that 1/3*q**3 + 0 + 8/3*q**2 + 7/3*q = 0.
-7, -1, 0
Let b(a) be the third derivative of 0*a - 5/1512*a**8 + 0 + 2*a**2 + 1/108*a**4 + 2/27*a**3 - 1/27*a**5 + 1/135*a**6 + 8/945*a**7. W