st derivative of -3*u**4/4 - u**3 + 3*u**2/2 + 3*u + 1. Factor g(q).
-3*(q - 1)*(q + 1)**2
Let v(w) be the third derivative of -w**5/90 + w**4/108 + 2*w**3/27 + 4*w**2. Factor v(d).
-2*(d - 1)*(3*d + 2)/9
Let b(f) be the third derivative of -f**8/42 - 3*f**7/35 - f**6/10 - f**5/30 + f**2. Find w, given that b(w) = 0.
-1, -1/4, 0
Let j be (-47)/(-3) - (-1)/(1/3). Let o be (56/(-10))/((-12)/70). Let 0 - j*p**2 + o*p**3 + 8/3*p = 0. What is p?
0, 2/7
Let a(i) = 12*i - 226. Let j be a(19). Factor -3/2*o + 1/2*o**j + 1.
(o - 2)*(o - 1)/2
Let m(c) = -c**5 + c**4 - c**2 + c - 1. Let s(f) = -2*f**5 - 14*f**4 + 40*f**3 - 46*f**2 + 26*f - 10. Let v(y) = 6*m(y) - s(y). Find x, given that v(x) = 0.
1
Solve -3/4*q**2 - 9*q - 27 = 0.
-6
Let a(c) = 1. Let g(p) = 22*p**2 + 19*p + 7. Let h(w) = 3*a(w) - g(w). Find x such that h(x) = 0.
-1/2, -4/11
Let p(x) be the third derivative of 4/9*x**3 + 0 - 3*x**2 + 1/90*x**5 - 1/9*x**4 + 0*x. Determine c so that p(c) = 0.
2
Factor -51*c**5 + 4 - c**4 - 7*c**2 + 52*c**5 + 4*c**4 - c**3.
(c - 1)**2*(c + 1)*(c + 2)**2
Let -8*r + 0 + 0*r**4 - 1/2*r**5 + 4*r**3 + 0*r**2 = 0. What is r?
-2, 0, 2
Let c(g) = -g**3 + 4*g**2 + 22*g + 2. Let b be c(9). Let d = 1029/5 + b. Factor 2/5*u**3 + 0 + 2/5*u**2 - d*u.
2*u*(u - 1)*(u + 2)/5
Let d = 7 - 3. Let o(m) be the first derivative of 1/14*m**d + 2/7*m**3 + 0*m**2 - 1 - 8/7*m. Determine n so that o(n) = 0.
-2, 1
Factor -8*y**5 + 2*y**4 - 13*y**5 + 7*y**4 + 6*y**3 + 24*y**5.
3*y**3*(y + 1)*(y + 2)
Let k = -11 - -17. Factor -2 - 2*z**2 - 2*z**3 - 2 + 2*z + k.
-2*(z - 1)*(z + 1)**2
Let t be 9/(-12)*(-200)/(-12). Let n = 13 + t. Factor -1/2*g**2 + 0 - n*g.
-g*(g + 1)/2
Let a(j) = 4*j**2 - 12*j + 12. Let b(m) = 4*m**2 - 12*m + 13. Let t(x) = 5*a(x) - 4*b(x). Factor t(v).
4*(v - 2)*(v - 1)
Factor -1/4*n - 1/4*n**2 + 0.
-n*(n + 1)/4
Let t = 56 + -158/3. Let -2/3*y**2 - 2 + t*y - 2/3*y**3 = 0. What is y?
-3, 1
Factor -5*l**3 + 0*l**3 + 51*l - 51*l + 5*l**4.
5*l**3*(l - 1)
Factor -340*i + 146 - 2*i**5 + 424*i**2 + 52*i**4 - 46 - 2*i**5 - 232*i**3.
-4*(i - 5)**2*(i - 1)**3
Solve -2/3 - 7/3*l**3 + 7/3*l + 2/3*l**2 = 0.
-1, 2/7, 1
Suppose -5*v - 37 = 2*l - 0*v, 0 = 5*l + 5*v + 55. Let n be (-1)/(-3) - 1/l. Suppose -n*i**2 + 7/2*i**4 - 2*i**5 - i**3 + 0*i + 0 = 0. Calculate i.
-1/4, 0, 1
Let v(u) be the third derivative of -u**6/40 + u**5/4 - u**4 + 2*u**3 + 15*u**2. Factor v(z).
-3*(z - 2)**2*(z - 1)
Let x(g) be the second derivative of -1/21*g**4 + 0*g**3 - 1/70*g**5 + g + 0*g**2 + 0. Solve x(z) = 0.
-2, 0
Let s(r) be the third derivative of r**6/60 - r**5/30 - 10*r**2. Let s(t) = 0. Calculate t.
0, 1
Factor 1/5*r**3 - 1/5*r + 1/5*r**2 + 0 - 1/5*r**4.
-r*(r - 1)**2*(r + 1)/5
Let h(j) be the first derivative of 12*j**5/25 + 69*j**4/20 + 6*j**3 - 27*j**2/10 - 24. Factor h(w).
3*w*(w + 3)**2*(4*w - 1)/5
Let i(a) = a - 5. Let n be i(7). Determine l so that -4 + 7*l - l - 2*l**n + 0*l = 0.
1, 2
Let l(m) be the first derivative of m**3/2 + 15*m**2/4 - 21*m - 51. Determine f so that l(f) = 0.
-7, 2
Let j be (-20)/16 - ((-27)/6)/3. Let b(z) be the third derivative of 0*z + j*z**5 + 2*z**3 + 0 + 3/2*z**4 + 3*z**2. What is p in b(p) = 0?
-2, -2/5
Let g = -3 - -5. Factor -26*j**g - 7*j - 4 - 2*j**3 - 6*j**3 - 5*j - 10*j.
-2*(j + 1)*(j + 2)*(4*j + 1)
Let c be 0/1*(-5)/10. Determine h so that 2/9*h**2 + c - 4/9*h = 0.
0, 2
Let z(d) be the first derivative of -d**8/672 + d**7/560 + d**6/60 + d**5/60 + 10*d**3/3 - 3. Let y(r) be the third derivative of z(r). Factor y(m).
-m*(m - 2)*(m + 1)*(5*m + 2)/2
Let k be -1*((-12)/18*9 - -6). Suppose k*h + 0 - 3/4*h**3 - 3/2*h**2 = 0. Calculate h.
-2, 0
Let z(w) be the third derivative of w**8/1008 - w**7/63 + w**6/9 - 4*w**5/9 + 10*w**4/9 - 16*w**3/9 + 2*w**2. Factor z(q).
(q - 2)**5/3
Suppose 2*n + 2*n = 12. Let f = 11 - 8. Suppose 1 + n*r - f*r - 2*r**2 + r = 0. What is r?
-1/2, 1
Let u(y) be the second derivative of -y**6/180 + y**4/3 - y**3/6 + 5*y. Let h(l) be the second derivative of u(l). Factor h(o).
-2*(o - 2)*(o + 2)
Factor 5*w**3 + 2*w**2 - 9*w**3 + 4*w + 1 - 3*w**2.
-(w - 1)*(w + 1)*(4*w + 1)
Let d = 44 + -87/2. Let y(n) be the first derivative of -1 + 1/6*n**6 - d*n**2 + 2/5*n**5 - 2/3*n**3 + 0*n**4 + 0*n. Factor y(l).
l*(l - 1)*(l + 1)**3
Let q = -6/73 + 85/146. Let o be (-2 + 1)*(-3)/6. Factor q + o*y**2 - y.
(y - 1)**2/2
Let m(j) = -j**3 - 5*j**2 + j - 1. Let s(a) = 7*a**3 + 31*a**2 - 5*a + 6. Let o = 10 - 4. Let b(c) = o*s(c) + 39*m(c). Solve b(q) = 0.
1
Let p(q) be the first derivative of -q**6/15 - q**5/5 - q**4/6 + 3*q - 4. Let o(i) be the first derivative of p(i). Factor o(k).
-2*k**2*(k + 1)**2
Let f(o) = o**5 + o**4 - o**2 - o - 1. Let m(y) = -8*y**5 + 7*y**4 - 15*y**3 + 11*y**2 + 5*y + 5. Let i(s) = -5*f(s) - m(s). Determine k so that i(k) = 0.
0, 1, 2
Let t(b) be the second derivative of b**5/80 + b**4/16 + b**3/8 + b**2/8 - 15*b. Find c, given that t(c) = 0.
-1
Let v(o) be the third derivative of o**9/40320 - o**8/13440 + o**5/20 + o**2. Let z(w) be the third derivative of v(w). Factor z(i).
3*i**2*(i - 1)/2
Let a = -15 - -17. Suppose 0 = -4*b + a*p + 4, b - 5*p - 2 = -10. Factor -8/3*n + 2/3*n**b + 8/3.
2*(n - 2)**2/3
Let o(f) = -3*f - 27. Let a be o(-10). Factor 8/5*p**4 + 6*p**2 + 14/5*p + 26/5*p**a + 2/5.
2*(p + 1)**3*(4*p + 1)/5
Suppose -2*a + 3 = 2*d - a, 5*d + 3*a = 7. Factor -10/9*j**d + 0 - 4/9*j.
-2*j*(5*j + 2)/9
Let k = 20 - -60. Let l be 64/k - 2/5. Factor -l*v**2 - 8/5 - 8/5*v.
-2*(v + 2)**2/5
Suppose 0 = 7*k - 5*k - 4. Factor -3/2*n - 1 - 1/2*n**k.
-(n + 1)*(n + 2)/2
Let w(j) be the second derivative of j - 1/9*j**7 + 1/9*j**6 + 0*j**4 + 0*j**3 + 0*j**2 + 1/15*j**5 + 0. Suppose w(s) = 0. What is s?
-2/7, 0, 1
Suppose 2*k = -2*k. Let j(b) be the third derivative of -1/210*b**7 + 0*b**3 + 1/60*b**6 + k - b**2 + 0*b**4 + 0*b - 1/60*b**5. What is u in j(u) = 0?
0, 1
Let i(w) be the third derivative of -w**8/448 - w**7/280 + w**6/160 + w**5/80 + 14*w**2. Factor i(l).
-3*l**2*(l - 1)*(l + 1)**2/4
Suppose 4*f = -5*v - 8, 2 = -4*v + 4*f + 10. Suppose 4/3*a + v + 2/3*a**4 + 2*a**3 - 2/3*a**5 - 10/3*a**2 = 0. Calculate a.
-2, 0, 1
Let p(x) be the second derivative of x**5/150 - x**4/90 - 10*x. Solve p(i) = 0 for i.
0, 1
Let h be (-8)/48*34/(-13). Let d = h - -3/13. Factor -2/3 + 4/3*l**3 - 4/3*l + 0*l**2 + d*l**4.
2*(l - 1)*(l + 1)**3/3
Let b(w) be the second derivative of -w**8/168 - 3*w**7/140 + w**6/90 + w**3/3 - 2*w. Let p(r) be the second derivative of b(r). Factor p(c).
-2*c**2*(c + 2)*(5*c - 1)
Let i(t) = t**3 - 6*t**2 + 4*t + 5. Let z be i(5). Let k be z/(3 - (3 + -2)). Let 1/2*x**4 + 1/4*x**5 + 1/4*x**3 + k*x**2 + 0*x + 0 = 0. What is x?
-1, 0
Suppose -4*m - v - 2*v = -5, -20 = -3*m + v. Let t(d) = -d**2 + 4*d + 5. Let n be t(m). Factor o**2 - 3*o**2 + o + n*o + 3*o.
-2*o*(o - 2)
Let d be (-35)/2 + (-2)/4. Let w be ((-1)/(-12))/((-6)/d). Factor w*b**3 - 1/2*b + 1/4*b**2 + 0.
b*(b - 1)*(b + 2)/4
Suppose 10 = 2*y + 3*y. Let l(x) be the third derivative of 0 + 0*x - 1/12*x**4 - 1/6*x**3 - x**y - 1/60*x**5. Determine m so that l(m) = 0.
-1
Let g be (-738)/(-21)*2/21. Let q = g + -2/147. Find l, given that 4/3 + 16/3*l**4 - 20/3*l**2 + 2/3*l - q*l**5 + 8/3*l**3 = 0.
-1, -2/5, 1
Let y(r) be the second derivative of r**4/60 + r**3/15 - 4*r. Let y(b) = 0. Calculate b.
-2, 0
Let r = 53 - 53. Factor -1/4*j**2 + r + 0*j.
-j**2/4
Let l(h) = 24*h**5 + 64*h**4 + 26*h**3 + 14. Let q(b) = 5*b**5 + 13*b**4 + 5*b**3 + 3. Let o(d) = -3*l(d) + 14*q(d). What is g in o(g) = 0?
-4, -1, 0
Let r(p) = -2*p**3 + 11*p**2 - 12*p + 35. Let h be r(5). Find x such that -2/7*x**4 + 4/7*x - 10/7*x**2 + h + 8/7*x**3 = 0.
0, 1, 2
Let x(k) be the first derivative of -1/8*k**4 + 0*k - 1 - 1/8*k**2 - 1/4*k**3. Solve x(p) = 0 for p.
-1, -1/2, 0
Let s(v) be the third derivative of v**7/560 - v**5/160 - 66*v**2. Find r, given that s(r) = 0.
-1, 0, 1
Let j be (-124)/(-30) - (-6)/(-45). Factor -2*a + 4*a**3 - j*a - 4*a + 6*a.
4*a*(a - 1)*(a + 1)
Let r(m) be the first derivative of 0*m - 1/9*m**2 - 4/27*m**3 + 0*m**4 - 5 + 1/27*m**6 + 4/45*m**5. Factor r(s).
2*s*(s - 1)*(s + 1)**3/9
Let j = 6 + -4. Factor 4*y**2 - 2*y + 2*y + 4*y + j*y**3 - 2*y.
2*y*(y + 1)**2
Let o = 716 - 716. Solve -1/2*c**2 + o + c = 0.
0, 2
Let v(b) = b**2 - 19*b + 40. Let g be v(17). Suppose -g*r 