 2
Let v(k) be the second derivative of -4*k + 1/60*k**4 + 1/10*k**2 - 1/15*k**3 + 0. Factor v(g).
(g - 1)**2/5
Suppose 2*x - 25 = 5*r, -x + 3*x - 3*r = 15. Find i such that -3*i**2 + x + 2 + 1 = 0.
-1, 1
Let f be ((-56)/(-48))/(56/108). Find p, given that -f*p**3 - 27/8*p**2 - 3/8*p**4 + 3/2*p + 9/2 = 0.
-3, -2, 1
Let v = 35974/20993 - -2/2999. Solve 4/7 - 5/7*c**3 + 3/7*c**2 + v*c = 0 for c.
-1, -2/5, 2
Let b(n) be the first derivative of -7 + 2*n**5 + 5/2*n**6 + 0*n - 65/4*n**4 - 40/3*n**3 + 10*n**2. Solve b(s) = 0 for s.
-2, -1, 0, 1/3, 2
Let j(l) = 40*l**3 + 172*l**2 + 268*l + 156. Let r(v) = -v**4 + 39*v**3 + 173*v**2 + 267*v + 155. Let t(u) = -5*j(u) + 4*r(u). Suppose t(y) = 0. Calculate y.
-5, -2
Let k = 27 + -539/20. Let x(g) be the second derivative of -1/15*g**3 - 1/100*g**5 + 0*g**2 + 0 + k*g**4 + 5*g. Find o such that x(o) = 0.
0, 1, 2
Let l(q) be the first derivative of -q**6/27 - 2*q**5/45 + q**4/6 + 2*q**3/27 - 2*q**2/9 - 73. Solve l(r) = 0 for r.
-2, -1, 0, 1
Let x(n) be the third derivative of -1/45*n**5 + 0*n - 1/9*n**3 + 0*n**6 - 2/27*n**4 - 32*n**2 + 0 + 1/945*n**7. Find v such that x(v) = 0.
-1, 3
Let k(a) be the second derivative of 27*a**5/100 + 9*a**4/5 + 24*a**3/5 + 32*a**2/5 + 4*a. Let k(b) = 0. What is b?
-4/3
Let q = -11 - -25. Solve -q - 3*n**4 + 14 + 2*n**4 = 0.
0
What is s in 25/2*s**4 + 65*s**3 + 0 + 23/2*s**2 - 5*s = 0?
-5, -2/5, 0, 1/5
Let q be 19/6 + (-5)/30. Let a = 1/1428 + 535/714. Determine h so that 1/4*h**2 + 1/4*h**5 + 0*h + 3/4*h**4 + 0 + a*h**q = 0.
-1, 0
Solve 1134 + 2/7*o**2 + 36*o = 0 for o.
-63
Let s(h) = -9*h**5 - 15*h**4 - 72*h**3 + 96*h**2 + 63*h + 33. Let m(b) = b**5 + 2*b**4 + 9*b**3 - 12*b**2 - 8*b - 4. Let o(v) = -33*m(v) - 4*s(v). Factor o(g).
3*g*(g - 2)**2*(g + 1)**2
Determine u so that 68 - 5*u + 8*u**2 + 44 - 188 + 44 + u**3 + u = 0.
-8, -2, 2
Let n = 204 + -201. Let -14*x**2 - 8/5 + 52/5*x - 49/5*x**n = 0. Calculate x.
-2, 2/7
Factor -15/4*a**3 + 15*a + 6 - 3/2*a**2.
-3*(a - 2)*(a + 2)*(5*a + 2)/4
Let d(x) = x**3 + 16*x**2 + 15*x + 8. Let m be d(-15). Let g be (-1 + m/5)/((-7)/(-80)). Factor -26/7*l - g*l**2 - 18/7*l**3 - 4/7.
-2*(l + 2)*(3*l + 1)**2/7
Let h(m) = -80*m**2 - 260*m - 305. Let d(p) = -29 - 17*p - 9*p**2 - 36*p - 5 + 24*p. Let r(v) = -35*d(v) + 4*h(v). Suppose r(l) = 0. Calculate l.
-3, -2
Let j(t) be the first derivative of 1/2*t**2 + 24 - 1/5*t**5 - 1/4*t**4 + 1/3*t**3 + 0*t. Factor j(x).
-x*(x - 1)*(x + 1)**2
Let n(x) be the second derivative of 4/21*x**3 + 0 - 3/2*x**2 - 1/21*x**4 + 1/210*x**5 + 5*x. Let s(g) be the first derivative of n(g). Factor s(j).
2*(j - 2)**2/7
Suppose -5*n - u = 4, 0 = -5*n + 7*u + 50 - 22. Let 3*s**2 - 3*s**4 - 1/4*s**3 + n - s**5 - s = 0. Calculate s.
-2, 0, 1/2
Let d be 6/27*3*3. Suppose 1/2*r**4 + d*r + 2 - 3/2*r**2 - r**3 = 0. What is r?
-1, 2
Let p(v) be the first derivative of 0*v - 2/9*v**2 - 1/6*v**4 - 10/27*v**3 + 2/45*v**5 - 14 + 1/27*v**6. Factor p(j).
2*j*(j - 2)*(j + 1)**3/9
Suppose 56*t**2 - 42*t**4 + 39*t**3 - 19*t + 52*t + 13*t**2 + 45*t**4 = 0. What is t?
-11, -1, 0
Suppose 3*w + c - 3*c - 12 = 0, 0 = c + 3. Factor 0*l**w + 0*l**3 + 5*l**3 + 6*l**2 - 2*l**3.
3*l**2*(l + 2)
Let s(g) be the third derivative of g**9/1512 + g**8/210 + g**7/70 + g**6/45 + g**5/60 - g**3/6 - g**2. Let n(y) be the first derivative of s(y). Factor n(h).
2*h*(h + 1)**4
Let y(z) be the second derivative of -1/3*z**2 + 0 - 1/60*z**5 + 1/18*z**4 + 1/18*z**3 + 14*z. Factor y(j).
-(j - 2)*(j - 1)*(j + 1)/3
Let c(j) = 13*j**2 + 103*j - 345. Let r(x) = 18*x**2 + 154*x - 519. Let o(v) = 7*c(v) - 5*r(v). Factor o(s).
(s - 45)*(s - 4)
Suppose 57*v - 569 = -11*v + 1811. Solve 15/2*i**4 + 0*i + 20*i**2 - v*i**3 + 0 = 0.
0, 2/3, 4
Let i(o) be the first derivative of -o**4/24 + o**3/6 - o**2/6 + 52. What is q in i(q) = 0?
0, 1, 2
Let o = 18217 + -18214. Factor 4/5*n**2 + 0 + 2/5*n**4 + 0*n + 6/5*n**o.
2*n**2*(n + 1)*(n + 2)/5
Let k(j) be the third derivative of -j**5/30 + 119*j**4/3 - 56644*j**3/3 - 781*j**2. Factor k(w).
-2*(w - 238)**2
Let y(v) be the first derivative of -v**4/4 - 4*v**3/3 - 3*v**2/2 + 255. Determine u, given that y(u) = 0.
-3, -1, 0
Suppose -1191*b**2 + 28*b**3 + 1127*b**2 - 8*b - 154*b**3 = 0. Calculate b.
-2/7, -2/9, 0
Suppose 0 = 5*y - 5*c - 70, -2*y = -y - 2*c - 18. Let p be (y - 6) + (-2)/1. Factor -2*r**3 + r**2 - 6*r**2 + 3*r**p.
-2*r**2*(r + 1)
Determine o so that -344*o + 3*o**2 + 483*o + 287*o = 0.
-142, 0
Let h(z) be the first derivative of -z**8/2520 + z**6/900 - 3*z**2/2 + 1. Let g(p) be the second derivative of h(p). What is u in g(u) = 0?
-1, 0, 1
Let g = -2729 + 2731. What is v in -27/8 + 9/4*v - 3/8*v**g = 0?
3
Let n(d) be the first derivative of d**6/240 - d**5/120 - 5*d**4/48 - d**3/4 - 6*d**2 + 6. Let i(m) be the second derivative of n(m). Factor i(t).
(t - 3)*(t + 1)**2/2
Let i(h) be the first derivative of 3/4*h**2 - 12 - 5/6*h**3 + 9/2*h + 1/8*h**4. Find t, given that i(t) = 0.
-1, 3
Let a(x) be the second derivative of x**4/3 - 22*x**3/15 + 12*x**2/5 - 201*x. Factor a(n).
4*(n - 1)*(5*n - 6)/5
Find c such that -54/5*c**4 + 36*c**3 + 3/5*c**5 - 168/5*c**2 + 0 + 0*c = 0.
0, 2, 14
Factor 23 + 2*w - 9*w - 7*w - 8*w - w**2.
-(w - 1)*(w + 23)
Suppose -h + h - h = 0. Suppose -1/3*q**2 + 1/3*q + h + 1/3*q**4 - 1/3*q**3 = 0. Calculate q.
-1, 0, 1
What is w in 2*w + 0 + 4*w**2 - 1/2*w**3 - 4*w**4 - 3/2*w**5 = 0?
-2, -1, -2/3, 0, 1
Let l(d) be the first derivative of 13 - 8/3*d**6 + 0*d - 2*d**2 + 28/3*d**3 - 15*d**4 + 52/5*d**5. Find o, given that l(o) = 0.
0, 1/4, 1
Suppose 6*p + 12 = 2*p. Let i be p + 6/(60/35). Factor i - 3*x + 9/2*x**2.
(3*x - 1)**2/2
Solve 7/3*b**2 + 8/3*b - 1/3*b**3 + 0 = 0 for b.
-1, 0, 8
Let x(k) be the second derivative of -k**9/21168 - k**8/3920 + k**6/630 - 2*k**3 - 5*k. Let i(s) be the second derivative of x(s). Let i(p) = 0. Calculate p.
-2, 0, 1
Let y(h) = 39*h**4 + 273*h**3 - 39*h**2 - 300*h + 27. Let d(w) = -3*w**4 - 21*w**3 + 3*w**2 + 23*w - 2. Let s(t) = 27*d(t) + 2*y(t). What is x in s(x) = 0?
-7, -1, 0, 1
Let u be 1463/(-171) - (-1 + -2). Let s = u - -268/45. Find n such that s*n**3 + 0*n - 1/5*n**5 + 0 - 1/5*n**4 + 0*n**2 = 0.
-2, 0, 1
Let j be ((-52)/(-8) - 9/6) + 14/8. Let -j*r**4 + 15/4*r**2 + 3/4*r + 9/4*r**3 + 0 = 0. What is r?
-1/3, 0, 1
Let p(y) be the first derivative of 0*y**3 - 2*y - 1/48*y**4 + 1/120*y**6 - 1 + 0*y**2 + 0*y**5. Let x(j) be the first derivative of p(j). Factor x(i).
i**2*(i - 1)*(i + 1)/4
Let n(k) be the first derivative of k**5/10 + k**4/3 - k**3 - 10*k + 12. Let m(l) be the first derivative of n(l). Find o, given that m(o) = 0.
-3, 0, 1
Suppose 11*n = 15*n - 8. Factor 2*g**n - 3*g**2 - 36 - 3*g**2 + 198*g - 158*g.
-4*(g - 9)*(g - 1)
Let s(f) = f**5 + 7*f**4 - 5*f + 5. Let h(b) = b**5 + 6*b**4 - 4*b + 4. Let u(a) = 5*h(a) - 4*s(a). Find n, given that u(n) = 0.
-2, 0
Suppose -115 = 4*y - 27*y. Let m(j) be the second derivative of 3/25*j**y + 0 - 1/15*j**3 + 0*j**2 + 1/6*j**4 + 3*j. Find w, given that m(w) = 0.
-1, 0, 1/6
Let w(v) be the second derivative of 0 + 0*v**2 - 1/180*v**5 - 1/54*v**4 - 1/54*v**3 - 5*v. Find o such that w(o) = 0.
-1, 0
Let n(i) be the third derivative of i**7/14 + 13*i**6/40 + i**5/5 - i**4/2 - 65*i**2. Let n(c) = 0. What is c?
-2, -1, 0, 2/5
Let z(n) be the second derivative of n**8/560 - n**6/40 + n**5/20 + 5*n**3/6 - 19*n. Let x(o) be the second derivative of z(o). Suppose x(a) = 0. Calculate a.
-2, 0, 1
Let v(x) = x**2 - 11*x - 3. Let o be v(12). Let r(j) be the third derivative of -o*j**2 + 0 - 9/20*j**5 + 0*j - 1/2*j**3 - 3/4*j**4. Factor r(c).
-3*(3*c + 1)**2
Let m(k) = -7*k**2 + 105*k - 2. Let o(i) = -15*i**2 + 210*i - 5. Let c(a) = 5*m(a) - 2*o(a). Factor c(v).
-5*v*(v - 21)
Let t(y) be the third derivative of y**8/3192 - 17*y**7/1995 + 21*y**6/380 + 27*y**5/190 - 158*y**2. Factor t(q).
2*q**2*(q - 9)**2*(q + 1)/19
Suppose -100 - 212*u - 2*u**4 + 11*u**3 + 57*u - 15*u**2 + 24*u**3 + 0*u**4 - 3*u**4 = 0. What is u?
-1, 4, 5
Let o(u) be the second derivative of 6*u**6/5 - 128*u**5/5 + 244*u**4/3 - 32*u**3 + u. Find v, given that o(v) = 0.
0, 2/9, 2, 12
Let t be (-2)/33 - (-1748)/3795. Factor -4/15*o**2 + 2/15*o**3 + 0 - t*o.
2*o*(o - 3)*(o + 1)/15
Factor 21/4*w**2 + 9/4*w + 0 + 3/4*w**4 + 15/4*w**3.
3*w*(w + 1)**2*(w + 3)/4
Let 