- 25*z + 10*z**3 + 870*z**2 = 0.
-2, -2/3, 0, 2
Determine f, given that -2/3*f**2 + 0 + 2/3*f**4 - 4/3*f**3 + 4/3*f = 0.
-1, 0, 1, 2
Let l = 32434/3 - 10810. Determine q, given that 2/3*q**4 + 0 - l*q - 2*q**2 + 0*q**3 = 0.
-1, 0, 2
Factor -1083/2 - 6*s**2 - 114*s.
-3*(2*s + 19)**2/2
Let r(q) be the first derivative of q**9/1512 - q**8/840 - q**7/420 + q**6/180 - 2*q**3/3 + 27. Let f(w) be the third derivative of r(w). Factor f(x).
2*x**2*(x - 1)**2*(x + 1)
Suppose -7*j = 5*j - 48. Let v(g) be the first derivative of -15/28*g**j - 24/7*g**2 - 17/7*g**3 + 2 - 12/7*g. Factor v(n).
-3*(n + 1)*(n + 2)*(5*n + 2)/7
Let p(r) = 44*r**3 - 75*r**2 + 15*r + 16. Let j(c) = -44*c**3 + 74*c**2 - 14*c - 16. Let h(f) = -3*j(f) - 2*p(f). Solve h(m) = 0 for m.
-4/11, 1
Factor 0 - 45*p**2 + 3/2*p + 243/2*p**3.
3*p*(3*p - 1)*(27*p - 1)/2
Let q be -2 + 4 - (6 - 7). What is a in -3206 - 4*a + 3206 + 2*a**q + 2*a**2 = 0?
-2, 0, 1
Let g be 196/(-147) - 174/(-117). Find q such that 2/13*q**4 - g*q**5 + 0*q + 0*q**2 + 0*q**3 + 0 = 0.
0, 1
Let r(m) be the first derivative of -27 - 1/4*m**3 + 9/2*m - 3/8*m**2. Factor r(p).
-3*(p - 2)*(p + 3)/4
Let c be (-84)/45 + 2 - (-11016)/8505. Let 0 - c*g**2 - 6/7*g**3 - 4/7*g = 0. What is g?
-1, -2/3, 0
Let y(p) be the first derivative of 3/20*p**4 + 1/5*p**2 - 1/30*p**6 + 0*p + 1/3*p**3 + 26 - 1/25*p**5. Factor y(w).
-w*(w - 2)*(w + 1)**3/5
Let m(w) = -7*w**2 + 8*w + 2. Let z(u) = u**2 + u - 1. Let g(c) = -c**2 + 8*c + 8. Let d be g(9). Let x(p) = d*m(p) + 3*z(p). Factor x(l).
5*(l - 1)*(2*l + 1)
Let x(n) be the first derivative of 2*n**5/25 + 3*n**4/10 - 2*n**3/15 - 3*n**2/5 - 54. Factor x(q).
2*q*(q - 1)*(q + 1)*(q + 3)/5
Let u(x) be the second derivative of x**5/15 - 2*x**4/9 - 82*x**3/9 + 28*x**2 - 181*x. Determine o, given that u(o) = 0.
-6, 1, 7
Let d(z) be the second derivative of -z**4/78 - 58*z**3/39 - 841*z**2/13 + 96*z. Factor d(l).
-2*(l + 29)**2/13
Let n(m) be the first derivative of 1/4*m**5 + 10/3*m**3 + 15/8*m**4 - 45/4*m - 23 - 15/4*m**2. What is h in n(h) = 0?
-3, -1, 1
Let l be -6*7/(-315)*(50 - -1). Let d = l + -218/35. Suppose d - 6/7*k + 2/7*k**2 = 0. Calculate k.
1, 2
Let o(r) = 3*r**4 + 2*r**2 - 4*r + 1. Let j be (-35)/(-10)*(-4)/(-2). Let a(v) = 10*v**4 - v**3 + 7*v**2 - 13*v + 4. Let m(u) = j*o(u) - 2*a(u). Factor m(f).
(f - 1)*(f + 1)**3
Let h(b) be the second derivative of 1/100*b**5 + 6*b + 0*b**2 + 0*b**4 + 0 + 1/150*b**6 + 0*b**3. Suppose h(k) = 0. What is k?
-1, 0
Factor 7/10*n**2 + 3/10*n**4 + 0 - 1/5*n - 4/5*n**3.
n*(n - 1)**2*(3*n - 2)/10
Let n(k) be the first derivative of -k**6/18 + k**4/3 - 2*k**3/9 - k**2/2 + 2*k/3 - 11. Determine m so that n(m) = 0.
-2, -1, 1
Solve 16/7*d**3 + 0*d - 4/7*d**5 + 0 + 8/7*d**4 - 32/7*d**2 = 0 for d.
-2, 0, 2
Let z(l) = -l**5 - l**4 + l**3 + 1. Let t(r) = 634*r**5 - 491*r**4 - 614*r**3 + 515*r**2 - 20*r - 24. Let o(c) = t(c) + 4*z(c). Suppose o(g) = 0. What is g?
-1, -1/6, 2/7, 2/3, 1
Let t(v) = -32*v - 15. Let n be t(-6). Find k such that -19 - 245*k**2 - n*k + 37*k - 1 = 0.
-2/7
Let n(g) be the first derivative of g**3/3 + 49. Let o(c) = -2*c**2 + 13*c + 12. Let v(m) = -3*n(m) - o(m). Determine d so that v(d) = 0.
-12, -1
Solve 71*v + 7*v**2 + 14 - 3*v**2 + 78 + 484 + 25*v = 0.
-12
Suppose -32 = -6*s + 2*s. Factor -12*f**3 + 7*f**3 - 12*f**2 + s*f**3 + 9*f.
3*f*(f - 3)*(f - 1)
Let c(p) be the third derivative of -p**6/480 + 19*p**5/48 - 2303*p**4/96 + 2209*p**3/24 - 36*p**2 + p. Factor c(r).
-(r - 47)**2*(r - 1)/4
Let i(p) = 60*p**3 - 5*p**2 + 4*p - 4. Let g(j) = -177*j**3 + 16*j**2 - 11*j + 11. Let t(u) = 4*g(u) + 11*i(u). What is o in t(o) = 0?
0, 3/16
Find i, given that -4*i**2 + 8*i**2 - 3*i + i - 2*i + 0*i**2 = 0.
0, 1
Let h be (22/51)/(-15 + (-966)/(-63)). Factor -30/17*q**2 - 4/17 + h*q**3 + 18/17*q - 6/17*q**4.
-2*(q - 1)**3*(3*q - 2)/17
Let x(v) be the first derivative of -v**6/3 - 7*v**5/4 + 5*v**4/2 + 35*v**3/6 - 10*v**2 - 24*v + 11. Let j(a) be the first derivative of x(a). Solve j(s) = 0.
-4, -1, 1/2, 1
Let i(c) be the third derivative of -c**7/42 - 7*c**6/12 + 4*c**5/3 + 35*c**4/12 - 25*c**3/2 - 35*c**2 + 2. Factor i(m).
-5*(m - 1)**2*(m + 1)*(m + 15)
Find a, given that -23*a - 3*a**2 + 3*a**4 + 2*a**3 - 15*a - 13 - 3*a**5 + 25*a**3 - 22*a - 23 = 0.
-2, -1, 2, 3
Let z(q) = -q + 4. Let g be z(3). Let f = g - -2. Factor 3*w + 1 + 3*w**2 - 5 - 5 + f.
3*(w - 1)*(w + 2)
Suppose 13 = -3*r + 46. Let -2*m**3 - m**2 - 3*m**3 + m**5 + r*m**3 - 3*m**3 - 3*m**4 = 0. Calculate m.
0, 1
Factor 0*u - 10/3*u**4 + 8/9*u**5 + 40/9*u**3 + 2/9 - 20/9*u**2.
2*(u - 1)**4*(4*u + 1)/9
Solve 8/17*y - 6/17 - 2/17*y**2 = 0.
1, 3
Factor -260/3*d + 5/3*d**4 + 90*d**2 - 100/3*d**3 + 85/3.
5*(d - 17)*(d - 1)**3/3
Suppose 9*h + 3*c - 351 = 6*h, 0 = 3*h - 3*c - 351. Let k = h + -115. Factor 4/11 - 6/11*x - 24/11*x**k - 14/11*x**3.
-2*(x + 1)**2*(7*x - 2)/11
Let n(y) = -y**2 + 10*y - 21. Suppose -4 - 10 = -5*w + 4*k, -5*k - 10 = -5*w. Let x be n(w). Factor -x*s - s**3 + 0*s + 6*s**4 - 14*s**3 + 12*s**2.
3*s*(s - 1)**2*(2*s - 1)
Let h(d) be the third derivative of 5*d**5/72 - d**4/72 + 125*d**2. Factor h(k).
k*(25*k - 2)/6
Let l(f) be the first derivative of -64/5*f - 4/15*f**3 + 9 + 16/5*f**2. Factor l(a).
-4*(a - 4)**2/5
Let v(r) = -5*r - 4. Let q be v(2). Let p be (-4)/q + (192/28)/4. Factor -p*i**2 - 2*i - 1/2*i**3 + 0.
-i*(i + 2)**2/2
Let y be (-2)/(-18) + 1456/504. Let d(q) be the second derivative of -7*q - 1/80*q**5 + 0 + 1/24*q**y + 1/8*q**2 - 1/48*q**4. Let d(n) = 0. Calculate n.
-1, 1
Let s = 5/3 + -11/12. Let v be 60/(-210) - 75/(-42). Factor 3/4*y - s*y**2 + v.
-3*(y - 2)*(y + 1)/4
Suppose 115*c - 6 = 114*c. Determine v so that -238*v**3 + 14 - c - 2*v**2 - 90*v**5 - 277*v**4 - 17*v**4 + 40*v = 0.
-2, -1, -1/3, 2/5
Factor 6495/4*r**2 + 13455/8*r + 1935/4*r**3 + 3/8*r**5 + 4563/8 - 225/8*r**4.
3*(r - 39)**2*(r + 1)**3/8
Let w(p) be the first derivative of 2*p**5/5 - 87*p**4/4 + 923*p**3/3 + 264*p**2 - 484*p + 1032. Factor w(i).
(i - 22)**2*(i + 1)*(2*i - 1)
Let z be -12*(1 - (-10)/(-8)). Suppose a - 1 = z. Factor -4 + 2*s - 6*s - s**a - 2 + 8*s**2 + 4*s**3 - s**4.
-2*(s - 3)*(s - 1)*(s + 1)**2
Let k = -219 - -219. Let u(j) be the third derivative of k*j - 1/4*j**4 - 1/20*j**5 + 3*j**2 + 0 - 1/2*j**3. Factor u(b).
-3*(b + 1)**2
Let m be 66/110*(-40)/(-2). Factor m*s**3 - 5 + 5 - 5*s - 7*s**3.
5*s*(s - 1)*(s + 1)
Let r be ((-246)/12 - -13)/(10/(-4)). Solve -16/7*u**r + 2/7*u**4 + 0 + 0*u + 32/7*u**2 = 0 for u.
0, 4
Let j(b) be the second derivative of -b**6/10 - 201*b**5/20 - 1449*b**4/4 - 8993*b**3/2 + 36501*b**2 + 3*b + 11. Find o such that j(o) = 0.
-23, 2
Let c be ((-72)/20 - (3 - 6))*(-30)/27. Factor -2*w**2 + 0*w**3 - 4/3*w + c*w**4 + 0.
2*w*(w - 2)*(w + 1)**2/3
Let n(x) be the third derivative of x**7/420 - 11*x**6/240 - 13*x**5/40 - 41*x**4/48 - 7*x**3/6 - 84*x**2 + x. Factor n(h).
(h - 14)*(h + 1)**3/2
Let r(k) = k**3 + 116*k**2 + 114*k - 113. Let d be r(-115). Suppose 3*u**d - 3/4*u + 3*u**4 - 3/4*u**5 - 9/2*u**3 + 0 = 0. What is u?
0, 1
Let x(f) = f**4 + 183*f**3 - 561*f**2 + 545*f - 192. Let i(d) = 5*d**4 + 1100*d**3 - 3365*d**2 + 3270*d - 1150. Let a(k) = 6*i(k) - 35*x(k). Factor a(w).
-5*(w - 36)*(w - 1)**3
Let j = -96 + 96. Let b(a) be the third derivative of j + 0*a**3 + 1/20*a**5 - 4*a**2 + 3/70*a**7 + 0*a**4 + 0*a - 1/10*a**6. Suppose b(s) = 0. Calculate s.
0, 1/3, 1
Suppose -d + 6 = -5*t - 4*d, -3*t - d - 2 = 0. Suppose -4*w - 2*p + 0*p + 20 = 0, t = w + p - 6. Find h, given that -6*h**2 + 5*h**2 + w*h + 3*h**2 = 0.
-2, 0
Let g(v) be the second derivative of -1/35*v**5 + 7*v + 0 - 1/420*v**6 + 7/2*v**2 - 8/21*v**3 - 1/7*v**4. Let i(p) be the first derivative of g(p). Factor i(c).
-2*(c + 2)**3/7
Let w = 1274 + -1270. Factor 0*d - 2/13*d**2 + 2/13*d**5 - 2/13*d**3 + 2/13*d**w + 0.
2*d**2*(d - 1)*(d + 1)**2/13
Let l = 300 + -301. Let q be l/(-20)*(-1)/((-9)/24). Factor 0 - 4/15*y + q*y**2.
2*y*(y - 2)/15
Find o such that 6*o**2 - 2/5*o**3 - 28/5*o + 0 = 0.
0, 1, 14
Let f(i) be the third derivative of -i**7/42 + 5*i**6/12 - 3*i**5 + 35*i**4/3 - 80*i**3/3 - 17*i**2 - 3. Find r such that f(r) = 0.
2, 4
Let m(l) = l + 11. Let o be m(-8). Factor 42*k**3 - 5*k**5 - k**4 - 2*k**o - 4*k**4 + 60*k**2.
-5*k**2*(k - 3)*(k + 2)**2
Let w be (0 + 2)/((-1)/(-3)). Wh