 -1/1512*r**8 + 1/54*r**4 + 0*r + 3*r**2 + 0*r**3 - 1/54*r**5 + 1/945*r**7 + 0 + 1/180*r**6. Factor b(x).
-2*x*(x - 1)**3*(x + 2)/9
Let h(s) be the third derivative of 0*s**4 + 0*s**3 + 4*s**2 + 0*s**6 + 0*s**5 + 0 + 0*s - 1/210*s**7 - 1/336*s**8. Suppose h(c) = 0. What is c?
-1, 0
Let j(g) be the first derivative of g**4/4 + 4*g**3/3 - 2*g**2 + 7*g + 2. Let h be j(-5). Factor -1/2*v**h + 0 + 3/2*v**3 - v.
v*(v - 1)*(3*v + 2)/2
Let r(a) = a**2 + 7*a + 9. Let n be r(-7). Let b(c) = c**2 - 9*c + 2. Let k be b(n). Suppose 0 + 0*j + 5*j**2 - 1 - 6*j**2 + k*j = 0. What is j?
1
Suppose -w + 6 + 11 = 3*q, 2*w + q = 14. Suppose 0 = w*a + x - 7, 0*a - 2*a - 5*x - 11 = 0. Factor 2/5*y**3 + 0 + 2/5*y**a + 0*y.
2*y**2*(y + 1)/5
Let i be (-10)/36*(0 + 4 - 7). Factor i*t**2 + 2/3 - 1/6*t**3 - 4/3*t.
-(t - 2)**2*(t - 1)/6
Let a(x) be the third derivative of 1/525*x**7 + 1/840*x**8 + 8*x**2 - 1/150*x**6 + 0*x + 0 + 0*x**5 + 0*x**3 + 0*x**4. Factor a(n).
2*n**3*(n - 1)*(n + 2)/5
Let h = 291 - 554. Let l = h - -537/2. What is t in -6*t**3 + 1/4 + 9/4*t**4 + l*t**2 - 2*t = 0?
1/3, 1
Let j(c) = 21*c - 1. Let s be j(1). Let m = 22 - s. Factor 0 + 0*q + 1/2*q**m + 1/2*q**3.
q**2*(q + 1)/2
Let k(d) be the third derivative of d**8/13440 - d**7/5040 - d**6/1440 + d**5/240 - d**4/6 + d**2. Let j(a) be the second derivative of k(a). Factor j(m).
(m - 1)**2*(m + 1)/2
Let s(m) be the first derivative of -2*m**5/25 + 2*m**3/15 - 8. Determine q, given that s(q) = 0.
-1, 0, 1
Let n(f) = -4*f**2 - 10*f + 12. Let l(k) = -k**3 - 20*k**2 - 50*k + 60. Let m(p) = -4*l(p) + 22*n(p). Find a such that m(a) = 0.
-2, 1, 3
Find i such that 22*i + 5*i**2 + 2*i**2 - 8*i**2 - 75 - 46 = 0.
11
Let f be 0 + 1 + (-238)/240. Let t(z) be the third derivative of 0 + 1/16*z**4 - f*z**5 + z**2 - 1/6*z**3 + 0*z. Find y such that t(y) = 0.
1, 2
Let t(q) = 25*q**5 + 85*q**4 - 85*q**2 - 95*q. Let w(m) = 2*m**5 + 7*m**4 - 7*m**2 - 8*m. Let h(b) = 3*t(b) - 35*w(b). Factor h(p).
5*p*(p - 1)*(p + 1)**3
Let z = -95 - -97. Let k(s) be the first derivative of 0*s + 17/15*s**5 + 1/3*s**2 + 2/9*s**6 + 2 + 13/9*s**3 + z*s**4. Determine r, given that k(r) = 0.
-2, -1, -1/4, 0
Let h(a) = -9*a**3 + 60*a**2 - 156*a + 105. Let w(q) = -2*q**3 + 15*q**2 - 39*q + 26. Let g(j) = 5*h(j) - 21*w(j). Factor g(p).
-3*(p - 1)**2*(p + 7)
Let d(l) be the first derivative of 4*l**5/25 - l**4/20 - 4*l**3/15 + l**2/10 - 26. What is z in d(z) = 0?
-1, 0, 1/4, 1
Let g(y) = 5*y - 25. Let p be g(5). Let b(c) be the second derivative of 1/12*c**4 + 1/5*c**5 + p - 1/10*c**6 + 0*c**2 - 3*c - 1/3*c**3. Factor b(w).
-w*(w - 1)**2*(3*w + 2)
Factor 0 + 7/2*c**2 + c**3 - 3/2*c**4 + c.
-c*(c - 2)*(c + 1)*(3*c + 1)/2
Let v(d) be the third derivative of -d**7/105 - d**6/15 - d**5/6 - d**4/6 - 22*d**2. Factor v(q).
-2*q*(q + 1)**2*(q + 2)
Let t(l) = -l + 8. Let r be t(4). Suppose 2*n + 1 = 3*f, 2*n + n - 5*f = -r. Find x such that -n*x**3 + 5*x**2 - 3*x**5 - 8*x**4 - 4*x**2 - 3*x**2 = 0.
-1, -2/3, 0
Let n(h) = -26*h + 133. Let j be n(5). Factor 0 - 1/4*f + f**4 + f**2 - 1/4*f**5 - 3/2*f**j.
-f*(f - 1)**4/4
Let w(p) be the first derivative of -4*p**3/3 + 2*p**2 + 8*p - 1. Determine o so that w(o) = 0.
-1, 2
Factor -24*b + 63/2*b**2 + 6 - 27/2*b**3.
-3*(b - 1)*(3*b - 2)**2/2
Let y(q) be the first derivative of -1/5*q**2 + 1/10*q**4 + 0*q**3 - 2 + 0*q. Find i such that y(i) = 0.
-1, 0, 1
Let l(a) = -a**4 - a**3 + a**2. Let q(u) = -u. Let n(y) = -l(y) + q(y). Factor n(o).
o*(o - 1)*(o + 1)**2
Let d(b) be the third derivative of -b**7/630 + b**6/90 - b**5/36 + b**4/36 + 10*b**2. Factor d(o).
-o*(o - 2)*(o - 1)**2/3
Let y(w) be the third derivative of -w**5/210 + w**4/84 + 8*w**2. Factor y(m).
-2*m*(m - 1)/7
Let h(y) be the first derivative of -2*y**2 - 2*y + 11/6*y**3 - 2 - 3/8*y**4. Suppose h(w) = 0. Calculate w.
-1/3, 2
Let x(v) be the third derivative of -9*v**6/40 + 31*v**5/20 - 14*v**4/9 + 2*v**3/3 - 8*v**2. Let x(p) = 0. What is p?
2/9, 3
Let u(l) be the third derivative of -5/126*l**7 - 1/18*l**6 + 0*l - 1/45*l**5 + 0*l**4 - l**2 + 0*l**3 + 0. Factor u(g).
-g**2*(5*g + 2)**2/3
Let m(h) be the second derivative of -h**7/3 + 58*h**6/15 - 64*h**5/5 + 16*h**4/3 + 2*h - 56. Factor m(j).
-2*j**2*(j - 4)**2*(7*j - 2)
Let h(g) be the third derivative of -g**5/330 + g**4/132 + 2*g**3/33 - 11*g**2. Factor h(s).
-2*(s - 2)*(s + 1)/11
Find z such that 13*z**3 + z**5 + 19*z**2 - 7*z**2 + 29*z - 25*z + 6*z**4 = 0.
-2, -1, 0
Let t = -35/2 + 19. Determine v, given that 3/2*v - 3*v**2 + 0 + t*v**3 = 0.
0, 1
Factor 5 - 40*f**3 + 3*f + 2*f + 35*f**3 - 5*f**2.
-5*(f - 1)*(f + 1)**2
Let k(v) be the second derivative of v**7/42 + v**6/30 - 14*v. Suppose k(n) = 0. What is n?
-1, 0
Let z(x) be the second derivative of -x**6/90 + x**5/20 - x**4/18 - 10*x. Factor z(r).
-r**2*(r - 2)*(r - 1)/3
Find z such that -9*z**2 - 67*z**3 + 70*z**3 + 27*z - 9*z**2 = 0.
0, 3
Let r(o) be the third derivative of o**11/665280 - o**10/100800 + o**9/60480 + o**5/60 - 3*o**2. Let i(j) be the third derivative of r(j). Factor i(b).
b**3*(b - 2)*(b - 1)/2
Let s be (-5 - -2)*(-551)/3. Let a = -3851/7 + s. Factor -6/7*u - 2/7*u**3 - 2/7 - a*u**2.
-2*(u + 1)**3/7
Suppose 4/7*a**4 + 8/7 - 12/7*a**2 - 4/7*a + 4/7*a**3 = 0. What is a?
-2, -1, 1
Let k(n) = n**3 - 6*n**2 - 3*n - 28. Let z be k(7). Let -2/11*f**4 + 2/11*f**2 + 2/11*f**3 - 2/11*f + z = 0. What is f?
-1, 0, 1
Let p(z) be the second derivative of 0*z**3 + 4*z + 2/3*z**2 + 1/60*z**5 - 1/12*z**4 + 0. Solve p(i) = 0.
-1, 2
Let y be (-2)/(-6) - (-35)/21. Suppose 3*s - 10 = -y*s. Solve 0*o + 0*o**s - 2/5*o**3 + 0 = 0 for o.
0
Let g be -4 - 2 - (-3 - -4). Let x = -7 - g. Factor -2*t**5 + 3*t**4 + x*t**4 - 3*t**3 + t**5 + t**2.
-t**2*(t - 1)**3
Let k = 14 - 11. Let w(p) = -4*p**2 + 3*p + 13. Let o(q) = 12*q**2 - 8*q - 40. Let y(j) = k*o(j) + 8*w(j). Determine h so that y(h) = 0.
-2, 2
Let i(m) be the first derivative of -2*m**3/21 + 5*m**2/7 - 12*m/7 + 31. Determine o so that i(o) = 0.
2, 3
Let s be -1 + 1 + (4 - 4). Suppose s = -3*d - 0 + 9. Let 2*l**4 - d*l**2 + 0*l**4 - l**2 + 2 = 0. What is l?
-1, 1
Let b(n) be the first derivative of -n**3/6 - 2*n**2 - 8*n - 3. Factor b(x).
-(x + 4)**2/2
Let m be 18/12*1/3. Factor g**3 + 0*g**2 + m - g - 1/2*g**4.
-(g - 1)**3*(g + 1)/2
Let j = -42401/20 + 2119. Let p = 5/4 + j. Factor 0 - 1/5*h**3 + p*h**2 + 0*h.
-h**2*(h - 1)/5
Let j be 80/(-14) - 14/49. Let r be (-2)/((-3)/((-27)/j)). Find p such that -2/5 - 2/5*p + 2/5*p**2 + 2/5*p**r = 0.
-1, 1
Let v(n) = 79*n - 78*n + 3 - 2. Let g(c) = -c**2 + 2*c + 1 - c + 1. Let l(j) = -g(j) + 2*v(j). Factor l(d).
d*(d + 1)
Let v(z) be the third derivative of -z**5/210 + z**4/7 - 12*z**3/7 - 24*z**2. Factor v(n).
-2*(n - 6)**2/7
Determine d so that -1/6*d**2 + 5*d - 75/2 = 0.
15
Let g(a) be the second derivative of -a**7/105 + a**6/75 + a**5/25 + 6*a. Factor g(i).
-2*i**3*(i - 2)*(i + 1)/5
Let t be (144/40)/((-4)/(-10)). Factor -13 + 3*q**2 + 7 - 6*q + t.
3*(q - 1)**2
Let l(j) be the first derivative of 42*j**5/5 + 13*j**4/2 - 38*j**3/3 - 13*j**2 - 4*j - 59. Find k such that l(k) = 0.
-1, -1/3, -2/7, 1
Suppose -3*w + 4 = -5. Let p be (1/(-2))/((-1)/6). Factor -f**3 + f**w - p*f**3 + f**5 + 2*f**2.
f**2*(f - 1)**2*(f + 2)
Let o = -27/571 - -16775/330609. Let q = 392/1737 - o. Factor 2/9*v**3 + 0 + q*v + 4/9*v**2.
2*v*(v + 1)**2/9
Let b(m) = 2*m**4 - 4*m**3 + 7*m**2 - 3*m. Let o(j) = j**4 + j**3 - j**2 + j. Let l(p) = 5*b(p) - 5*o(p). Factor l(q).
5*q*(q - 2)**2*(q - 1)
Suppose 1/9*w**4 - 2/9 + 1/9*w**2 - 1/3*w**3 + 1/3*w = 0. Calculate w.
-1, 1, 2
Let f(c) be the second derivative of c**6/30 - c**5/20 + 2*c. Let d(v) = -6*v**4 + 2*v**3 + 4*v**2. Let r(h) = -d(h) - 4*f(h). Factor r(t).
2*t**2*(t - 1)*(t + 2)
Let u = 90 + -90. Let z(r) be the third derivative of 0*r**6 - 1/3*r**3 + u + 0*r - 1/105*r**7 - 4*r**2 + 1/15*r**5 + 0*r**4. Solve z(d) = 0.
-1, 1
Factor 9/5*b**4 + 9/5*b**3 + 0*b + 0 + 3/5*b**2 + 3/5*b**5.
3*b**2*(b + 1)**3/5
Let s(g) be the first derivative of -g**4/6 + 2*g - 2. Let c(h) be the first derivative of s(h). Factor c(z).
-2*z**2
Suppose 0 = -3*w - 3*z - 45, 2*w - 4*z = w. Let y be w/(-42)*(-14)/(-10). Factor 4/5*l**3 + 4/5*l**2 + y - 6/5*l**4 - 6/5*l + 2/5*l**5.
2*(l - 1)**4*(l + 1)/5
Let r = 5 + 2. Suppose r*f - 3*f**2 - 9*f + f**2 = 0. What i