g(q) be the first derivative of -q**6/360 + q**5/90 + 2*q**2 + 17. Let t(l) be the second derivative of g(l). Find b such that t(b) = 0.
0, 2
Let i(j) be the first derivative of -2*j**3/33 + 3*j**2 + 402. Factor i(n).
-2*n*(n - 33)/11
Let x(m) = m**3 + 2*m**2 + m. Let s(v) = -2*v**3 - 20*v**2 + 54*v - 72. Let f(k) = s(k) + 3*x(k). Factor f(b).
(b - 8)*(b - 3)**2
Suppose -2*q - 3*p - 14 - 3 = 0, -2*q + 4*p + 18 = 0. Let c be (q/5)/(1/((-40)/24)). Factor -2/3*u**2 + 1/3*u**3 + 0 + c*u.
u*(u - 1)**2/3
Let h(a) be the first derivative of 2*a**6 + 21*a**5/5 - 9*a**4/2 - 7*a**3 + 3*a**2 - 12. Suppose h(x) = 0. Calculate x.
-2, -1, 0, 1/4, 1
Let o(x) be the third derivative of -x**7/504 - 5*x**6/72 - 25*x**5/24 - 5*x**4/12 - 13*x**2. Let g(d) be the second derivative of o(d). Factor g(y).
-5*(y + 5)**2
Let 2/9*h**3 + 8/3*h**2 + 58/9*h + 4 = 0. Calculate h.
-9, -2, -1
Let d(r) = r**4 + 160*r**3 + 2918*r**2 + 17492*r. Let z(i) = 2*i**4 + 479*i**3 + 8755*i**2 + 52474*i. Let c(x) = -7*d(x) + 2*z(x). Factor c(w).
-3*w*(w + 18)**3
Suppose -4*x + 1472 = -3*h + 7*h, -3*x + 1144 = -5*h. What is a in -x - a**2 - 2*a + 3*a + 373 = 0?
0, 1
Let m(f) = 7*f**3 - 4*f**2 - 6*f + 10. Let l(o) = 38*o**3 - 21*o**2 - 31*o + 51. Let g(d) = -2*l(d) + 11*m(d). What is z in g(z) = 0?
-2, 2
Let r(l) be the second derivative of -l**7/112 + l**6/80 - 25*l + 2. Factor r(d).
-3*d**4*(d - 1)/8
Let t(g) be the first derivative of 1 + 1/3*g**3 - 1/12*g**4 + 3/2*g**2 - 5*g. Let s(n) be the first derivative of t(n). Determine z, given that s(z) = 0.
-1, 3
Let i(l) be the second derivative of -l**7/630 + l**6/45 - 2*l**5/15 - l**4/4 + 20*l. Let m(u) be the third derivative of i(u). Suppose m(o) = 0. Calculate o.
2
Let i(m) be the first derivative of -m**6/30 + 2*m**5/15 - m**4/6 + 6*m**2 + 22. Let b(j) be the second derivative of i(j). Suppose b(r) = 0. What is r?
0, 1
Let c = -53 + 55. Factor -17 - 2*m - 7 + 15*m**3 + 42*m + 55*m**c + 4.
5*(m + 2)**2*(3*m - 1)
Let n(h) = 4*h + 32. Let w be n(-13). Let d be (-28)/w - (-18)/30. Factor 18/13 + 2/13*v**3 + 30/13*v + 14/13*v**d.
2*(v + 1)*(v + 3)**2/13
Let y(s) = 5*s**3 + 1. Let d be y(-1). Let f = d - -6. Factor 0 - g**2 - g + 4 + f - 5 + g**3.
(g - 1)**2*(g + 1)
Let l(u) be the third derivative of u**7/4200 - u**5/600 + 8*u**3/3 + 15*u**2. Let z(f) be the first derivative of l(f). Let z(w) = 0. What is w?
-1, 0, 1
Let w(n) be the third derivative of 0*n**4 + 0 + 0*n**5 + 0*n**3 + 0*n - 2/21*n**7 - 5*n**2 - 1/24*n**6. Factor w(m).
-5*m**3*(4*m + 1)
What is p in 37632*p + 23*p**4 - 804*p**3 - 3864*p**2 + 44185 + 57*p**4 + 22*p**4 + 87527 - 3*p**5 = 0?
-4, 14
Let l(p) be the first derivative of p**5/4 - 5*p**4/12 - 5*p**3/6 + 5*p**2/2 + 4*p + 16. Let j(t) be the first derivative of l(t). Factor j(a).
5*(a - 1)**2*(a + 1)
Let r(u) be the second derivative of -u**5/7 + 26*u**4/21 - 50*u**3/21 + 8*u**2/7 - 53*u. Find g, given that r(g) = 0.
1/5, 1, 4
Let i(b) be the second derivative of -6 + 7/4*b**2 + 1/2*b**3 + 3*b - 3/20*b**5 - 1/3*b**4 + 1/60*b**6. Factor i(p).
(p - 7)*(p - 1)*(p + 1)**2/2
Let t(p) = p**3 + 3*p**2 - 2*p - 3. Let a be t(-3). What is h in -5*h**a + 3*h + 8*h**4 + 2*h - 5*h**2 - 3*h**4 = 0?
-1, 0, 1
Let v(y) be the second derivative of y**3/3 - 4*y**2 - 5*y. Let n be v(6). Factor -n*o**3 - 2*o**2 + o**5 + o**2 + o**4 + 3*o**2 - 6*o**2.
o**2*(o - 2)*(o + 1)*(o + 2)
Let x(z) be the third derivative of -1/42*z**4 + 1/735*z**7 + 0 - 1/21*z**3 + 2*z**2 + 0*z**5 + 0*z + 1/210*z**6. Determine w so that x(w) = 0.
-1, 1
Let a(r) = 10*r - 4. Let s be a(2). Factor s*q - 4*q**2 + 5*q**4 - 16*q - q**2.
5*q**2*(q - 1)*(q + 1)
Let p = 14446 + -14444. Factor 0 - 2/11*u**3 + 0*u - 2/11*u**p.
-2*u**2*(u + 1)/11
Suppose -10*n + 13*n + 2*j = 2, -j = 5*n - 1. Let -1/4*v**5 + n*v + 0 - 1/4*v**4 + 1/4*v**2 + 1/4*v**3 = 0. What is v?
-1, 0, 1
Let s = -99/70 + 17/10. Let w(l) be the first derivative of s*l - 6/35*l**5 - 3/7*l**2 - 6 + 1/7*l**4 + 4/21*l**3 + 1/21*l**6. Solve w(y) = 0.
-1, 1
Let o(d) be the third derivative of 1/6*d**4 + 1/168*d**8 + 0*d + 3/20*d**6 + 6*d**2 + 0 - 7/30*d**5 - 1/21*d**7 + 0*d**3. Factor o(s).
2*s*(s - 2)*(s - 1)**3
Let y = 15/11 - -43/33. Suppose 2/3*m**3 + 4/3 + 10/3*m + y*m**2 = 0. What is m?
-2, -1
Let c = -5 - -7. Suppose 3*z + 6 = -5*g, -4*z + 8*z - 15 = g. Factor 3/5 + 8*v**c + 16/5*v**z - 23/5*v.
(v + 3)*(4*v - 1)**2/5
Let x(p) be the first derivative of 5*p**6/3 - 34*p**5/5 + 8*p**4 - 8*p**3/3 - 105. Solve x(t) = 0 for t.
0, 2/5, 1, 2
Let d(o) be the third derivative of -o**8/280 + 13*o**7/525 - 17*o**6/300 + o**5/50 + 2*o**4/15 - 4*o**3/15 + 91*o**2 - 2*o. Determine i so that d(i) = 0.
-2/3, 1, 2
Let a(m) = 6*m**3 + 54*m**2 + 136*m - 192. Let z(q) = 13*q**3 + 109*q**2 + 270*q - 382. Let p(u) = -5*a(u) + 2*z(u). Factor p(c).
-4*(c - 1)*(c + 7)**2
Let p(i) be the second derivative of i**3/6 - 4*i**2 - 8*i. Let z be p(11). Factor 6*h**3 - 6*h + h**3 - 3*h**4 + z*h**2 - h**3.
-3*h*(h - 2)*(h - 1)*(h + 1)
Let n = 18415/2 - 9207. Factor -1/2 - s - n*s**2.
-(s + 1)**2/2
Suppose -76*z - 14 = -75*z. Let u be (z/16 - -1)*2. Find t, given that -1/4*t**4 + 1/2*t - 1/2*t**3 + 0 + u*t**2 = 0.
-2, -1, 0, 1
Let n(y) be the third derivative of 0*y**5 - 3/16*y**4 - 1/2*y**3 + y + y**2 + 0 + 1/80*y**6. Factor n(z).
3*(z - 2)*(z + 1)**2/2
Suppose -9 = -57*s + 105. Find x such that -2/3*x**s + 4*x - 2/3*x**3 + 0 = 0.
-3, 0, 2
Factor 28/3*c - 2/3*c**2 + 10.
-2*(c - 15)*(c + 1)/3
Find f such that -86/17*f + 60/17 - 276/17*f**2 + 88/17*f**4 - 48/17*f**3 + 6/17*f**5 = 0.
-15, -1, 1/3, 2
Let i(h) be the first derivative of 4*h**5/5 + 3*h**4 - 8*h**3 - 56*h**2 - 96*h - 134. Determine v, given that i(v) = 0.
-2, 3
Factor 0*u + 0 + 2/3*u**4 - 20/3*u**2 + 2*u**3.
2*u**2*(u - 2)*(u + 5)/3
Let -3626764*q - 154*q**3 - 2*q**4 - 153228*q**2 - 7916412*q - 750*q**3 - 326094722 = 0. What is q?
-113
Let w(p) be the first derivative of -4*p**5/5 + p**4 + 8*p**3/3 - 109. Factor w(r).
-4*r**2*(r - 2)*(r + 1)
Let i(f) be the first derivative of -6*f**5/35 + 4*f**4/7 - 2*f**3/3 + 2*f**2/7 - 20. Determine a, given that i(a) = 0.
0, 2/3, 1
Let v = 587/6 + -17609/180. Let w(s) be the third derivative of 0*s**3 - 1/72*s**4 - v*s**5 - 6*s**2 + 0*s + 0. Find j such that w(j) = 0.
-1, 0
Let k be (-6)/10 - 0 - -1. Suppose 34*j + 18*j = 11*j - 29*j. Factor -k*l - 2/5*l**4 + j + 2/5*l**2 + 2/5*l**3.
-2*l*(l - 1)**2*(l + 1)/5
Let d be 4 - (12 + -4) - -3. Let w be 3/(2 + d) - (-2 - -3). Suppose -2/3*x**w - 10/9*x - 4/9 = 0. What is x?
-1, -2/3
Let o(l) be the first derivative of 1/42*l**3 + 0*l**2 - 5*l + 1/35*l**5 - 1 - 5/84*l**4. Let p(c) be the first derivative of o(c). Factor p(k).
k*(k - 1)*(4*k - 1)/7
Let m = 91 - 75. Suppose -m*f + 12*f**2 + 11*f**3 - 19*f**4 - 8*f**3 + 13*f**3 + 21*f**4 - 14 = 0. What is f?
-7, -1, 1
Let b(l) be the second derivative of -l**4/48 + 3*l**3/4 - 81*l**2/8 + 3*l - 17. Find v such that b(v) = 0.
9
Factor -5116 + 104*u + 10037 - 5023 - 2*u**2.
-2*(u - 51)*(u - 1)
Let q be ((-197)/(-4))/(-1) + (-33)/44. Let v be (160/q)/(4/(-6)). Determine m, given that -44/5*m - 12/5*m**2 - v = 0.
-3, -2/3
Let t be 4 - 4 - 1/(-1). Let a(q) = -1. Let k(n) be the third derivative of n**5/60 + n**3/6 + 13*n**2. Let m(z) = t*a(z) + k(z). Factor m(b).
b**2
Let w(u) = -u**2 - 2. Let b(q) = -3*q**2 - 76*q + 82. Let v(c) = b(c) + w(c). Let v(s) = 0. What is s?
-20, 1
Let x(y) = 2*y**5 + y**4 - 4*y**3 + y**2 + 2*y + 1. Let h(z) = -z**5 - z**4 + 2*z**3 - z**2 - z - 1. Let q(n) = 4*h(n) + 4*x(n). Factor q(k).
4*k*(k - 1)**2*(k + 1)**2
Let q(k) be the third derivative of k**6/270 - k**5/45 + k**4/27 + 324*k**2. Factor q(x).
4*x*(x - 2)*(x - 1)/9
Factor -3/2*l**5 - 3*l**4 + 3 + 12*l**2 + 3*l**3 + 21/2*l.
-3*(l - 2)*(l + 1)**4/2
Let n = 1211/7338 - -2/1223. Let m(s) be the third derivative of -n*s**4 - 1/30*s**6 + 0*s + 0*s**3 + 0 + 2/15*s**5 + 7*s**2. Factor m(k).
-4*k*(k - 1)**2
Let p = -4/567 - -5111/1134. Factor p*t + 3 + 3/2*t**2.
3*(t + 1)*(t + 2)/2
Let n(z) = 6*z**3 - 12*z**2 + 4*z + 4. Let m = 54 + -58. Let c(p) = p**3 - p**2 - p + 1. Let g(q) = m*c(q) + n(q). Find l such that g(l) = 0.
0, 2
Let k(m) = -16*m**2 + 97*m - 36. Let x(l) = l**2 - l. Let s(o) = k(o) + x(o). Factor s(f).
-3*(f - 6)*(5*f - 2)
Let s(v) be the first derivative of v**4/22 - 82