). Suppose s(m) = 0. What is m?
1, 2
Let s(x) be the first derivative of -5 - 1/3*x**3 + 0*x**4 + 1/15*x**5 + 0*x + 1/3*x**2. Factor s(n).
n*(n - 1)**2*(n + 2)/3
Let i(f) be the third derivative of -f**6/24 - 31*f**5/6 - 4805*f**4/24 - 82*f**2 + 2. Factor i(m).
-5*m*(m + 31)**2
Suppose -68 = -7*q - 27*q. Let n(x) be the first derivative of 1/9*x**3 - 1/12*x**4 - 1/30*x**5 - 1 + 1/36*x**6 - 1/6*x + 1/12*x**q. Factor n(w).
(w - 1)**3*(w + 1)**2/6
Let y(p) be the third derivative of p**7/42 + p**6/3 + 5*p**5/4 - 5*p**4/3 - 40*p**3/3 + 98*p**2. Find s such that y(s) = 0.
-4, -1, 1
Let p(s) = 3*s**2 + 3*s - 3. Let j be p(2). Let k = 39/2 - j. Factor 6*b**2 + k*b - 3/2.
3*(b + 1)*(4*b - 1)/2
Let d = 1618/49 - -370/49. Let c = d - 3650/91. Determine p so that -2/13*p**2 + c + 4/13*p = 0.
-1, 3
Suppose -60 - 116 = -11*n. Factor -3*p**3 + 2*p**4 + 2*p + n*p - 6*p + 8 - 10*p**2.
(p - 2)**2*(p + 2)*(2*p + 1)
Suppose -55*o = -151*o + 192. Suppose 10/3*r**o - 2/3*r**3 + 2 - 14/3*r = 0. What is r?
1, 3
Let m = -2/929 + 1880/10219. Suppose -c - 1 + 4 = 0. Factor 2/11*v**2 - 2/11*v - 2/11 + m*v**c.
2*(v - 1)*(v + 1)**2/11
Suppose -4*i + 0 = -88. Factor -13*m**2 - 2*m + 18*m - 13*m**2 - 12 + i*m**2.
-4*(m - 3)*(m - 1)
Suppose -55*k + 12 = -20*k - 58. Factor 2*p + 12/13 + 4/13*p**k.
2*(p + 6)*(2*p + 1)/13
Let h = -7657/45 + 851/5. Let f(q) be the first derivative of -1/9*q**2 + h*q**5 + 2/9*q**3 - 1/6*q**4 + 0*q + 8. Suppose f(z) = 0. Calculate z.
0, 1
Factor -2820 + 3*p**2 + 2820 + 87*p.
3*p*(p + 29)
Let h(a) = -17*a**3 - a + 2. Let s be h(1). Let j be ((-5)/70)/(2/s). Solve j*p + 2/7*p**2 + 2/7 = 0 for p.
-1
Suppose -3*n + 5*w = 2*w, 3*n - 2*w - 4 = 0. Suppose -4*z + 8 = -n*x, 0 = -z - x - 4*x + 2. Factor 0*h**2 + z*h - 2*h**2 - 4 + 8 - 4*h.
-2*(h - 1)*(h + 2)
Let p(w) = 13*w**3 - w**2 + 109*w - 107. Let j(c) = -138*c**3 + 9*c**2 - 1089*c + 1071. Let m(n) = 2*j(n) + 21*p(n). What is d in m(d) = 0?
-7, 1, 5
Let k = 17 - 14. Let o(f) = -f**k + 1 - f + 0*f**3 + 0 - f**2 + 0*f**3. Let m(v) = v**3 + 7*v**2 + 3*v - 3. Let h(t) = -m(t) - 3*o(t). Factor h(w).
2*w**2*(w - 2)
Suppose -40 = -4*v - 4*k, 2*v = -2*k - 2*k + 26. Suppose 0 = -5*x + 4*x + v*x. Factor 1/2*z**2 + 0*z + x.
z**2/2
Determine f, given that -6/11*f + 1/11*f**2 + 8/11 = 0.
2, 4
Let i be (28/(-98))/((-3)/(-21)). Let t be 10 - 6 - (i/4 + -3). Find k such that -5/2*k**5 + 0 - t*k**3 + 0*k - 5/2*k**2 - 15/2*k**4 = 0.
-1, 0
Suppose 2*f + b - 1 = 0, 0*b - 5*b - 5 = 5*f. Suppose -5*a = -m - 6*a, 0 = f*m - a. Solve m + 1/2*y**2 - 1/2*y = 0 for y.
0, 1
Let b(r) = 5*r**4 + 21*r**3 + 10*r**2 - 6*r. Let s(x) = 10*x**4 + 43*x**3 + 21*x**2 - 12*x. Let v(i) = -14*b(i) + 6*s(i). Factor v(f).
-2*f*(f + 1)*(f + 3)*(5*f - 2)
Let z(x) be the third derivative of -17*x**6/90 + 31*x**5/60 - 3*x**4/8 + x**3/9 - 682*x**2. Let z(r) = 0. What is r?
2/17, 1/4, 1
Let m be (((-138)/(-8))/3)/((-1)/(-4)). Factor l**2 + 5*l - 19*l**2 + m*l**2.
5*l*(l + 1)
Find l, given that 11/9 - 5/9*l**2 - 6*l = 0.
-11, 1/5
Let m = 33 + -30. Suppose -5*b - 5 = 3*r - 0*r, m*r = 3*b - 21. Factor 22 - 4*i**b + 16 - 34.
-4*(i - 1)*(i + 1)
Let b be (4/(-12))/((-1)/3). Suppose -b = -3*r + 8. Let -14/9*i**r - 4/9*i**2 + 14/9*i + 4/9 = 0. What is i?
-1, -2/7, 1
Let w(x) be the third derivative of 0*x**4 + 0 + 0*x + 0*x**3 + 9/70*x**7 + 1/5*x**5 + 1/2*x**6 + 7*x**2. Factor w(g).
3*g**2*(g + 2)*(9*g + 2)
Let f(l) be the first derivative of 2*l**5/55 + 7*l**4/11 + 40*l**3/11 + 104*l**2/11 + 128*l/11 - 634. Factor f(n).
2*(n + 2)**3*(n + 8)/11
Let -4*x**3 - 75 + 98*x**2 - 6*x + x + 9*x**3 - 23*x**2 = 0. Calculate x.
-15, -1, 1
Determine z, given that 338/25 - 52/25*z + 2/25*z**2 = 0.
13
Suppose y + 9 = 2*g, 0*g + 9 = y + g. Factor 36*q - 12*q**2 - 36 + 4/3*q**y.
4*(q - 3)**3/3
Let o(s) be the first derivative of s**3/27 - 7*s**2/18 + 2*s/3 - 1. Suppose o(d) = 0. What is d?
1, 6
Find k, given that -2/3*k**2 + 2 - 4/3*k = 0.
-3, 1
Let o(h) = h**2 + 6*h + 7. Let v be o(-5). Let x(n) be the second derivative of -1/42*n**4 - 5*n + 0 + 1/7*n**3 + 0*n**v. Factor x(a).
-2*a*(a - 3)/7
Let u = -8027 - -8029. Determine j, given that -2*j + 2/7*j**u + 12/7 = 0.
1, 6
Let u(p) be the second derivative of -10*p**7/21 + 4*p**6/5 + 14*p**5/5 - 28*p**4/3 + 10*p**3 - 4*p**2 + 17*p - 1. Solve u(l) = 0 for l.
-2, 1/5, 1
Factor 0*x + 3/5*x**4 - 18/5*x**3 + 3/5*x**5 + 0*x**2 + 0.
3*x**3*(x - 2)*(x + 3)/5
Factor -24 + a**2 + 46 - 2*a - 25.
(a - 3)*(a + 1)
Suppose -3*y + 5 = -1. Let c be 0 + (-3)/((-6)/2) - -13. Determine a, given that c - 4*a**y - 14 = 0.
0
Suppose -m + 0*m - 32 = 0. Let x be m/(-20) - (-4)/10. Let -4*q**2 + q**2 + 4*q**2 + x*q = 0. Calculate q.
-2, 0
Let q(a) = 3*a - 46. Let x be q(13). Let k(y) = 2*y**2 + 16*y + 16. Let f be k(x). Factor -1/2*n + 1 - 1/2*n**f.
-(n - 1)*(n + 2)/2
Let c(s) be the second derivative of -3/11*s**2 + 20*s - 1/33*s**4 + 5/33*s**3 + 0. Determine n, given that c(n) = 0.
1, 3/2
Let -1/2*i**3 + 3/2*i**2 + 1/2*i - 3/2 = 0. Calculate i.
-1, 1, 3
Let l = 29/333 - -5/37. Let i(x) be the third derivative of 3*x**2 + 0*x - l*x**3 - 1/60*x**6 - 1/45*x**5 + 0 + 7/36*x**4. Determine k, given that i(k) = 0.
-2, 1/3, 1
Let l(w) be the second derivative of 1/24*w**3 + 1/48*w**4 + 0 + 0*w**2 + 22*w. Determine j, given that l(j) = 0.
-1, 0
Factor 12 - 12*c**2 + 500*c**3 + 34*c - 6*c - 528*c**3.
-4*(c - 1)*(c + 1)*(7*c + 3)
Suppose -2*p = -w - 12, -6*p + 4*p - w = -8. Suppose 0 = z + 3*v - 9, -3*v = -3*z - p - 4. Suppose 1/4 + z*s - 1/4*s**2 = 0. Calculate s.
-1, 1
Let n(o) be the third derivative of -o**8/112 + o**6/5 + 3*o**5/10 - 7*o**4/8 - 3*o**3 - 120*o**2 - o. Determine k, given that n(k) = 0.
-2, -1, 1, 3
Let y = 21757/230 + -939/10. Suppose -y*p**2 - 40/23*p - 2/23*p**3 - 32/23 = 0. What is p?
-4, -2
Let t = -144/23 + 311/46. Factor t*q**2 + 0 + 0*q + 1/2*q**4 + q**3.
q**2*(q + 1)**2/2
Suppose 0 = -7*c + 17 + 18. Suppose -c*b**4 - 134 + 134 + b**4 = 0. Calculate b.
0
Let k(n) be the second derivative of n**4/12 + 3*n**3 + 17*n**2/2 + 148*n. What is f in k(f) = 0?
-17, -1
Let n(u) = 2*u**2 + 6*u - 5. Let k be n(2). Suppose 15*c - k*c + c**3 + 2*c**3 = 0. What is c?
0
Factor -1/4*p**4 - 15/4*p**2 - 1 + 13/4*p + 7/4*p**3.
-(p - 4)*(p - 1)**3/4
Let z(b) be the first derivative of b**6/2160 + b**5/180 + b**4/36 - 10*b**3/3 + 14. Let n(q) be the third derivative of z(q). Factor n(k).
(k + 2)**2/6
Let k(g) be the first derivative of -4*g**3/3 - 116*g**2 - 3364*g - 56. Factor k(c).
-4*(c + 29)**2
Let b be 1/4 + (-21)/84. Let l(y) be the third derivative of 8*y**2 + 3/8*y**4 + y**3 + 1/20*y**5 + 0*y + b. Factor l(s).
3*(s + 1)*(s + 2)
Let m(t) be the first derivative of t**7/70 - t**6/40 - t**5/20 + t**4/8 - 9*t**2/2 - 9. Let p(l) be the second derivative of m(l). Factor p(c).
3*c*(c - 1)**2*(c + 1)
Let h = -68439/40 - -1711. Let b(q) be the second derivative of 0 - 21/80*q**5 - 5/2*q**3 - 9*q + 9/8*q**4 + h*q**6 + 3*q**2. Factor b(j).
3*(j - 2)**3*(j - 1)/4
Let n(r) be the third derivative of 7*r**6/200 - 97*r**5/300 - 2*r**4 + 38*r**3/15 - 394*r**2. Find w such that n(w) = 0.
-2, 2/7, 19/3
Let u be 2 - (-10 - (-4)/2). Let d = 17 - u. What is c in -4*c - 2*c**2 - d + 0 + 1 + 4 = 0?
-1
Let c(b) be the second derivative of -4*b**2 - 34/3*b**3 - 23*b - 12*b**4 + 0. Factor c(o).
-4*(4*o + 1)*(9*o + 2)
Let i be (-1)/((-5)/(-618)) + 0. Let w = 124 + i. Factor -w*b - 32/5*b**3 - 16/5*b**2 + 0.
-2*b*(4*b + 1)**2/5
Let p(a) be the second derivative of -1/42*a**4 + 0 + 27*a - 4/21*a**3 - 3/7*a**2. Factor p(k).
-2*(k + 1)*(k + 3)/7
Let c = -802 - -21656/27. Let i(d) be the first derivative of 2/9*d**2 + 0*d + 1 - c*d**3. Solve i(g) = 0 for g.
0, 2
Let t(o) = 12*o**2 + 256*o + 1460. Let z(p) = -8*p**2 - 171*p - 973. Let v(a) = -5*t(a) - 8*z(a). Factor v(b).
4*(b + 11)**2
Suppose -81*y + 166 = 2*y. Suppose 0 - 3/5*g**y - 3/5*g**3 + 6/5*g = 0. What is g?
-2, 0, 1
Let p(b) = 9*b**2 - 3*b - 6. Let r = 3 - 2. Let d(z) = z**2 - 1. Let h = 151 - 157. Let o(w) = h*d(w) + r*p(w). Solve o(f) = 0 for f.
0, 1
Let b be 16/(-1)*(-14)/56. Suppose -3*d - b = -4*d. Factor 4*m**5 + 12*m**3 + 12*m**d + m**2 + 0*m**2 + 3*m**2.
4*m**2*(m + 1)**3
Let v = 28/125 + 47/125. Factor 2/5 - c**2 + v*c.
-(c - 1)*(5*c + 2)/5
Let f(y) be the third derivative of -y**6/360 + y**5/15 - 128*y**3/9 