).
b*(b + 2)/4
Suppose 14*q - 6*q + 7*q - q**3 + 2*q**3 + 2*q**3 + 18*q**2 = 0. What is q?
-5, -1, 0
Let h(o) = 5*o + 78. Let a be h(-15). Let v(r) be the second derivative of 0 - a*r + 1/48*r**4 + 1/12*r**3 + 0*r**2. Factor v(s).
s*(s + 2)/4
Let s(x) be the second derivative of -2/33*x**4 - 1/110*x**5 + 1/11*x**3 + 18/11*x**2 - 1 - 11*x. Find n such that s(n) = 0.
-3, 2
Suppose -74*q - 59*q + 220 = -23*q. Factor 16/5 + 4/5*g**q - 4*g.
4*(g - 4)*(g - 1)/5
Let h(u) be the third derivative of u**6/120 + u**5/60 - 4*u**4 - 66*u**3 - 501*u**2. Find v, given that h(v) = 0.
-6, 11
Let q(x) = -x**2 - x. Let i(g) = -4*g**3 + 45*g**2 + 5*g - 44. Let y(t) = i(t) + q(t). Determine d, given that y(d) = 0.
-1, 1, 11
Let c(w) be the first derivative of -3*w**4/4 + 13*w**3 + 3*w**2/2 - 39*w - 55. Determine g, given that c(g) = 0.
-1, 1, 13
Let b(s) be the third derivative of -11*s**6/480 + s**5/10 - s**4/24 - 4*s**2 - 2*s. Factor b(y).
-y*(y - 2)*(11*y - 2)/4
Let b(o) = o**3 + o**2 - o + 1. Let j(n) be the third derivative of 2*n**7/105 - 2*n**6/15 + 2*n**4/3 - 2*n**3 - 26*n**2. Let h(d) = 4*b(d) + j(d). Factor h(f).
4*(f - 2)*(f - 1)**2*(f + 1)
Let w(m) = -3*m**3 + 10*m**2 + 60*m + 76. Let y(f) = 3*f**3 - 11*f**2 - 60*f - 77. Let a(o) = -5*w(o) - 4*y(o). Factor a(j).
3*(j - 6)*(j + 2)**2
Let k(o) be the third derivative of -o**6/150 - 7*o**5/25 - 3*o**4/5 + 16*o**3/3 + 720*o**2. Suppose k(y) = 0. Calculate y.
-20, -2, 1
Let x(f) = -279*f + 3073. Let v be x(11). Factor 0*y + 1/2*y**2 - 1/4 - 1/4*y**v + 0*y**3.
-(y - 1)**2*(y + 1)**2/4
Let z(h) be the third derivative of h**7/5040 + h**6/320 + h**5/120 - 5*h**4/6 + 25*h**2. Let y(l) be the second derivative of z(l). Factor y(g).
(g + 4)*(2*g + 1)/4
Let b(k) = -2*k**4 + 3*k**3 + 39*k**2 - 10*k + 6. Let f(r) = -6*r**4 + 10*r**3 + 116*r**2 - 26*r + 17. Let v(y) = 17*b(y) - 6*f(y). Find w, given that v(w) = 0.
-2, -1/2, 0, 7
What is k in -4/5*k**2 + 688/5 + 684/5*k = 0?
-1, 172
Let t(x) = -17*x**3 - 55*x**2 - 115*x - 45. Let s(d) = 6*d**3 + 18*d**2 + 39*d + 15. Let a(q) = -8*s(q) - 3*t(q). Factor a(z).
3*(z + 1)**2*(z + 5)
Let q be -4 + 6/(-270)*-183. Let s(l) be the second derivative of -2/5*l**2 + q*l**3 - 5*l + 0 + 1/30*l**4. Factor s(t).
2*(t - 1)*(t + 2)/5
Suppose 6*f = -7*f + 78. Suppose 24*o - 18 = f. What is y in -o - 5/4*y - 1/4*y**2 = 0?
-4, -1
Let c(l) be the first derivative of -1/6*l**4 - 7 + 0*l**3 + 0*l + 1/6*l**5 + 1/5*l**6 + 3/2*l**2. Let v(r) be the second derivative of c(r). Factor v(i).
2*i*(3*i + 2)*(4*i - 1)
Suppose -p - 4 = 2*p - 4*r, -1 = -r. Let o(g) be the first derivative of -1/25*g**5 + 4 + 0*g**2 + p*g**4 + 2/15*g**3 - 1/5*g. Solve o(s) = 0 for s.
-1, 1
Let j(p) = -2*p + 15. Let z(b) = b - 8. Let m(g) = 2*j(g) + 5*z(g). Let c be m(12). Factor 5*s**2 - s**2 + c*s**2 - 3*s**2.
3*s**2
Suppose -2*w = -3*w + 4*m - 16, 2*m - 2 = 2*w. Suppose i + w*i - 10 = 0, -a - 2*i + 4 = 0. Factor a*t**2 + 0 - 3/5*t**3 + 0*t.
-3*t**3/5
Suppose -4*s = -2*s + h - 104, -5*h - 260 = -5*s. Factor 207*p**2 - 114*p**3 + 14*p**3 - 44*p - s*p**2 + 9*p - 20.
-5*(p - 1)*(4*p + 1)*(5*p - 4)
Let o(k) = -2*k**2 - k. Let r(g) = 14*g**2 + 12*g. Let d(s) = 6*o(s) + r(s). Factor d(v).
2*v*(v + 3)
Let i(t) be the third derivative of t**7/630 - 49*t**6/720 + 23*t**5/360 + t**4/6 - 258*t**2. Determine s so that i(s) = 0.
-1/2, 0, 1, 24
Suppose -2*n - 3*g - 14 = 0, -2*n - 2696*g + 28 = -2700*g. Determine b, given that -9/4*b**3 - 10*b + 33/4*b**n + 4 = 0.
1, 4/3
Factor 45/8 + 3/8*f**2 - 6*f.
3*(f - 15)*(f - 1)/8
Let x = 109 - 104. Suppose 0 = x*d + 5*f - 5, d = 4*f - 3*f + 3. What is u in -1/4*u**d + 0 + 1/4*u = 0?
0, 1
Let z be (260/(-24))/(-13)*(-3)/(-15). Let h(c) be the second derivative of -1/36*c**4 + z*c**2 + 0 + c + 0*c**3. Solve h(s) = 0 for s.
-1, 1
Let d(g) be the first derivative of g**5/20 - 7*g**4/12 + 4*g**3/3 + 8*g**2 - 2*g - 10. Let l(f) be the first derivative of d(f). Suppose l(x) = 0. Calculate x.
-1, 4
Let v = 28897/33705 + -1/4815. Let -204/7*o + 1734/7 + v*o**2 = 0. What is o?
17
Let v(l) be the second derivative of l**7/735 + l**6/420 - 7*l**2/2 - l. Let m(n) be the first derivative of v(n). What is i in m(i) = 0?
-1, 0
Let u(s) be the first derivative of 5*s**4/4 + 10*s**3/3 - 35*s**2/2 + 20*s + 294. Factor u(o).
5*(o - 1)**2*(o + 4)
Let i be (-5 + 85/15)/(2/(-54)). Let s be 26 + -25 - (i/14 - -2). Factor 4/7*o - s*o**2 + 0.
-2*o*(o - 2)/7
Let l(r) be the third derivative of 2*r**7/105 + r**6/15 - r**5/15 - r**4/3 + 98*r**2 - 1. Factor l(z).
4*z*(z - 1)*(z + 1)*(z + 2)
Suppose -5*l = -z + 3*z + 73, -z = 3*l + 44. Let y be (-2)/l + 888/90. What is p in -10*p + 8*p**2 + 19 - 18 - y*p - 13 = 0?
-1/2, 3
Suppose -2*m - 3*m - 150 = 0. Let q be (-2)/(-5) + (-48)/m. Factor -5/8*i - 1/4*i**q - 1/4.
-(i + 2)*(2*i + 1)/8
Let i be (-1267)/(-28) - 3/12. Let g be (-3)/i*3*-8. Solve -2/5*o**3 + g*o**4 + 2/5*o + 0 - 8/5*o**2 = 0.
-1, 0, 1/4, 1
Suppose 5*v - 4*n = 11, n + 10 = v + 8. Let f(k) be the first derivative of -8 + 2/3*k**v + k**2 - 2/5*k**5 + 0*k - 1/2*k**4. Factor f(p).
-2*p*(p - 1)*(p + 1)**2
Let o(f) be the third derivative of f**7/1960 + f**6/280 + f**5/140 - 8*f**3/3 - 4*f**2. Let u(c) be the first derivative of o(c). What is w in u(w) = 0?
-2, -1, 0
Let y = 281/9 - 31. Let i be 150/(-54) + -4 - -7. Factor -i*s**5 + 4/9*s**3 - 4/9*s**2 + y + 2/9*s**4 - 2/9*s.
-2*(s - 1)**3*(s + 1)**2/9
Factor 14/9*t + 0 - 2/9*t**2.
-2*t*(t - 7)/9
Suppose 4*p + 3*a - 23 = 0, 5*p - 3*p - 11 = -a. Factor -15*t**4 + 5*t**5 + t**3 - 5*t**2 - t**3 + p*t**3 + 10*t**3.
5*t**2*(t - 1)**3
Let a(n) = -6*n + n**2 - 4*n**2 + 2*n**2 + 2 - 6*n**2 - n**3. Let w be a(-6). Factor -f**w + 2*f**3 - 6*f**3 - f**4 + 3*f + 2 + f**3.
-(f - 1)*(f + 1)**2*(f + 2)
Let i(q) be the second derivative of -2*q**6/15 - 49*q**5/20 - 8*q**4 - 61*q**3/6 - 5*q**2 + q - 56. Factor i(c).
-(c + 1)**2*(c + 10)*(4*c + 1)
Let w(j) be the first derivative of 5*j**3/3 - 75*j**2 + 1125*j + 86. Factor w(f).
5*(f - 15)**2
Let j be 7*1 + -178 + 175. Let l(o) be the second derivative of 3/20*o**5 + 1/2*o**3 + 0*o**2 + 0 + 3*o + 1/2*o**j. Factor l(u).
3*u*(u + 1)**2
Let i(y) = -3*y**2 - 2*y - 5. Let b(l) = -8*l**2 - 7*l - 14. Let m(j) = -4*b(j) + 11*i(j). Let a be m(5). Let 4 - a*c**2 - 1 - 4*c + 0 + c = 0. Calculate c.
-1, 1/2
Let b(z) be the third derivative of 0*z**6 + 1/18*z**3 + 0*z + 13*z**2 + 0 + 1/630*z**7 + 0*z**4 - 1/90*z**5. What is q in b(q) = 0?
-1, 1
Suppose -2*x + 2 = -2, -3*u - 4*x = -14. Let w be (-45)/10*8/(-18). Solve 3*y**u + 3*y**2 - 7*y**w - y = 0.
-1, 0
Suppose b = 5 - 2. Let y = 80 - 76. Factor -4*h - 23*h**3 - y*h**2 + 12*h**3 + 4 + 15*h**b.
4*(h - 1)**2*(h + 1)
Let g(b) be the second derivative of 5*b**4/36 - 62*b**3/9 - 25*b**2/6 + 128*b. Factor g(x).
(x - 25)*(5*x + 1)/3
Let v be -2 + 3 + 3 + -2. Suppose v*w + 8 = 16. Factor w*c**3 + 4*c**4 + 0 + 2 - 2.
4*c**3*(c + 1)
Let q(t) be the second derivative of -t**7/84 - 7*t**6/40 - 11*t**5/16 + 23*t**4/48 + 35*t**3/8 - 25*t**2/4 - 360*t. What is f in q(f) = 0?
-5, -2, 1/2, 1
Factor -16/3 + 68/3*t**2 - 56/3*t - 6*t**3.
-2*(t - 2)**2*(9*t + 2)/3
Let l = 126 - 124. Suppose -32/11*j**3 - 512/11*j + 2/11*j**4 + 512/11 + 192/11*j**l = 0. Calculate j.
4
Let i(a) be the third derivative of -a**6/120 + 7*a**5/60 - 5*a**4/12 - 101*a**2 - 2*a. Factor i(x).
-x*(x - 5)*(x - 2)
Let f(q) be the second derivative of q**5/105 + 5*q**4/21 + 50*q**3/21 - 17*q**2/2 - 5*q. Let r(n) be the first derivative of f(n). Let r(w) = 0. What is w?
-5
Let r(s) be the first derivative of 2*s**3/9 - 190*s**2 + 54150*s + 254. Factor r(b).
2*(b - 285)**2/3
Let q(j) be the first derivative of j**6/20 - 9*j**5/40 + j**4/4 - 8*j - 13. Let x(i) be the first derivative of q(i). Factor x(t).
3*t**2*(t - 2)*(t - 1)/2
Let f(c) be the third derivative of -4*c**2 + 1/20*c**5 + 0*c + 9/2*c**3 - 3/4*c**4 + 0. Factor f(g).
3*(g - 3)**2
Let a = 16 - -16. Factor 28*z**2 - 8*z - 48*z**2 - 4*z**4 + a*z**2.
-4*z*(z - 1)**2*(z + 2)
Let k(t) be the third derivative of -t**7/1050 + t**6/300 + 2*t**2 - 12. Factor k(i).
-i**3*(i - 2)/5
What is i in 4*i + 0*i - 4*i**2 - 5*i**4 + 116*i**3 - 11*i**2 - 101*i**3 + i = 0?
0, 1
Suppose l - 16 = -14. Let v be 3/(-6)*10/(-25). Solve v*y + 0*y**l - 2/5*y**3 + 0*y**4 + 0 + 1/5*y**5 = 0.
-1, 0, 1
Suppose 12*l -