be j(-10). Determine p so that 6*p + 2*p**5 - 4*p**3 + p - f*p = 0.
-1, 0, 1
Suppose -4*c - 18 = -30. Factor 3*t**2 + c*t + t - 4*t - t**3 - 2*t.
-t*(t - 2)*(t - 1)
Let k(o) be the second derivative of o**6/15 - 7*o**5/10 + 4*o**4/3 + 16*o**3/3 - 178*o. Let k(x) = 0. What is x?
-1, 0, 4
Let j(a) be the third derivative of -a**5/90 - a**4/12 - 2*a**3/9 + 112*a**2. Factor j(d).
-2*(d + 1)*(d + 2)/3
Let m(z) = -z**2 + 45*z + 70. Let p(l) = -l**2. Let w(y) = -m(y) + 6*p(y). Factor w(c).
-5*(c + 2)*(c + 7)
Factor -2/7*w**2 - 160/7 - 48/7*w.
-2*(w + 4)*(w + 20)/7
Determine p, given that 3/7*p**4 + 0 + 0*p**3 + 6/7*p - 9/7*p**2 = 0.
-2, 0, 1
Let b(z) be the third derivative of -49*z**5/30 + 175*z**4/6 - 625*z**3/3 + 205*z**2. Factor b(i).
-2*(7*i - 25)**2
Let r(n) be the first derivative of -n**7/735 - n**6/210 - n**5/210 - 17*n**2 + 26. Let u(k) be the second derivative of r(k). Find z such that u(z) = 0.
-1, 0
Solve -10/11*w**3 + 6/11*w**2 - 6/11*w**4 + 2/11*w**5 + 8/11*w + 0 = 0.
-1, 0, 1, 4
Let n(l) = -l**2 + l + 10. Let i be n(0). Factor -s**4 + 8*s**4 - 2*s**4 - 3*s**4 + i*s**2 - 12*s**3.
2*s**2*(s - 5)*(s - 1)
What is s in 222*s**3 - 18*s**4 - 16*s**4 + 375 - 4*s**4 - 225*s - 330*s**2 - 5*s**4 - 2*s**4 + 3*s**5 = 0?
-1, 1, 5
Let s = 111765/31934 + 2/15967. Find x, given that -18 - 13/2*x**2 + s*x**4 - 66*x + 15*x**3 = 0.
-3, -2/7, 2
Let m(u) = 63*u**2 - 108*u + 18. Let p(k) = k**2 - 1. Let j(s) = -131*s**2 + 217*s - 32. Let b(w) = -j(w) - 4*p(w). Let c(v) = -3*b(v) + 5*m(v). Factor c(i).
-3*(2*i - 3)*(11*i - 2)
Suppose 110*a**3 + 220*a**2 + 35/3*a**4 - 650/3*a - 125 = 0. Calculate a.
-5, -3/7, 1
Suppose 0 = -3*k + 3*n - 3, 3*n = -k - n - 11. Let o(f) = f**2 + f - 4. Let i be o(k). Determine q, given that 7*q - i*q**3 + 0*q + q + 2*q**4 - 4*q**3 = 0.
-1, 0, 2
Let c = 12 - 82/7. Suppose -9*b - r + 16 = 0, 127 - 125 = -b - 2*r. Factor -18/7*j**4 + c*j**5 + 60/7*j**3 - 92/7*j**b - 18/7 + 66/7*j.
2*(j - 3)**2*(j - 1)**3/7
Let r(s) = 2*s**2 + s + 3. Let j be r(-3). Let b be 1 - (j/(-9) - (-16)/6). Factor -2/3*c**3 - b*c + c**2 + 0.
-c*(c - 1)*(2*c - 1)/3
Suppose q - 4 = -3*a, 6*a + 4*q = 3*a - 2. Find c, given that -2/3*c**a + 10/3*c - 2 - 2/3*c**3 = 0.
-3, 1
Let 0 + 1/2*b**2 + 0*b**4 + 0*b - 1/4*b**5 + 3/4*b**3 = 0. What is b?
-1, 0, 2
Let s(h) = -30*h + 3. Let b be s(-1). Factor -b*n + 4*n**3 - 3*n**3 + 18*n + 10 + 4*n**3.
5*(n - 1)**2*(n + 2)
Suppose 0 + 1/7*f**3 - 10/7*f**2 - 11/7*f = 0. What is f?
-1, 0, 11
Let i(x) = 13*x + 5*x - x**2 - 14 - 9*x + 0*x**2. Let a be i(7). Factor 0*s**3 + 0*s + a*s**4 + 0*s**2 + 2/3*s**5 + 0.
2*s**5/3
Find g, given that -81*g**2 - 81*g - 3/4*g**5 + 0 + 6*g**4 + 27/4*g**3 = 0.
-3, -1, 0, 6
Let o be 1 - 0/2 - (-10 - 7). Let r = 18 - o. Find t such that 2/7*t + r - 5/7*t**2 + 4/7*t**3 - 1/7*t**4 = 0.
0, 1, 2
Let z = -63/4 + 331/20. Find s such that -2/5 - 6/5*s**4 + z*s**5 - 4/5*s**3 + 0*s + 8/5*s**2 = 0.
-1, -1/2, 1
Let m = 70155/140314 + 1/70157. Factor 1/4*v**3 + 0 + m*v - 3/4*v**2.
v*(v - 2)*(v - 1)/4
Determine u so that 0*u + 0 - 1/4*u**5 - 50*u**2 - 11/2*u**4 - 35*u**3 = 0.
-10, -2, 0
Let i(u) = 7*u + 31. Let f be i(-4). Suppose 6 + 0 = f*y. Factor -4/3*n + y*n**2 + 0 - 2/3*n**4 + 0*n**3.
-2*n*(n - 1)**2*(n + 2)/3
Let a be (200/5)/(2 - 230/122). Let k = -348 + a. Factor 2/7*p**2 + 2/7*p**3 + 0*p - k*p**4 + 0.
-2*p**2*(p - 1)*(2*p + 1)/7
Factor 0 - 2/7*w**4 - 10/7*w - 6/7*w**3 + 18/7*w**2.
-2*w*(w - 1)**2*(w + 5)/7
Suppose -20*z - 50 + 23*z**2 + 21*z**2 - 46*z**2 = 0. Calculate z.
-5
Let i(g) be the third derivative of g**8/168 + 12*g**7/35 + 27*g**6/5 + 107*g**2. Factor i(x).
2*x**3*(x + 18)**2
Let v be (-174)/(-36) + (-9)/(-18). Factor 4/3*d**3 + v*d - 16/3*d**2 + 0.
4*d*(d - 2)**2/3
Let -4*t**2 + 1/2*t**3 + 15/2*t + 0 = 0. Calculate t.
0, 3, 5
Let v(n) be the second derivative of -3*n + 1/210*n**5 - 1/420*n**6 + 0*n**3 + 0 + 0*n**4 + 1/2*n**2. Let d(b) be the first derivative of v(b). Factor d(l).
-2*l**2*(l - 1)/7
Let o(a) = 44*a**4 - 54*a**3 - 162*a**2 + 486*a + 26. Let c(g) = -5*g**4 + 6*g**3 + 18*g**2 - 54*g - 3. Let i(h) = 52*c(h) + 6*o(h). Factor i(d).
4*d*(d - 3)**2*(d + 3)
Let y = 8 - -5. Factor y*r**2 - 3*r**3 + 6*r**2 - 25*r**2.
-3*r**2*(r + 2)
Suppose 18 = 6*h - 12. Let m(s) = -3*s**4 + 2*s**3 - 7*s**2. Let g(r) = -7*r**4 + 3*r**3 - 15*r**2 - r. Let u(w) = h*m(w) - 2*g(w). Solve u(p) = 0 for p.
0, 1, 2
Let s(y) be the second derivative of 0 + 0*y**3 + 0*y**5 + 3/2*y**2 - 1/6*y**4 + 4*y + 1/120*y**6. Let a(x) be the first derivative of s(x). Factor a(d).
d*(d - 2)*(d + 2)
Suppose -3*i + 2*h - 6 = -23, 4*i + 2*h = 4. What is n in -9/2*n**i + 3/2*n**5 + 0 + 3*n - 3/2*n**4 + 3/2*n**2 = 0?
-1, 0, 1, 2
Let m(c) = -5*c + 75. Let x be m(15). Suppose -6*z + 26 - 14 = x. Factor 0*u + 3/5 - 3/5*u**z.
-3*(u - 1)*(u + 1)/5
Let n(w) = 5*w**4 - 7*w**3 - 3*w**2 - w + 2. Let l(t) = -11*t**4 + 15*t**3 + 7*t**2 + 3*t - 5. Let q(h) = -4*l(h) - 9*n(h). Suppose q(a) = 0. What is a?
-1, 1, 2
Let u = 97654 - 879820/9. Let a = u + 104. Factor 4/9*t**2 + 0*t + 0 + a*t**3.
2*t**2*(t + 2)/9
Let t(d) = 7*d**2 + 7*d + 4. Let x = 62 - 61. Let f(i) = -i**2 - i - 1. Let z(b) = x*t(b) + 4*f(b). Factor z(p).
3*p*(p + 1)
Let f(b) be the second derivative of -b**5/30 - 3*b**4/2 - 26*b**3/9 + b + 239. Factor f(u).
-2*u*(u + 1)*(u + 26)/3
Let s(c) be the third derivative of -c**9/15120 + c**8/5040 + c**7/630 - 19*c**5/60 - 6*c**2. Let l(q) be the third derivative of s(q). Factor l(t).
-4*t*(t - 2)*(t + 1)
Suppose -2*l = 3*h - 18, 2*l = -0*h + h + 2. Let l*k**2 - 6*k**2 - 16*k + 4*k = 0. What is k?
-4, 0
Let v(j) = 11*j**2 - 1056*j. Let m be v(96). Find i, given that 3/8*i + m - 3/8*i**2 = 0.
0, 1
Determine k so that 14 - k**2 + 110*k + 81 + 16 = 0.
-1, 111
Let d(s) be the second derivative of 2/9*s**3 + 1/72*s**4 + 0 + 19*s + 1/3*s**2 - 1/40*s**5. Factor d(w).
-(w - 2)*(w + 1)*(3*w + 2)/6
Suppose 15 = -2*s + 7*s. Let a be (0 - s)*(-2 - -1). Determine g, given that g**4 + 2*g**4 - 18*g**5 + 6*g**a + 15*g**5 = 0.
-1, 0, 2
Let c(l) = -l**5 + 19*l**4 - 35*l**3 + 7*l**2 + 5. Let k(p) = p**4 - 2*p**3 - p**2 + 1. Let n(r) = -c(r) + 5*k(r). Factor n(j).
j**2*(j - 12)*(j - 1)**2
Let z = -17 + 31. Suppose 2*y + z - 46 = 0. Let 14*s**2 + 4 + 6*s**4 - y*s**3 - 9 - 4*s + 5 = 0. What is s?
0, 2/3, 1
Determine i, given that 22 - 14*i - 26 + 16 + i**2 + 24 - i = 0.
3, 12
Suppose -2*z + 396 = 2*z. Determine h so that 4 - 5 + 97*h - z*h - h**2 = 0.
-1
Let p be (-2)/(((-3)/(-2 + -1))/(-1)). Factor -161*o**p + 82*o**2 - 24*o + 21 + 82*o**2.
3*(o - 7)*(o - 1)
Let l = -20/17 + 57/34. Let i = 29/68 - 3/17. Suppose 1/4*v**2 - i*v - l = 0. Calculate v.
-1, 2
Suppose 3*k + 4*q = 924, -3*k + q + 1563 = 2*k. Suppose -4*b - k = -5*w + w, 3*b = -4*w + 291. Let -75*x + w*x - 2*x**2 - 2*x**2 = 0. Calculate x.
0
Factor 156/11*y - 6/11*y**2 + 0.
-6*y*(y - 26)/11
Let s(b) = -b**2 + 3. Let v be s(0). Let x(d) = -43*d**2 - 4*d**2 + 11*d**2 + 15*d - d + 22*d**v. Let k(y) = y**3 - y. Let a(t) = 6*k(t) + x(t). Factor a(u).
4*u*(u - 1)*(7*u - 2)
Let t = 30 + -3. Factor -t*n**4 + 3*n**5 + 8*n**3 - 3*n**2 - 15*n**5 - 26*n**3.
-3*n**2*(n + 1)**2*(4*n + 1)
Let f(m) be the first derivative of -7*m**6/6 - 16*m**5/5 + 13*m**4 + 16*m**3/3 - 69. What is y in f(y) = 0?
-4, -2/7, 0, 2
Let r be 4 - ((-182)/(-56) + (-3)/(-4)). Factor 1/4*b**2 + 0*b + r + 1/8*b**3.
b**2*(b + 2)/8
Let w(j) be the third derivative of 5*j**2 + 3/40*j**5 + 0 + 0*j + 1/16*j**4 + 1/70*j**7 - 1/16*j**6 - 1/4*j**3. Factor w(o).
3*(o - 1)**3*(2*o + 1)/2
Let u(w) be the third derivative of -w**5/180 - 11*w**4/72 + 2*w**3/3 + 105*w**2. Factor u(n).
-(n - 1)*(n + 12)/3
Let -1003*q - 650*q**3 + 328*q + 5*q**5 - 25*q**4 + 58*q**4 - 170 - 1000*q**2 - 183*q**4 = 0. Calculate q.
-1, 34
Let s(b) be the first derivative of 1/120*b**5 - 1/48*b**4 + 8 + 0*b + 0*b**3 + 1/2*b**2. Let c(a) be the second derivative of s(a). Factor c(d).
d*(d - 1)/2
Suppose -4845*h + 3*h**3 + 16 + 4842*h - 24*h**2 + 8 = 0. What is h?
-1, 1, 8
Let t(c) be the second derivative of -1/30*c**4 + 2/15*c**3 + 0 - 5*c - 1/5*c**2. Let t(g) = 0. What is g?
1
Suppose 5*w - 25 = 0, -2*w + 31 = u + 3*w. Suppose 3*r + u*v - v - 4 = 0, 5*r + 2*v = 13. Find h such that 6*h**r - 3*h**5 - 144*h**2 + 3*h**4 + 144*h**2 = 0.
-1, 0, 2
Let k be 4/2 + 18 + -16. Let 