8
Let i(z) be the third derivative of -z**5/140 - 13*z**4/42 - 17*z**3/42 - 66*z**2. Find k, given that i(k) = 0.
-17, -1/3
Factor -66/5*z + 36 + 6/5*z**2.
6*(z - 6)*(z - 5)/5
Suppose -1639*p = 3*y - 1640*p - 10, -y + 5*p = -22. Factor 0 + 2/9*n**y - 2/9*n.
2*n*(n - 1)/9
Let i = 69 - 67. Let y(a) = -a**5 - 5*a**4 - 3*a**3 + 9*a**2 + a - 1. Let k(t) = -t**3 + t**2 + t - 1. Let z(q) = i*k(q) - 2*y(q). Factor z(d).
2*d**2*(d - 1)*(d + 2)*(d + 4)
Let c = 4 - 2. What is l in 4*l + 5*l**4 - 7*l**4 - 4*l + c*l**5 = 0?
0, 1
Let l(v) be the first derivative of v**6/24 + 3*v**5/10 + v**4/4 - 2*v**3 - 4*v**2 - 468. Factor l(d).
d*(d - 2)*(d + 2)**2*(d + 4)/4
Let m = 11 - 1. Determine h, given that -m*h + 11*h - 3*h - 2*h**2 = 0.
-1, 0
Let f be (5/3)/((-15)/(-45)). Find t, given that -10*t**4 - 4*t**5 + 75*t**3 - 70*t**3 - 11*t**f = 0.
-1, 0, 1/3
Suppose -9/4*d + 5 - 1/8*d**2 = 0. What is d?
-20, 2
Let a = 16042/18027 - 2/2003. Determine k so that 4/9*k + 4/9*k**5 + 0 - a*k**3 + 0*k**2 + 0*k**4 = 0.
-1, 0, 1
Let p(n) be the second derivative of -n**6/195 - n**5/130 + 2*n**4/13 + 12*n + 12. Factor p(v).
-2*v**2*(v - 3)*(v + 4)/13
Let f = 21/139 - 9767/2085. Let b = f + 26/5. Let 0 + b*s**2 - 2/3*s = 0. What is s?
0, 1
Let k(m) be the first derivative of -6 + 2/3*m + 2/9*m**3 - 2/3*m**2. Factor k(y).
2*(y - 1)**2/3
Suppose 4/3*d**5 - 20*d**4 - 542/3*d**2 + 99*d**3 + 116*d - 24 = 0. What is d?
1/2, 2, 6
Let y(r) be the second derivative of -r**6/360 + r**5/40 - r**4/12 - 5*r**3/6 + 2*r. Let b(m) be the second derivative of y(m). Determine n so that b(n) = 0.
1, 2
Let f(x) = -x + 13. Let g be f(8). Find m such that -246*m**3 + 2*m + 216*m**4 + 12 - 48*m**g + 70*m + 15*m**2 - 21*m**3 = 0.
-1/4, 1, 2
Let c be (12/(-390))/((-4)/40). Let i = 11706/13 - 900. Solve 4/13 - c*l**2 + i*l = 0 for l.
-1/2, 2
Let k = -50 - -49. Let f(c) = c + 1. Let w(y) = y**2 - 20*y + 43. Let h(s) = k*w(s) - 6*f(s). What is b in h(b) = 0?
7
Let g(n) = -n**2 - 2*n + 2. Suppose -v = -9*v. Let m be g(v). Let -10/9*k + 4/9 + 4/9*k**m = 0. Calculate k.
1/2, 2
Let r(q) = -3*q**3 + 15*q**2 + 18*q - 6. Let h(s) = -5*s**3 + 31*s**2 + 36*s - 11. Let g(c) = -6*h(c) + 11*r(c). Factor g(l).
-3*l*(l + 1)*(l + 6)
Let t be (-70)/(-35) + (12*(-2)/(-21))/(-1). Factor 6/7*p**3 + 0 - 2/7*p**4 + 2/7*p - t*p**2.
-2*p*(p - 1)**3/7
Factor 1/2*t**5 + 1/2*t**3 + 0*t + 0 + t**4 + 0*t**2.
t**3*(t + 1)**2/2
Let r = -801 - -80101/100. Let g(i) be the third derivative of -1/525*i**7 + r*i**6 + 0*i**4 + 0*i**3 - 1/75*i**5 - 6*i**2 + 0 + 0*i. Let g(y) = 0. What is y?
0, 1, 2
Let t be 8 + 44/28*119/(-34). Factor -5/2*q - t*q**2 + 0.
-5*q*(q + 1)/2
Factor -4/7*i**2 - 2/7*i + 2/7*i**3 + 4/7.
2*(i - 2)*(i - 1)*(i + 1)/7
Let s(x) be the first derivative of -x**4 + 15*x**3 - 11*x**2/2 - 390. Factor s(n).
-n*(n - 11)*(4*n - 1)
Let l(b) = -57*b - 40. Let i be l(-2). Let d = -71 + i. Factor 0 + 0*v**2 + 2/5*v - 2/5*v**d.
-2*v*(v - 1)*(v + 1)/5
Let w(q) be the second derivative of 5*q - 1/42*q**4 + 1/7*q**2 + 0 + 0*q**3. Determine t, given that w(t) = 0.
-1, 1
Let l be (55/88)/(2/(-12) + 18/18). Factor 1/4 + 5/4*n - 9/4*n**3 + l*n**2.
-(n - 1)*(3*n + 1)**2/4
Let n(t) be the third derivative of -t**7/210 - t**6/30 + 7*t**5/20 - t**4/6 - 14*t**3/3 + 116*t**2. Factor n(a).
-(a - 2)**2*(a + 1)*(a + 7)
Let l(p) be the first derivative of -17*p**5/5 - 9*p**4 + 44*p**3 + 8*p**2 + 248. Factor l(c).
-c*(c - 2)*(c + 4)*(17*c + 2)
Let w be 749/321*12/(-14)*12/(-27). Factor 0 + w*n**4 - 10/9*n**3 + 2/9*n**2 + 0*n.
2*n**2*(n - 1)*(4*n - 1)/9
Let v be ((-52)/(-12) + -1)*-3. Let r be (-5)/v*(0/3)/2. Factor -2/11*f**5 - 2/11*f**2 + 2/11*f**3 + 2/11*f**4 + 0 + r*f.
-2*f**2*(f - 1)**2*(f + 1)/11
Let b = 113 - 102. What is v in 11*v**3 - 37*v**3 + b*v**3 + 18*v**3 - 12*v = 0?
-2, 0, 2
Let d(p) = -210*p + 1473. Let c be d(7). Let 0*j + 0 + 4/9*j**2 - 2/9*j**c = 0. What is j?
0, 2
Suppose -4*f - 2 - 10 = -2*y, 5*y = 4*f + 6. Let n be f/24 - 663/(-90). Suppose -2/5 - n*r**3 - 8/5*r**2 + 12/5*r + 24/5*r**5 + 2*r**4 = 0. What is r?
-1, 1/4, 1/3, 1
Let n(c) = 3*c - 24. Let t be n(8). Let p(j) be the second derivative of -21/40*j**5 + 2*j + 5/8*j**4 + t + 1/2*j**3 + 0*j**2. Factor p(i).
-3*i*(i - 1)*(7*i + 2)/2
Let b(m) = 3*m**2 - 35*m - 38. Let j(d) = 35*d**2 - 420*d - 455. Let k be (0 + -25)/(1/(4/4)). Let p(q) = k*b(q) + 2*j(q). Let p(i) = 0. What is i?
-1, 8
Factor -45/4*t**2 - 39/4 - 81/4*t - 3/4*t**3.
-3*(t + 1)**2*(t + 13)/4
Let y(i) = -i**2 + i. Let m(p) = -73*p**2 + 42*p**2 + 37*p**2 - 3*p. Let b(l) = -2*m(l) - 10*y(l). Suppose b(r) = 0. Calculate r.
-2, 0
Let d(q) be the second derivative of q**7/15120 + 7*q**6/4320 + q**5/120 - 7*q**4/2 + 35*q. Let m(k) be the third derivative of d(k). Factor m(l).
(l + 1)*(l + 6)/6
Let n(h) = 4*h**3 - 20*h**2 - 64*h - 40. Let m(r) = -10*r**3 + 60*r**2 + 190*r + 120. Let p(d) = 3*m(d) + 8*n(d). Determine b so that p(b) = 0.
-5, -4, -1
Suppose 8 = 4*n - 0, q - 7 = -2*n. Let a be (1 - 0) + (4 - 258/54). Factor -4/9*p - a*p**5 - 2*p**q + 10/9*p**4 + 0 + 14/9*p**2.
-2*p*(p - 2)*(p - 1)**3/9
Let x(o) be the third derivative of o**5/15 - o**4/6 - 4*o**3 + 6*o**2 + 2*o. Factor x(a).
4*(a - 3)*(a + 2)
Let l(j) = j**4 - j**2 + j + 1. Let q(w) = -7*w**4 + 2*w**3 + 6*w**2 - 8*w - 5. Let f(k) = 6*l(k) + q(k). Determine z, given that f(z) = 0.
-1, 1
Let z(t) be the third derivative of -t**5/75 + 14*t**4/15 - 392*t**3/15 + 17*t**2 - 2. What is w in z(w) = 0?
14
Let h(v) be the first derivative of v**5/36 - 5*v**4/12 + 23*v**2/2 + 36. Let a(k) be the second derivative of h(k). Factor a(x).
5*x*(x - 6)/3
Let m(x) = -x - 1 - x**2 - 3*x**3 + 2*x**3 + 0 + 0*x**3. Let v(z) = 8*z**3 + 4*z**2 + 6*z + 6. Let h(i) = 6*m(i) + v(i). Factor h(l).
2*l**2*(l - 1)
Let l be 6/20*85/204. Let j(o) be the first derivative of -l*o**2 + 10 - 5/8*o**4 - 13/24*o**3 + 0*o. What is s in j(s) = 0?
-2/5, -1/4, 0
Let f(y) = 9*y**2 - 33*y - 58. Let l be f(5). Solve 0 + 0*x**4 + 1/7*x**5 + 0*x**l + 4/7*x - 5/7*x**3 = 0.
-2, -1, 0, 1, 2
Solve 35*b - 9/2*b**3 - 57 + 27/4*b**2 - 1/4*b**4 = 0.
-19, -3, 2
Let l(p) be the first derivative of 5*p**3/3 + 25*p**2 + 120*p + 196. What is i in l(i) = 0?
-6, -4
Let c be -8 - -4 - (-63)/7. Suppose -c*q - 4*j = 7 - 13, 4*q - 4*j - 12 = 0. Solve -3/5*l**q + 6/5*l - 3/5 = 0.
1
Let g = -85 - -142. Find i, given that 7*i - 45 - g + 38 + 25*i - 4*i**2 = 0.
4
Let p = 259/1180 - -9/295. Factor 0*m + 0 + p*m**2.
m**2/4
Find s, given that 288 + 78*s - 1/2*s**3 + 2*s**2 = 0.
-6, 16
Let w(m) be the first derivative of -2*m**3/3 + m**2 + 40*m + 231. Suppose w(v) = 0. Calculate v.
-4, 5
Suppose -3*h = 75*c - 78*c + 12, 0 = -2*h + 4*c - 16. Determine q, given that h*q + 0*q**3 - 2/5*q**4 + 4/5*q**2 - 2/5 = 0.
-1, 1
Let g(s) = 6*s**5 - 2*s**4 - 7*s**3 + 3*s**2 + 8*s - 8. Let r(j) = j**5 - j**3 - j**2 + 3*j - 2. Let a(f) = -g(f) + 5*r(f). Factor a(x).
-(x - 1)**4*(x + 2)
Let a be (-3)/((-132)/(-11)) - (-3)/4. Let o(y) be the third derivative of 0*y + 1/20*y**5 + a*y**4 + 0 + 2*y**3 + 5*y**2. Let o(u) = 0. Calculate u.
-2
Suppose -36 = 34*p - 33*p - 4*p. Factor -27*k**2 - 3/2*k**4 - 15/2 + p*k**3 + 24*k.
-3*(k - 5)*(k - 1)**3/2
Let 5110*d + 3*d**3 - 5118*d + d**3 + 12*d**2 - 12*d**4 + 4*d**5 = 0. Calculate d.
-1, 0, 1, 2
Let m(v) = v**3 - 9*v**2 + 6. Let l(a) = -60 + 34 + 31 + 3*a**2 - 13*a**2. Let b(d) = -6*l(d) + 5*m(d). Factor b(j).
5*j**2*(j + 3)
Let u be 0 + (-22)/(-18) + 72/(-324). Let r be u/(-3) + ((-66)/(-90))/1. Let 0*v + 2/5 - r*v**2 = 0. Calculate v.
-1, 1
Suppose -3*t - 4*q = -192, 0*t + 3*q - 59 = -t. Let f be ((-2)/(-6))/((t/(-24))/(-17)). Solve -1/3*r + 0 + r**f = 0 for r.
0, 1/3
Let i = 2824/669 + 2/2007. Determine n, given that -14/9*n**5 - 2/9*n**3 + 16/9*n - 46/9*n**2 + 8/9 + i*n**4 = 0.
-1, -2/7, 1, 2
Let s(b) be the second derivative of b**7/28 - b**6/4 + 27*b**5/40 - 7*b**4/8 + b**3/2 - 42*b. Solve s(i) = 0.
0, 1, 2
Let r(n) be the second derivative of -n**5/90 + n**3/27 + 51*n. What is m in r(m) = 0?
-1, 0, 1
Let y be -48 - -31 - (-122)/6. Solve -5*t**4 + 0 + 10/3*t + 5*t**2 - y*t**3 = 0.
-1, -2/3, 0, 1
Find n, given that -125/2*n**4 - 90 + 25*n**3 - 30*n + 295/2*n**2 = 0.
-1, 6/5
Let t(o) be the third derivative of 17*o**6/180 - o**5/90 - o**4/2 + 766*o**2. Factor t(u).
2*u*(u + 1)*(17*u - 18)/3
Suppose 3