- 2/7*t**3 + p = 0. Calculate t.
-1, 0, 2
Let i(k) be the second derivative of k**6/120 + k**5/20 - k**4/48 - 2*k**3/3 - 3*k**2/2 + k + 113. Find j such that i(j) = 0.
-3, -2, -1, 2
Let v be (12/60*4)/((-2)/(-5)). Factor 18/11 + 12/11*q + 2/11*q**v.
2*(q + 3)**2/11
Let q(n) = 9*n**4 - 2*n**3 - 4*n - 5. Let a(r) = 2*r**4 - r**3 - 1. Let b(w) = 5*a(w) - q(w). Factor b(t).
t*(t - 2)**2*(t + 1)
Suppose h = 4*d + 5*h - 36, 3*d + 3 = 3*h. Find l such that -21*l**4 + 30*l**2 - 8*l - 11*l**2 - d + 6*l**2 + 8*l**3 = 0.
-1, -2/7, 2/3, 1
Let j be (15/(-9))/((-35)/28). Let m(w) be the first derivative of -1/3*w**2 + 2 + 0*w - j*w**3. Factor m(x).
-2*x*(6*x + 1)/3
Factor 0 - 32/3*q + 4*q**3 + 8*q**2 - 4/3*q**4.
-4*q*(q - 4)*(q - 1)*(q + 2)/3
Let q(k) be the first derivative of 4 + 1/1620*k**6 + 1/12*k**4 + 8/3*k**3 + 0*k - 1/90*k**5 + 0*k**2. Let c(v) be the third derivative of q(v). Factor c(h).
2*(h - 3)**2/9
Let p(d) = 20*d**3 - 184*d**2 + 436*d + 16. Let k(a) = -4*a**3 + 37*a**2 - 87*a - 3. Let q(l) = 16*k(l) + 3*p(l). Factor q(h).
-4*h*(h - 7)*(h - 3)
Let h(j) be the third derivative of -1/36*j**4 + 12*j**2 + 0 + 0*j**3 - 1/450*j**5 + 0*j. Factor h(u).
-2*u*(u + 5)/15
Suppose -12*c + 76 = 16. Find p such that -12*p**3 - 2/3*p - c*p**2 - 9*p**4 + 0 = 0.
-2/3, -1/3, 0
Suppose -2*r - 4*w - 80 = 0, -5*r + 0*w = -5*w + 140. Let q be (-1 + -14)/(r/8). Suppose -9/4*a**2 + 3*a**4 - q*a**3 - 3/4 + 15/4*a = 0. What is a?
-1, 1/4, 1
Let q(x) be the third derivative of -5/2*x**4 - 2/5*x**5 - 16/3*x**3 + 0*x + 1/30*x**6 + 0 + 27*x**2. Factor q(h).
4*(h - 8)*(h + 1)**2
Suppose 9*a = 181 - 82. Suppose -4*l + 30 = a*l. Suppose -2/13*c - 2/13*c**3 + 4/13*c**l + 0 = 0. What is c?
0, 1
Solve 10*n**3 + 11*n - 213*n**2 - 121*n + 388*n**2 + 5*n**4 - 80*n**3 = 0 for n.
0, 1, 2, 11
Let x(j) = -5*j**3 - 4*j**2 - 2. Let z(c) = 36*c**3 + 30*c**2 + 15. Let n(s) = 15*x(s) + 2*z(s). Determine h so that n(h) = 0.
0
Let u = 2 + 5. Let t be (3/2)/(-3 + (-35)/(-10)). Find v, given that -u*v**3 + 19*v**t - 12*v**2 - 16*v - 4*v**2 + 3*v**5 + v**5 + 16*v**4 = 0.
-2, -1, 0, 1
Suppose 4*f = -12, -9*g + 5*g = -f + 5. Let b be (0 + g/(-30))/(11/66). Factor 12/5*k - 18/5 - b*k**2.
-2*(k - 3)**2/5
Let d(a) = -a**2 - a + 272. Let z be d(-17). Let v(c) be the first derivative of -3 + 1/3*c**2 + 0*c + z*c**3 - 1/6*c**4. Factor v(o).
-2*o*(o - 1)*(o + 1)/3
Let i = -1852 + 24080/13. Solve i - 4/13*c**2 + 6/13*c - 6/13*c**3 = 0.
-1, -2/3, 1
Let w = 25 - 17. Let c be -2 - 0 - w/(-2). Solve -3/2 + 8*x**3 - 28*x**c + 25/2*x = 0 for x.
1/4, 3
Let m(g) be the first derivative of 20/21*g**3 - 1/6*g**6 + 3/4*g**4 + 0*g + 2/7*g**2 - 2/35*g**5 - 4. Let m(b) = 0. What is b?
-1, -2/7, 0, 2
Factor -116/5*l + 2/15*l**2 + 346/15.
2*(l - 173)*(l - 1)/15
Let s(p) be the third derivative of -1/630*p**7 + 1/60*p**5 + 1/180*p**6 + 0 - 1/18*p**4 + 0*p - 2*p**2 - 2/9*p**3. Let s(f) = 0. Calculate f.
-1, 2
Determine d, given that 3*d**3 + 40 + 75 - 3*d**2 + 32 - 147*d = 0.
-7, 1, 7
Let a(i) be the second derivative of -2/3*i**3 - 3*i + 0 + 5/6*i**4 + 0*i**2 + 3/10*i**5. Factor a(t).
2*t*(t + 2)*(3*t - 1)
Let p be (5/((-90)/24))/(5/(-15)). Let j(l) be the second derivative of -100/3*l**3 + 4*l + 40*l**2 + 125/12*l**p + 0. Solve j(w) = 0 for w.
4/5
Let x(k) be the first derivative of k**7/2100 - k**6/450 + k**5/300 + k**3/3 - 6. Let a(m) be the third derivative of x(m). Factor a(d).
2*d*(d - 1)**2/5
Let w be -2 + -1 - 6/(72/(-44)). Let b be 14/(-6) + (7 - (0 + 3)). Factor 0 + b*d**4 + w*d**3 - 2/3*d - 5/3*d**2.
d*(d - 1)*(d + 1)*(5*d + 2)/3
Let b = -16887 + 16889. Factor -1/6*a**b + 1/2 + 1/3*a.
-(a - 3)*(a + 1)/6
Suppose 68*n - 121 - 15 = 0. Factor -5/4*i**3 - 15/4*i**n - 15/4*i - 5/4.
-5*(i + 1)**3/4
Let a be (23 - (16 - -12))/(-2). Find k, given that -2*k**4 + a*k**5 + k**2 + 1 + 11/2*k - 8*k**3 = 0.
-1, -1/5, 1, 2
Let n(f) = 11 - f**2 + 4*f + 2*f - 2*f. Let c(l) = -l**2 - l + 1. Let d(i) = 2*c(i) - n(i). Let d(u) = 0. Calculate u.
-3
Let x(p) be the third derivative of -p**7/1890 - p**6/1080 + 41*p**5/540 - 37*p**4/72 + 4*p**3/3 + 10*p**2 + 3. Factor x(s).
-(s - 3)**2*(s - 1)*(s + 8)/9
Determine h, given that 9*h**4 - 36*h**2 - 38*h + 5*h**5 - h**5 - h**5 - 6*h**3 + 14*h + 0*h = 0.
-2, -1, 0, 2
Let p(a) = -25*a**3 - 287*a**2 + 17*a. Let d(r) = -9*r**3 - 96*r**2 + 6*r. Let b(w) = -17*d(w) + 6*p(w). Factor b(g).
3*g**2*(g - 30)
Let f(k) be the third derivative of k**5/20 - 7*k**4/8 + 3*k**3 + 3*k**2 - k. Solve f(q) = 0 for q.
1, 6
Let r(g) be the first derivative of 9*g**4/4 + 56*g**3/5 + 21*g**2/2 + 18*g/5 - 81. What is k in r(k) = 0?
-3, -2/5, -1/3
Let v(h) be the first derivative of -2*h**3/15 + 2*h**2 - 42*h/5 + 472. Factor v(s).
-2*(s - 7)*(s - 3)/5
Let x = 0 - -3. Suppose x*a + 3*u - 6 = 0, 4*a = 5*u - u + 32. Let 2*y**5 + 0*y**5 + 4*y**3 + 0*y**3 - 4*y**a - 2*y = 0. Calculate y.
-1, 0, 1
Let q = -12830/11 + 1168. Let w be (-1)/(30/(-4)) - 24/(-495). Determine b so that -32/11 - q*b**2 + 48/11*b + w*b**3 = 0.
1, 4
Suppose -5*t - 2*v + 17 + 1 = 0, v - 8 = -2*t. Factor 0*p**2 - t*p**3 - 8*p**2 + 4*p**2.
-2*p**2*(p + 2)
Suppose -a = a. Let h = 6 + a. Factor 3*d**3 + 5*d**3 + 12*d**2 + 3*d**4 + 3*d**2 + h*d + 4*d**3.
3*d*(d + 1)**2*(d + 2)
Let z(n) = -2*n**2 + 1. Let t(r) = 7*r**2 + 45*r + 40. Let q(v) = t(v) + 2*z(v). Factor q(m).
3*(m + 1)*(m + 14)
Determine w, given that 267*w**3 - 44*w**2 - 62*w - 136*w**3 - 18 - 2*w**4 + 14*w - 147*w**3 = 0.
-3, -1
Let m(t) = -t**3 - t**2. Let i(n) = n + 1. Let j = 22 + -10. Suppose -3*c - j = 5*h - 4*c, -h + c = 0. Let u(z) = h*m(z) - 3*i(z). Factor u(v).
3*(v - 1)*(v + 1)**2
Suppose o - 19 = 4*s, 245*s = 4*o + 241*s - 28. Let j = -40/9 + 494/99. Let -2/11*r**2 + 0*r + j*r**o - 6/11*r**4 + 2/11*r**5 + 0 = 0. Calculate r.
0, 1
Let d(w) be the second derivative of -3*w**5/80 - 5*w**4/4 - 16*w**3 - 96*w**2 - 17*w - 7. Factor d(m).
-3*(m + 4)*(m + 8)**2/4
Let 7/2*m + 3 - 3/2*m**2 + 1/2*m**4 - 3/2*m**3 = 0. Calculate m.
-1, 2, 3
Suppose 0 = 5*w + 109 - 34. Let m be 30/w*2/(-12). Suppose 5/3*l**2 + 0 - m*l = 0. What is l?
0, 1/5
Let z(h) be the first derivative of h**6/2160 + 7*h**5/360 + 49*h**4/144 - 5*h**3 + 9. Let f(d) be the third derivative of z(d). Factor f(t).
(t + 7)**2/6
Let i(o) be the third derivative of o**8/65520 - o**7/4680 + o**6/1560 + o**5/30 - 12*o**2. Let n(r) be the third derivative of i(r). Factor n(c).
2*(c - 3)*(2*c - 1)/13
Let c(g) = 5*g**4 + 23*g**3 - 35*g**2 - 50*g. Let v(y) = -5*y**4 - 22*y**3 + 35*y**2 + 50*y. Let k(i) = 2*c(i) + 3*v(i). Factor k(u).
-5*u*(u - 2)*(u + 1)*(u + 5)
Let j(v) be the third derivative of 0*v - 1/6*v**4 + 1/30*v**5 + 0*v**3 + 0 + 13*v**2 + 1/60*v**6. Factor j(b).
2*b*(b - 1)*(b + 2)
Let y(n) = n**2 + 7*n + 12. Let b be y(-5). Suppose b*v + 0*v = 6. Find i such that 24*i**3 + i - 2*i - 25*i**v + 2*i**2 = 0.
0, 1
Let x(u) be the second derivative of -u**6/3060 - u**5/340 - u**4/102 + u**3/3 + 12*u. Let d(g) be the second derivative of x(g). Factor d(i).
-2*(i + 1)*(i + 2)/17
Factor 1/2*k**4 + 0*k + 1/2*k**3 + 0 - k**2.
k**2*(k - 1)*(k + 2)/2
Let u(h) be the third derivative of -h**5/390 - 7*h**4/156 - 2*h**3/13 + 64*h**2. Find z, given that u(z) = 0.
-6, -1
Let x(j) be the third derivative of 4*j**6/75 + 4*j**5/25 - 9*j**4/4 + 20*j**3/3 + 368*j**2. What is k in x(k) = 0?
-4, 5/4
Let j be -1871*(-1)/30*-6. Let c = -373 - j. Let 2/5*o - 6/5*o**2 - 2/5*o**4 + 0 + c*o**3 = 0. Calculate o.
0, 1
Let u = 79 - 77. Let y be (-1)/(1/(-4)*2). Factor 2/3*w**u - y + 4/3*w.
2*(w - 1)*(w + 3)/3
Let y(v) be the second derivative of v**8/504 + v**7/126 + v**6/90 + v**5/180 + 9*v**2 - 21*v. Let w(u) be the first derivative of y(u). Solve w(a) = 0 for a.
-1, -1/2, 0
Suppose 3*c = -25 - 23. Let l be ((-52)/c - 3)*8. Find s, given that -2/7*s**3 + 2/7*s - 4/7*s**l + 4/7 = 0.
-2, -1, 1
Let d(a) = -a**2 - 12*a + 135. Let c be d(-19). Let z(k) be the second derivative of -8*k - 4/5*k**c + 0 + 0*k**3 + 1/30*k**4. Let z(i) = 0. Calculate i.
-2, 2
Let i(n) = -13*n**4 + 29*n**3 - 6*n**2 - 137*n - 110. Let m(a) = -7*a**4 + 14*a**3 - 3*a**2 - 68*a - 56. Let q(r) = 4*i(r) - 7*m(r). Factor q(f).
-3*(f - 4)**2*(f + 1)**2
Suppose 138/7*d**3 + 2/7*d**4 - 426/7*d**2 + 430/7*d - 144/7 = 0. Calculate d.
-72, 1
Let m be 52/130 + (-7)/30 + (-22)/132. Let m + 20/3*w + 