(d + 1)*(d + 3)
Let a = 2468 - 177703/72. Let s = 1/8 - a. Find k, given that -2/9*k**3 + 2/9*k**2 - 2/9 + s*k = 0.
-1, 1
Let o(t) = -4*t - 28. Let y be 4 - 14 - 3/1*-1. Let d be o(y). Solve 2/3*v**3 + 0 - 2/3*v + d*v**2 = 0.
-1, 0, 1
What is o in 1/2*o**2 + 15 + 13/2*o = 0?
-10, -3
Suppose -84*a + 283 - 115 = 0. Factor -2/3*p**a + 8/9 - 4/9*p**3 + 8/9*p + 2/9*p**4.
2*(p - 2)**2*(p + 1)**2/9
Let u(x) = x**3 + 11*x**2 + 4*x + 3. Let w(h) = 8*h**3 + 76*h**2 + 28*h + 20. Let o(f) = -f + 11. Let q be o(8). Let r(z) = q*w(z) - 20*u(z). Factor r(d).
4*d*(d + 1)**2
Let b(r) be the third derivative of -1/30*r**5 + 0*r + 1/108*r**4 + 3*r**2 - 4/945*r**7 + 11/540*r**6 + 0 + 1/27*r**3. Find q, given that b(q) = 0.
-1/4, 1
Let a be (-1)/(-3)*-1 + (-940 - -942). Factor 0 - 2*h - 1/3*h**3 + a*h**2.
-h*(h - 3)*(h - 2)/3
Let g(l) be the second derivative of l**4/30 - 86*l**3/5 + 16641*l**2/5 - 5*l - 21. Factor g(z).
2*(z - 129)**2/5
Factor 19/4*r**2 + 41/4*r + 21/4 - 1/4*r**3.
-(r - 21)*(r + 1)**2/4
Let o(l) = 15*l**2 - 136*l. Let c(s) = 5*s**2 - 46*s. Let w(f) = -8*c(f) + 3*o(f). Factor w(h).
5*h*(h - 8)
Let c(k) be the first derivative of -k**6/180 + 2*k**5/15 - 7*k**4/12 - 6*k**3 - 50. Let l(w) be the third derivative of c(w). Factor l(f).
-2*(f - 7)*(f - 1)
Suppose 5*j + 12 = -z, -5*z + 8 + 1 = 2*j. Let 3*v**2 - 5*v**z + 0*v**3 - 10*v + 12*v**2 = 0. What is v?
0, 1, 2
Factor 0 + 0*d + 1/8*d**3 - 9/8*d**2.
d**2*(d - 9)/8
Let r(w) be the second derivative of w**7/147 + w**6/35 + 2*w + 117. Suppose r(k) = 0. Calculate k.
-3, 0
Let a = 55 - 54. Let c be a/(-3) - 4/((-60)/35). Find w, given that -3/2 + 3/2*w**c + 0*w = 0.
-1, 1
Let n = -1 + 5. Suppose n*v = 41 - 9. Let -v*k + k + 5*k**3 + 2*k = 0. Calculate k.
-1, 0, 1
Let i(l) = -l**3 + l**2 + l + 5. Let o(t) = 30 - 4*t**3 + 27*t - 22*t - t**3 + 5*t**2 + 0*t**2. Let v(r) = -35*i(r) + 6*o(r). Let v(d) = 0. What is d?
-1, 1
Let p(q) be the third derivative of q**6/6 + 71*q**5/5 + 62*q**4/3 - 56*q**3 + 4*q**2 - 32. Let p(l) = 0. What is l?
-42, -1, 2/5
Suppose 3*x + 6 = 15. Factor -33*f**2 - 5*f - 5*f**3 + 13*f**2 + 3*f**x - 18*f**3.
-5*f*(2*f + 1)**2
Let r(k) = k**2 - 3*k. Let u be r(3). Suppose u = -2*q + 2*x + x + 21, -q = -4*x - 23. Factor 9*l**2 + 10*l**3 - 7*l**q + 0*l + 6*l.
3*l*(l + 1)*(l + 2)
Find p such that -11 + 12*p + 21*p**2 + 2*p**2 - 5 - 19*p**2 = 0.
-4, 1
Solve 6*l**3 - 78/7*l**2 + 38/7*l + 0 - 2/7*l**4 = 0 for l.
0, 1, 19
Let r = -35 + 38. Let s(w) = -w**3 - w**2 - 1. Let l(o) = 3*o**3 + 7*o**2 + 4. Let a(d) = r*l(d) + 12*s(d). Factor a(c).
-3*c**2*(c - 3)
Let d = -83 - -158. Suppose -5*n - d = f - 6*f, -f = 3*n + 5. Solve -5*t**3 - 12/5*t**4 - 8/5 + f*t**2 - 12/5*t + 7/5*t**5 = 0.
-2, -2/7, 1, 2
Factor 152/3*r**2 - 4/9*r**3 + 219488/9 - 5776/3*r.
-4*(r - 38)**3/9
Suppose 12 = n + 21. Let h be ((-12)/n)/(3*2/18). Find r, given that 10*r**h + r**2 + 0 + 9/2*r**5 + 0*r + 13/2*r**3 = 0.
-1, -2/9, 0
Let m be -6 + (((-69)/(-42))/1 - -5). Let q(k) be the first derivative of -1/7*k**3 - m*k**2 - 6/7*k + 7. Let q(b) = 0. Calculate b.
-2, -1
Let w be (3/2)/((-24)/(-80)). Find t such that -w*t**2 - 4*t + 18*t**3 - 19*t**3 + t**2 = 0.
-2, 0
What is v in 0 + 2/3*v**3 - 2/3*v - 1/3*v**2 + 1/3*v**4 = 0?
-2, -1, 0, 1
Let c be (-93)/15 - -4 - (-1 - 2). Suppose -2*v - 4 = -0*v - 5*q, -v = 3*q - 9. What is p in 0*p + 0 - 4/5*p**v + c*p**2 = 0?
0, 1
Let l(h) be the second derivative of -h**4/78 - 3*h**3/13 + 10*h**2/13 + 3*h - 83. What is o in l(o) = 0?
-10, 1
Let d = 48 - 34. Let h(r) = -9*r**3 + 24*r**2 - 12*r + 2. Let o(j) = j**3. Let n(p) = d*o(p) - 2*h(p). Solve n(q) = 0.
1/2
Let x(u) be the third derivative of -u**8/1008 + u**7/210 - u**6/270 + u**3 + 3*u**2. Let b(l) be the first derivative of x(l). Suppose b(o) = 0. What is o?
0, 2/5, 2
Let f = -1700 - -5116/3. Solve 16/3 - f*b + 4/3*b**2 = 0 for b.
2
Let j(p) = -4*p + 50. Let d be j(12). Suppose 2*y - 3 = -1, -2*f = -3*y - 9. Factor -f*s**d + 9/2*s + 3/2*s**3 + 0.
3*s*(s - 3)*(s - 1)/2
Let j(l) be the first derivative of -10*l**3 - 26*l - 27*l**2 + 25 - 1/2*l**4. Factor j(t).
-2*(t + 1)**2*(t + 13)
Let v(q) be the second derivative of 0*q**5 + 6*q + 0 + 0*q**3 + 0*q**4 + 0*q**6 - 1/63*q**7 + 0*q**2. Factor v(o).
-2*o**5/3
Let f(x) be the second derivative of 5*x**4/12 - 5*x**3 - 100*x**2 + 2*x + 113. Factor f(l).
5*(l - 10)*(l + 4)
Let j(u) = 7*u**2 - 4*u - 5. Let p(h) = -h + h**2 - h - h**3 + h - 1. Let l(s) = -2*j(s) + 6*p(s). Factor l(n).
-2*(n + 1)**2*(3*n - 2)
Factor 0 + 1/4*j**2 + 7/4*j.
j*(j + 7)/4
Suppose 68*o + 222 = 90*o + 89*o. Factor -5 + 15/2*t - 5/2*t**o.
-5*(t - 2)*(t - 1)/2
Let b = -12268 - -12271. Solve -3/11*j**2 - 3/11*j - 1/11 - 1/11*j**b = 0 for j.
-1
Let m be (-15)/25*10/(-2). Factor 4 - 4*o**2 - 3 + m + 4*o - 4*o**3.
-4*(o - 1)*(o + 1)**2
Let w be ((-18)/20 - -1)*(7 + -5). Factor -1/5*v**2 - 2/5*v - w.
-(v + 1)**2/5
Suppose -8*n = -4*a - 11*n - 3, -4*a + 3*n = -27. Factor 2*c**a + 103*c - 56*c - 51*c + 2*c**2.
2*c*(c - 1)*(c + 2)
Let x(g) = -4*g - 70. Let y be x(-18). Factor -y*k - 4/3*k**3 + 3*k**2 + 1/3.
-(k - 1)**2*(4*k - 1)/3
Let t be 0 - 5 - (-3 - (-18)/(-8)). Suppose 0 = c + n + 5, -c = -2*n - 1 - 9. Factor 1/4 + c*v - t*v**2.
-(v - 1)*(v + 1)/4
Factor -20*i**2 - 8*i - 321668*i**3 + 321670*i**3 + 58*i**2 - 152.
2*(i - 2)*(i + 2)*(i + 19)
Let g = -63 - -69. Let m(t) = -t**3 + 7*t**2 - 6*t + 3. Let h be m(g). Solve -1/3*n**h + 9 - 9*n + 3*n**2 = 0 for n.
3
Let v(c) be the second derivative of -c**5/40 - c**4/6 - c**3/3 + 2*c + 19. Factor v(q).
-q*(q + 2)**2/2
Let x(g) be the third derivative of -g**7/840 + g**6/480 + 7*g**5/240 - g**4/96 - g**3/4 + 60*g**2 - g. Solve x(c) = 0 for c.
-2, -1, 1, 3
Let h = -1976 - -31617/16. Let m(l) be the second derivative of 0 + 0*l**3 - 5/48*l**4 - 11*l + 0*l**2 - h*l**5. Find s such that m(s) = 0.
-1, 0
Let m(n) = -9*n - 48*n**3 - n**2 + 56*n**3 - n**4 + 9 + 10*n**2. Let w(q) = 2*q**3 + 2*q**2 - 2*q + 2. Let l(c) = 4*m(c) - 18*w(c). Solve l(s) = 0.
-1, 0
Suppose 0 = -l + 3*r + 16 - 2, 0 = 2*r + 8. Let s(k) be the first derivative of -3/4*k**4 + 0*k + 0*k**2 + 2 - l*k**3. Factor s(y).
-3*y**2*(y + 2)
Let v(s) = -s**2 + 102*s - 570. Let x(y) = -6*y**2 + 508*y - 2852. Let b(j) = 14*v(j) - 3*x(j). Solve b(r) = 0 for r.
12
Let j(v) be the third derivative of -19/192*v**4 - v**2 - 25*v - 7/24*v**3 + 1/960*v**6 + 0 - 1/120*v**5. Factor j(y).
(y - 7)*(y + 1)*(y + 2)/8
Let c(y) = 29*y**4 - 963*y**3 + 1066*y**2 + 1324*y + 304. Let b(p) = p**4 - 2*p**3 - 2*p**2 + 2. Let r(a) = 4*b(a) - c(a). Factor r(h).
-(h - 37)*(h - 2)*(5*h + 2)**2
Let o(l) be the first derivative of l**4/20 - 4*l**3/15 + 3*l**2/10 + 63. What is v in o(v) = 0?
0, 1, 3
Let q = 1827 + -3651/2. Let 3/2*g**3 + 0 + 3/2*g**2 - q*g - 3/2*g**4 = 0. Calculate g.
-1, 0, 1
Let i be (-1)/36 - (-925)/1332. Factor -2*h + 2/9*h**3 - i*h**2 - 10/9.
2*(h - 5)*(h + 1)**2/9
Let q(b) be the first derivative of b**5 + 15*b**4/2 + 5*b**3/3 - 60*b**2 + 80*b + 62. Factor q(s).
5*(s - 1)**2*(s + 4)**2
Factor -269*y + 16*y**4 + 538*y + 39*y**2 - 265*y + 78*y**3 - 6*y**3 - 6*y**2.
y*(y + 4)*(4*y + 1)**2
Let n(p) be the second derivative of p**5/24 + 59*p**4/36 - 4*p**3/3 + 21*p + 5. Factor n(k).
k*(k + 24)*(5*k - 2)/6
Suppose 0 = -11*c + 41 + 3. Suppose -5*z - c = 4*j - 45, 3*z - 15 = 0. Solve -1/4 - 1/4*y + 1/2*y**3 + 1/2*y**2 - 1/4*y**5 - 1/4*y**j = 0 for y.
-1, 1
Factor 3/4*f**2 - 131/2*f - 44.
(f - 88)*(3*f + 2)/4
Let y(l) be the second derivative of l**5/70 + l**4/7 + l**3/7 - 10*l**2/7 - 36*l. Solve y(h) = 0 for h.
-5, -2, 1
Let o(d) be the third derivative of 4*d**2 - 7/132*d**4 + 0 - 1/165*d**5 + 0*d - 4/33*d**3 + 1/660*d**6. Factor o(y).
2*(y - 4)*(y + 1)**2/11
Determine r, given that -3/2*r**2 + 6 - 6*r + 3/2*r**3 = 0.
-2, 1, 2
Let n(i) = -i**2 - 16*i + 3*i + 12*i. Let w(s) = -4*s**2 + 4. Let x(j) = 8*n(j) - w(j). Solve x(t) = 0.
-1
Factor -2/7*s**3 + 4/7 - 2/7*s**4 + 6/7*s**2 + 10/7*s.
-2*(s - 2)*(s + 1)**3/7
Let v(w) be the second derivative of -1/20*w**5 + 1/12*w**4 + 0*w**2 + 0*w**3 - 6*w + 1/120*w**6 + 0. Factor v(k).
k**2*(k - 2)**2/4
Let n(p) = -12*p**4 - 64*p**3 - 64*p**2 - 24*p - 4. Let w(j) = j**5 + 12*j**4 + 65*j**3 + 63*j**2 + 24*j + 5. Let m(o) = -5*n(o) - 4*w(o). Factor m(k).
-4*k*(k - 6)*(k + 1)**3
Let x(g) be the first derivative