*b.
3*(b + 1)**2*(b + 2)*(9*b + 2)
Let y = 1430/2163 + 4/721. Determine f so that -y*f + 8/3 - 8/3*f**2 + 2/3*f**3 = 0.
-1, 1, 4
Let z be 19/5 + (-80)/100. Let v(f) be the first derivative of 1/3*f**2 - 1/6*f**4 - 2/9*f**z + 2/3*f - 1. Determine l so that v(l) = 0.
-1, 1
Let n(x) be the third derivative of -2*x**7/35 + x**6/6 - x**5/15 - x**4/6 - 69*x**2 + x. Factor n(l).
-4*l*(l - 1)**2*(3*l + 1)
Let j(g) = g**4 - g**3 - 1. Let c(p) = -6*p**4 + 2*p**3 + 3. Let r(q) = c(q) + 3*j(q). Factor r(x).
-x**3*(3*x + 1)
Let k(j) be the first derivative of -j**2 - 3 + 0*j - 8*j**3 + j**4 - 1/20*j**5. Let h(p) be the second derivative of k(p). Let h(q) = 0. Calculate q.
4
Let t = -6 - -9. Suppose 0 = t*w - 61 + 19. Factor -22*r**3 + 2*r**4 + w*r**3 - 4*r**4 - 8*r**2.
-2*r**2*(r + 2)**2
Let t(k) be the first derivative of -3/4*k**2 + 7/6*k**3 + 0*k - 1/4*k**4 + 23. Factor t(r).
-r*(r - 3)*(2*r - 1)/2
Let -72/7*a**2 + 108/7 - 148/7*a**4 + 356/7*a**3 + 18/7*a**5 - 486/7*a = 0. What is a?
-1, 2/9, 3
Let r(t) be the second derivative of t**4/3 + 14*t**3/3 + 12*t**2 - 77*t - 2. Let r(w) = 0. What is w?
-6, -1
Suppose 5*h - 9 = -0*h - 3*w, 3*h = 3*w + 15. Factor 2/7*a**2 - 10/7*a + 2/7*a**h + 6/7.
2*(a - 1)**2*(a + 3)/7
Let k(c) be the first derivative of 0*c**5 + 7 - 1/2*c**2 + 2/3*c + 1/3*c**4 - 1/18*c**6 - 2/9*c**3. Factor k(o).
-(o - 1)**3*(o + 1)*(o + 2)/3
Let t = -112 + 117. Let i(j) be the second derivative of 6/5*j**5 + 7*j - 3/2*j**2 + 0 + 17/4*j**3 - t*j**4. Factor i(g).
3*(g - 2)*(4*g - 1)**2/2
Suppose -7*h = 1286 - 1300. Let f(a) be the third derivative of 1/15*a**5 - 4*a**h - 2/3*a**3 + 0 + 0*a + 0*a**4. Factor f(k).
4*(k - 1)*(k + 1)
Let v = -10 - -16. Factor 6 - 18*x + v*x**2 + 35*x - 32*x + 0.
3*(x - 2)*(2*x - 1)
Let l be (-20)/(6882/1382 - 5). Let c = 991 - l. Solve -3/7*k**2 - 18/7*k - c = 0 for k.
-3
Let i be -4 - (-54 + 18)/(21/4). Factor -i*d + 2/7*d**2 + 18/7.
2*(d - 9)*(d - 1)/7
Let n(p) = 12*p**3 + 4*p**2 + 16*p - 8. Let b(c) = -136 + 135 + c**2 + c**3 + c - 2*c**2. Let m(f) = 8*b(f) - n(f). What is z in m(z) = 0?
-2, -1, 0
Let i(x) = -2*x**2 + 2*x - 1. Let d(s) = 8*s**2 + 24*s + 42. Let v(h) = d(h) + 2*i(h). Factor v(m).
4*(m + 2)*(m + 5)
Let c(v) = v**2 + v + 1. Let a(q) be the second derivative of -7*q**4/12 - 7*q**3/6 - 2*q**2 - 16*q. Let d(o) = -a(o) - 6*c(o). Factor d(p).
(p - 1)*(p + 2)
Let z be (6/(-4))/(11/(-4) + 2). Let 3*x**5 + 4*x**3 + 9*x**4 + 2*x**3 + 70*x**z - 70*x**2 = 0. Calculate x.
-2, -1, 0
Let q(r) be the second derivative of -r**8/10080 - r**7/1260 + 17*r**4/12 + 8*r. Let k(p) be the third derivative of q(p). Let k(f) = 0. What is f?
-3, 0
Suppose 4*f - 2 = 2*f + 2*a, -7 = -f - 5*a. Factor -4*k**4 - 24*k**3 - 22*k**2 - 4*k**2 - 10*k**f + 0*k**2.
-4*k**2*(k + 3)**2
Let n(q) = 2*q**2 - 4*q + 2. Let i be n(1). Let l(r) be the first derivative of -4/55*r**5 - 1/11*r**2 + 1/33*r**6 + 0*r**4 - 4 + i*r + 4/33*r**3. Factor l(s).
2*s*(s - 1)**3*(s + 1)/11
Factor -3*h**2 + 13*h**4 + 6*h**3 - h**4 - 3*h**4 - 6*h**4 - 6*h**4.
-3*h**2*(h - 1)**2
Let r(u) be the third derivative of -1/240*u**6 - 1/40*u**5 + 0 - 1/24*u**4 - 35*u**2 + 0*u**3 + 0*u. Factor r(t).
-t*(t + 1)*(t + 2)/2
Let h(g) be the second derivative of -g**4/12 - 29*g**3/6 - 14*g**2 - 212*g. Suppose h(p) = 0. Calculate p.
-28, -1
Suppose b - 638 = -4*g - 79, 2*g = -b + 551. Solve -3*w**3 - b*w + 129*w + 72*w**2 + 1536 - 162*w = 0.
8
Let l be (8/10)/((-7)/(385/(-66))). Let x be ((-28)/18)/(4/(-12)). Determine i so that 0 - x*i**3 - 4/3*i**2 - 8/3*i**4 + l*i = 0.
-1, 0, 1/4
Let b be 3/(-18)*-2*6. Factor 2*y - 12 + b - 17*y - 5*y**2.
-5*(y + 1)*(y + 2)
Let w(k) be the second derivative of 3*k**5/160 + 45*k**4/16 + 675*k**3/4 + 10125*k**2/2 - 336*k. Suppose w(c) = 0. Calculate c.
-30
Let m(p) = -22*p + 3. Let t be m(1). Let n = 21 + t. Factor 0*v - 2*v + 17*v**3 - n*v - 13*v**3 - 8 + 8*v**2.
4*(v - 1)*(v + 1)*(v + 2)
Find t, given that 2/17*t**2 - 54/17 + 52/17*t = 0.
-27, 1
Let c be -2*(-3)/(-6) - 5. Let k = c - -8. Suppose -16*b**3 + 2 + 33*b - 23*b**3 + 6*b**3 - 6*b**k + 4 = 0. What is b?
-1, -2/11, 1
Let m(o) be the third derivative of o**5/420 - 51*o**2 + 2. Find u, given that m(u) = 0.
0
Let h = -2409/10 + 241. Let z(g) be the first derivative of -4 - 1/15*g**3 + 0*g + h*g**2. Find b such that z(b) = 0.
0, 1
Let m(b) be the second derivative of 0 + 2/21*b**3 + 2/35*b**5 + 1/7*b**2 + b - 1/6*b**4. Factor m(k).
2*(k - 1)**2*(4*k + 1)/7
Let q(v) be the second derivative of -v**6/6 + v**5 + 290*v. Find o, given that q(o) = 0.
0, 4
Let f = 17 - 14. Let q be (-4)/8*-6*f. What is l in -8*l - q*l - 3*l**3 + 14*l + 6*l**2 = 0?
0, 1
Let t(a) be the first derivative of a**6/6 + 13*a**5/15 - 5*a**4/12 - 5*a**3 - 19*a**2/3 - 8*a/3 + 4. Suppose t(f) = 0. Calculate f.
-4, -1, -1/3, 2
Let k(h) be the third derivative of h**5/6 + 51*h**4/4 - 62*h**3/3 + 721*h**2. Suppose k(b) = 0. What is b?
-31, 2/5
Let y(b) = -25*b**2 + 40*b + 18. Suppose 3*c + 0*w - w = -19, 0 = -4*c + 2*w - 28. Let f(n) = -50*n**2 + 80*n + 35. Let s(g) = c*y(g) + 2*f(g). Factor s(p).
5*(p - 2)*(5*p + 2)
Let i(a) be the second derivative of -a**6/90 - a**5/5 - a**4 - 48*a. Suppose i(f) = 0. Calculate f.
-6, 0
Let s(o) be the third derivative of 0*o - 8/9*o**3 - 1/3*o**4 + 6*o**2 - 1/180*o**6 + 0 - 1/15*o**5. Factor s(x).
-2*(x + 2)**3/3
Let k = 9187 - 9183. Determine y, given that 1/5*y**k + 9/5*y**2 - y**3 + 2/5 - 7/5*y = 0.
1, 2
Let q(k) be the first derivative of k**3 - 105*k**2 + 3675*k - 32. Determine f so that q(f) = 0.
35
Factor -26/3*i + 8 + 2/3*i**2.
2*(i - 12)*(i - 1)/3
Let h(m) = 2*m**3 - 2*m**2 - 2*m - 1. Let d(b) = 22*b + b**3 - 2*b**2 - 12*b - 12*b + b**3. Let o(r) = -6*d(r) + 4*h(r). Determine q so that o(q) = 0.
-1, 1
Solve 17/3 + 1/3*m**2 + 6*m = 0.
-17, -1
Let u be (-28)/(-4) + -939*(-9)/(-1215). Let l(m) be the third derivative of 1/450*m**5 - u*m**3 + 0 - 1/180*m**4 + 0*m - 3*m**2. Factor l(z).
2*(z - 2)*(z + 1)/15
Factor 98/3*n + 50/3*n**3 + 0 - 140/3*n**2.
2*n*(5*n - 7)**2/3
Let u(j) = -7*j**2 - 7*j. Let l(q) = -2*q + 0*q + 4*q**2 - 5*q**2 + q. Suppose h = -3*h - 4. Let s(a) = h*u(a) + 5*l(a). Suppose s(f) = 0. Calculate f.
-1, 0
Let u(d) be the second derivative of -d**9/3024 + d**7/504 + 5*d**4/4 + 24*d. Let w(n) be the third derivative of u(n). Factor w(a).
-5*a**2*(a - 1)*(a + 1)
Let h be ((-1)/2)/(16 + (-390)/24). Factor -10/11*z**h - 4/11*z - 8/11*z**3 - 2/11*z**4 + 0.
-2*z*(z + 1)**2*(z + 2)/11
Let q(h) = h**2 - 13*h - 90. Let s be q(18). Let g(p) be the second derivative of s + 3*p - 1/48*p**4 + 0*p**2 + 0*p**3. Factor g(t).
-t**2/4
Let c(x) = 7*x**3 + 96*x**2 - 144*x + 30. Let u(o) = -o. Let f(i) = -2*c(i) + 22*u(i). Factor f(d).
-2*(d - 1)*(d + 15)*(7*d - 2)
Suppose 12 + 8 = 5*u. Suppose 5*o + 1 = 3*a - 4, o = -u*a + 22. Suppose 0 - 2*h**o + 6*h - 2 - 5 + 3 = 0. Calculate h.
1, 2
Let p(g) be the third derivative of 13/300*g**6 + 2/15*g**3 + 3/50*g**5 + 14*g**2 - 11/525*g**7 + 0*g + 0 - 13/60*g**4. Let p(i) = 0. Calculate i.
-1, 2/11, 1
Suppose 36 + 0 = 11*l - 19. Factor 0*d**4 + 0*d**2 + 0 - 4/19*d**3 + 2/19*d**l + 2/19*d.
2*d*(d - 1)**2*(d + 1)**2/19
Let k(v) be the third derivative of -v**5/15 - 7*v**4/6 - 4*v**3 + v**2 + 33*v. Let k(p) = 0. Calculate p.
-6, -1
Let t = -6 - -12. Suppose 9 = h - 5*k, t*h - h - 19 = -k. Determine d, given that -1/6*d**5 - 1/2*d**h + 0*d + 0 - 1/3*d**3 + 0*d**2 = 0.
-2, -1, 0
Let v(y) = 2*y**2 - 39*y - 18. Let f be v(20). Suppose -f*k**2 + 6 - 2*k + 2*k - k**2 + 3*k = 0. What is k?
-1, 2
Let m(v) = v**3. Let d(z) = 12*z**3 - 28*z**2 + 44*z - 20. Let p(j) = -d(j) + 8*m(j). Factor p(w).
-4*(w - 5)*(w - 1)**2
Suppose 4*r + 2 = 10. What is s in 38*s**4 - 5*s**2 + 0*s**3 + 3*s**3 - 5*s + r*s**3 - 33*s**4 = 0?
-1, 0, 1
What is r in -169/5*r + 7/10*r**2 + 48/5 = 0?
2/7, 48
Suppose -2*v + 184 = -6*v - 3*a, -5*v = -2*a + 207. Let i = v + 130/3. Solve -i*r**4 + 0 + 0*r - 2/3*r**2 + r**3 = 0.
0, 1, 2
Let u(v) be the third derivative of v**8/504 - v**7/105 + v**6/60 - v**5/90 + 7*v**2 - v. Determine q, given that u(q) = 0.
0, 1
Let -67*f + 92 + 272*f + 42*f**3 - 37*f**3 + 158 + 260*f**2 + 300*f = 0. Calculate f.
-50, -1
Let d be (9/3)/((-3)/(-10)). Suppose 0 = -5*g - 5*b - d, -4*b - 14 = 3*g - 2*g. Factor q**3 + 3*q**2 - 12*q + 2*q**2 - 8*q**2 + g*q**3 +