h**2 + 5*h - 2*h + 3*h**2 + 2*h**2 = 0. Calculate h.
-1, 0
Let x be 2 + 1 + 2 + 13. Suppose 13*n + 10 = x*n. Factor 6/11*c**3 + 0 + 4/11*c + 10/11*c**n.
2*c*(c + 1)*(3*c + 2)/11
Let x(o) be the second derivative of -o**7/77 - 107*o**6/165 + 381*o**5/110 - 349*o**4/66 + 26*o**3/11 + o - 220. Determine q so that x(q) = 0.
-39, 0, 1/3, 1, 2
Suppose 42 - 33 = -3*f. Let w(d) = -6*d**2 + d + 1. Let c(b) be the first derivative of 7*b**3/3 + 2. Let k(z) = f*c(z) - 4*w(z). Find v, given that k(v) = 0.
-2/3, 2
Let -32*z + 2*z**2 + 224/3 + 1/3*z**3 = 0. Calculate z.
-14, 4
Suppose 60/7*a**2 - 2/7*a**4 + 250 + 800/7*a - 16/7*a**3 = 0. What is a?
-5, 7
Let p(k) be the third derivative of 7*k**5/20 - k**4/2 - 74*k**2 + 2*k. Factor p(l).
3*l*(7*l - 4)
Let l = -38908/3 - -194546/15. Factor -18/5*u + 4 - l*u**2.
-2*(u - 1)*(u + 10)/5
Suppose -6*i = -7*i + 5. Factor 15*b**4 + 21*b**4 - 4*b**i - 64*b**3 - 4*b**4.
-4*b**3*(b - 4)**2
Let -7 + 32*t**5 + 1 + 18939*t**4 + 18*t**3 - 106*t**2 - 50*t - 18827*t**4 = 0. What is t?
-3, -1, -1/4, 1
Let f(d) be the third derivative of 33*d**2 + 1/60*d**6 - 1/12*d**4 + 1/30*d**5 + 0*d + 0*d**3 + 0 - 1/105*d**7. Solve f(l) = 0.
-1, 0, 1
Let s(b) be the third derivative of b**3 - 1/40*b**6 + 1/5*b**5 + 0 + 0*b - 5/8*b**4 - 3*b**2. Factor s(c).
-3*(c - 2)*(c - 1)**2
Let a be ((-10)/(-4) + 1)/((-1)/(-7)). Let s(f) be the first derivative of -4*f**2 - a*f**4 + 5 + 56/3*f**3 + 0*f. Let s(u) = 0. Calculate u.
0, 2/7
Let f(h) be the third derivative of h**8/420 - h**6/150 - 310*h**2. Factor f(l).
4*l**3*(l - 1)*(l + 1)/5
Let w(t) = -t**3 - 6*t**2 + 37*t + 183. Let h be w(-4). What is a in 1/5*a**5 - 6/5*a**4 - 16/5*a**2 + 9/5*a - 2/5 + 14/5*a**h = 0?
1, 2
Let j(q) = q + 25. Let p be j(-15). Suppose 2*s - p = -a, 3*s - 4 = 2*a + s. Find d, given that -4*d + 6*d**2 + 2 + 6*d**a - 10*d**2 = 0.
1
Suppose -68*g + 25 = -176 - 139. Factor -1/3*s**3 + 0*s + 1/3*s**g + 0 - 2/3*s**2 + 2/3*s**4.
s**2*(s - 1)*(s + 1)*(s + 2)/3
Let d = 1653/5 - 985/3. Let t(g) be the first derivative of 8/5*g + 1/2*g**4 - 6 + d*g**3 + 16/5*g**2. What is l in t(l) = 0?
-2, -1, -2/5
Suppose -4*p - 29 = -3*r, -11 - 10 = -2*r + p. Suppose -r*h + 13*h = 6. Suppose h - 3*x**3 - 6 + 3 - 2*x + 5*x**2 = 0. Calculate x.
0, 2/3, 1
Factor 2/5*c**2 + 6/5*c + 0.
2*c*(c + 3)/5
Let q be 5*5/10*12/10. What is z in z - 8*z**4 + 11*z**3 + z**3 + 4*z**4 - 12*z**2 + q*z = 0?
0, 1
Suppose 0 = -4*t - 2*z - 7 + 19, -5*t - 4*z + 21 = 0. Find m, given that 4 - 3*m**2 + 6*m - 5 + t = 0.
0, 2
Suppose 33*d - 1 = -2*g + 28*d, 2*d = 3*g - 11. Determine o so that -50/9 + 16/3*o**2 + 20/9*o**g + 2/9*o**4 - 20/9*o = 0.
-5, -1, 1
Factor 3*f + 21/2 - 1/6*f**2.
-(f - 21)*(f + 3)/6
Let f(i) be the first derivative of -i**9/12096 - i**8/2240 + i**6/360 + 10*i**3/3 - 26. Let t(h) be the third derivative of f(h). Factor t(x).
-x**2*(x - 1)*(x + 2)**2/4
Let w(t) = -10*t**3 - 2*t**2 - 24*t - 16. Let j(z) = 1 - 2*z + 73*z**2 + z**3 + 3*z - 74*z**2. Let h(o) = -8*j(o) - w(o). Suppose h(l) = 0. What is l?
-2, -1
Let s = -20 - -23. Determine j so that 4*j + 3*j - 6*j + s*j + 4*j**2 = 0.
-1, 0
Let 0*r**2 + 3*r**3 - 3*r**2 + 12*r + 0*r**2 - 30*r = 0. What is r?
-2, 0, 3
Suppose -72*z - 107*z + 358 = 0. Determine t, given that 0*t - 2/7 + 2/7*t**z = 0.
-1, 1
Suppose -15 = 3*u, -2*n - 2*n + 140 = -4*u. Let 216*f + 312*f**2 + n + 24*f + 2 + 144*f**4 - 508*f**3 = 0. Calculate f.
-1/4, -2/9, 2
Let k(a) = a**3 + 6*a**2 - 8*a - 3. Suppose 2*d - 31 = 5*j + d, -41 = 3*j + 5*d. Let i be k(j). Factor 3*u**2 - 12 + 9*u**5 + 12 + 15*u**3 + 21*u**i.
3*u**2*(u + 1)**2*(3*u + 1)
Let x(z) = -4*z**4 + 133*z**3 + 209*z**2 - 250*z - 76. Let q(j) = 10*j**4 - 265*j**3 - 416*j**2 + 499*j + 151. Let v(l) = 4*q(l) + 7*x(l). Solve v(s) = 0 for s.
-2, -1/4, 1, 12
Suppose 0 = -7*r + 3*r + 20. Let v(z) = -12. Let c be (-3)/(-7) - 54/(-21). Let u(y) = -y**2 + 24. Let p(q) = c*u(q) + r*v(q). Suppose p(k) = 0. What is k?
-2, 2
Let r(g) = -90*g**2 + 4*g - 2. Let t be r(1). Let i = t - -90. What is b in -7/2*b**3 + b**i + 7/2*b - 1 = 0?
-1, 2/7, 1
Let y be 0 - (-7 + 4) - 0. Suppose 0*k**2 + 0*k**3 + 3*k**y - 3*k**2 = 0. What is k?
0, 1
Let c be (6 - 15/3) + 3. Factor 15*j**c + 18*j**3 - 5557*j**2 + 5557*j**2 - 3*j**5.
-3*j**3*(j - 6)*(j + 1)
Suppose -25 = 64*s - 69*s. What is m in -5 - 12*m**4 + 6*m**2 + 8*m**s - 2*m**2 + 5 = 0?
-1/2, 0, 1
Let t(j) be the first derivative of -j**3/5 + 9*j**2/10 - 6*j/5 + 287. Let t(n) = 0. What is n?
1, 2
Let j(y) = 10*y**3 - 20*y**2 - 22*y + 8. Let l(n) = -4*n**3 + 8*n**2 + 9*n - 3. Let s(b) = 5*j(b) + 12*l(b). Factor s(o).
2*(o - 2)*(o - 1)*(o + 1)
Suppose b - 19 = 3*z - 0, -b - 2*z + 4 = 0. Let d be 0*2/b + 2. Factor -22*q + 2*q**d - q**2 + 22*q.
q**2
Let a = -98 - -94. Let x be (-6)/(-15)*(1 - a)*1. Suppose 1/6*q**3 + 0*q**x - 1/3 - 1/2*q = 0. Calculate q.
-1, 2
Factor 6*m - 9*m**3 - 4*m**2 - 11*m**3 + 19*m**3 + 6*m.
-m*(m - 2)*(m + 6)
Let q be 0/(4 + (-3 - 3)). Let g(x) be the second derivative of 1/105*x**6 + q*x**2 + x - 1/21*x**3 + 1/14*x**4 + 0 - 3/70*x**5. Solve g(b) = 0.
0, 1
Let z(l) = 7*l**3 + 420*l**2 + 2948*l + 24. Let o(u) = -2*u**3 - 140*u**2 - 983*u - 9. Let a(h) = -8*o(h) - 3*z(h). Factor a(s).
-5*s*(s + 14)**2
Let v(z) be the third derivative of -1/1620*z**6 + 0*z + 0 - 1/180*z**5 - 10*z**2 - 1/54*z**4 + 5/3*z**3. Let f(c) be the first derivative of v(c). Factor f(x).
-2*(x + 1)*(x + 2)/9
Let u(d) = 3*d + 41. Let h be u(-13). Factor 7*s**4 + 13*s**3 - 5*s**4 - 11*s**3 - h*s - 2*s**2.
2*s*(s - 1)*(s + 1)**2
Let v be -2 + 7/4 - 225/(-20). Factor 11 + 3*m**3 + 3*m**2 - v - 6*m + 0.
3*m*(m - 1)*(m + 2)
Let y be -2 + 8 - (-2)/(-2). Suppose 5*l + 4*k = 34, y*l - 1 = 3*k + 26. Factor -6 + h**3 - 2*h**2 + h**3 + l.
2*h**2*(h - 1)
Let c(h) be the second derivative of -h**4/6 - 70*h**3/3 + 3*h + 19. Solve c(l) = 0 for l.
-70, 0
Suppose -27 - 3/2*l**2 - 57/2*l = 0. Calculate l.
-18, -1
Let w be -1 + (-4)/(-4) - (5 + -7). Suppose 0 = s - 2*y - 11, 3*y + 29 = 3*s - 2*y. Suppose -k**s + 7*k + 2*k**w - 7*k = 0. Calculate k.
0, 2
Let z = -23178 - -23180. Solve 0*l + 9/5 - 1/5*l**z = 0.
-3, 3
Let w(o) be the first derivative of -o**3/3 - 5*o**2/2 + 6*o + 79. Factor w(z).
-(z - 1)*(z + 6)
Let f = -21 - -29. Suppose f*i + 12*i**2 - 10*i + 10*i = 0. Calculate i.
-2/3, 0
Let l(u) be the first derivative of -12*u + 10 - 16*u**3 - 6*u**4 - 20*u**2 - 4/5*u**5. Suppose l(w) = 0. What is w?
-3, -1
Let z(k) = k**2 - 7*k + 10. Let q be z(6). Let n(u) be the second derivative of -1/24*u**5 + 0*u**2 - 7/72*u**q + 0 - 2*u - 1/18*u**3. Let n(l) = 0. What is l?
-1, -2/5, 0
Let b be (336/(-49))/(-3) + 2/(-7). Factor 0*y**b + 8*y**4 + 7*y**3 + 7*y**5 + 2*y**2 - 4*y**5.
y**2*(y + 1)**2*(3*y + 2)
Let a be (1*3/(-4))/(12/(-80)). Let u(b) be the first derivative of 3 + 1/3*b**3 + 0*b + 1/2*b**2 - 1/4*b**4 - 1/5*b**a. Factor u(n).
-n*(n - 1)*(n + 1)**2
What is s in 5*s**2 - 5 + 17 + 4*s - 12*s**2 + s**3 = 0?
-1, 2, 6
Let n(j) be the first derivative of -4*j**3/3 + 68*j**2 - 1156*j - 19. Factor n(z).
-4*(z - 17)**2
Suppose 3*f = -0*f, -25 = -5*v - 4*f. Determine t, given that 10*t**2 - 2*t**4 - 8 + 2*t**v + 38*t - 10*t**3 - 13*t - 17*t = 0.
-2, -1, 1, 2
Let v(t) be the third derivative of -t**5/84 + t**4/56 + t**3/21 - 44*t**2. Find g, given that v(g) = 0.
-2/5, 1
Let t(z) be the third derivative of 1/90*z**6 - 1/45*z**5 + 0 + 2/315*z**7 + 0*z - 1/18*z**4 + 0*z**3 + z**2. Suppose t(a) = 0. What is a?
-1, 0, 1
Solve -1/3*l**2 - 12*l - 108 = 0 for l.
-18
Let l(j) = -j**3 - 4*j**2 + 7*j + 12. Suppose 2*p - 25 = k + 7*p, 2*k + 2 = 2*p. Let o be l(k). Suppose -16/7 - 1/7*d**o - 8/7*d = 0. What is d?
-4
Suppose 6*r - 4*r + 4 = -3*d, 5*d = -4*r - 10. Let a = -3153/11 + 287. Solve -2/11*g - a*g**d + 0 = 0.
-1/2, 0
Let t be 3/(-63)*-6 + 60/(-14). Let n(j) = -j**4 + 1. Let m(r) = 10*r**4 + r**2 - 11. Let a(v) = t*m(v) - 44*n(v). Solve a(y) = 0.
-1, 0, 1
Let i(g) be the second derivative of g**4/8 - 3*g**3 + 2*g + 112. Determine t so that i(t) = 0.
0, 12
Let i(o) be the second derivative of -o**5/15 - 23*o**4/9 - 86*o**3/9 - 14*o**2 - 113*o. Suppose i(a) = 0. What is a?
-21, -1
Let x(c) be the first derivative of -c**7/840 - c**6/90 - c**5/30 + 7*c**3/3 + 8. Let o(g) be the third derivative of x(g). Solve o(k) = 0 for k.
-2, 0
Let l = 1