- 13*q(t). Determine v, given that u(v) = 0.
1
Let v(g) be the first derivative of g**6/24 - g**5/10 - g**4/16 + g**3/6 - 3. Factor v(o).
o**2*(o - 2)*(o - 1)*(o + 1)/4
Let a(i) be the first derivative of 3*i**4/20 - 3*i**3/5 + 9*i**2/10 - 3*i/5 + 5. Factor a(o).
3*(o - 1)**3/5
Let y(w) be the second derivative of -w**6/60 + w**4/8 - w**3/6 + 9*w + 3. Determine a, given that y(a) = 0.
-2, 0, 1
Let k(y) be the first derivative of -2/9*y**3 + 0*y**2 + 2/15*y**5 + 0*y + 6 + 0*y**4. Find s such that k(s) = 0.
-1, 0, 1
Let w be 1 + (5 - 1)/2. Find p, given that -8*p**2 - 2*p + 4*p**w + 8*p - 2*p = 0.
0, 1
Let r = 5 + -5. Let d(t) be the second derivative of r + 0*t**3 + 0*t**2 - 1/40*t**6 - 1/168*t**7 - 3*t - 1/48*t**4 - 3/80*t**5. Find s such that d(s) = 0.
-1, 0
Let l be ((-4)/(-5))/(-4 + (-88)/(-20)). Factor 2/3 + 0*u**l - 2/3*u**4 + 4/3*u - 4/3*u**3.
-2*(u - 1)*(u + 1)**3/3
Let t(s) = 8*s**3 + 6*s**2. Let y(z) = z**4 - z**3 - z**2. Let c(d) = -t(d) - 2*y(d). Factor c(g).
-2*g**2*(g + 1)*(g + 2)
Let a = -61 + 62. Let n(l) be the first derivative of 2*l - a + 0*l**2 - 2/3*l**3. Factor n(o).
-2*(o - 1)*(o + 1)
Determine k, given that -8 + 12*k**3 - 93*k + 236*k - 40*k**2 - 107*k = 0.
1/3, 1, 2
Factor -2/15*j**4 + 2/3*j**2 - 2/15*j**5 + 0 + 2/5*j**3 + 4/15*j.
-2*j*(j - 2)*(j + 1)**3/15
Let t(n) be the second derivative of 2/15*n**3 + n + 0*n**2 + 1/50*n**5 + 0 - 1/10*n**4. Factor t(v).
2*v*(v - 2)*(v - 1)/5
Let z(o) be the third derivative of 49*o**6/120 - 35*o**5/12 + 11*o**4/3 - 2*o**3 + 6*o**2. Factor z(c).
(c - 3)*(7*c - 2)**2
Suppose 3*c + 2*c + 729 = -3*z, 242 = -z - 2*c. Let r be (-8)/44 + z/(-396). Let 2/9*m - r*m**2 + 2/9*m**3 + 0 = 0. What is m?
0, 1
Solve 0 + 0*q**2 + 2/5*q - 4/5*q**3 + 2/5*q**5 + 0*q**4 = 0.
-1, 0, 1
Suppose -r + 6 - 3 = 0. Factor -3*f + r*f - 4*f**3 + 2*f**4 + 2*f**2 + 0*f.
2*f**2*(f - 1)**2
Factor 1/2*m - 1/4 - 1/4*m**2.
-(m - 1)**2/4
Let a(j) be the third derivative of -j**8/3360 - j**7/420 - j**6/180 - j**4/8 + 6*j**2. Let l(x) be the second derivative of a(x). Factor l(m).
-2*m*(m + 1)*(m + 2)
Let u be (-1)/4 - (-9)/84. Let c = u - -9/14. Factor -1/2*w**2 + c - 1/2*w + 1/2*w**3.
(w - 1)**2*(w + 1)/2
Suppose -16 = 4*g - 4*r, -5*g - 8 = -3*r + 8. Let x(j) = -8*j**2 + 8*j. Let n(m) = -m**2 + m. Let y(h) = g*x(h) + 14*n(h). What is c in y(c) = 0?
0, 1
Factor 2*i**2 + 14*i**3 - 16*i**3 - 10*i**2 - 12 + 22*i.
-2*(i - 1)**2*(i + 6)
Let u(b) be the third derivative of b**5/120 - b**4/24 - 5*b**2. Let u(o) = 0. Calculate o.
0, 2
Let h be 114/(-18) + 2/6. Let r = 9 + h. Factor 12*b**2 - 6*b**4 - 77*b**r - 44*b**2 - 4*b - 43*b**4.
-b*(b + 1)*(7*b + 2)**2
Let c(a) be the first derivative of 3*a**4/28 + 30*a**3/7 + 450*a**2/7 + 3000*a/7 - 43. Factor c(d).
3*(d + 10)**3/7
Let p(i) = 9*i**2 + i + 14. Suppose -22 + 2 = -5*t. Let r(h) = 5 + 3*h + 3*h**2 - 3*h + 0*h**2. Let y(g) = t*p(g) - 11*r(g). Solve y(b) = 0.
-1, -1/3
Let n = -238/5 + 48. Let -4/5*x - 2/5 - n*x**2 = 0. What is x?
-1
Let p(z) be the first derivative of 17/10*z**4 - 2 - 4/5*z + 9/25*z**5 + 4/5*z**2 + 37/15*z**3. Factor p(y).
(y + 1)**2*(y + 2)*(9*y - 2)/5
Let o(x) be the second derivative of x**7/42 + x**6/15 - x**5/10 - x**4/3 + x**3/6 + x**2 - 35*x. Suppose o(u) = 0. What is u?
-2, -1, 1
Let m = 2 - -3. Let r be (1 - 26/(-22)) + -1 + -1. Let -4/11*t**2 - 2/11*t + 4/11*t**4 + 0 + 0*t**3 + r*t**m = 0. Calculate t.
-1, 0, 1
Let -3*k**5 + k**3 + 10*k**3 - 7*k**3 + 17*k**3 - 24 + 6*k**2 - 36*k = 0. Calculate k.
-2, -1, 2
Let i(b) = 5*b + 5. Let o(f) = f**2 - 1. Let a(n) = i(n) + 15*o(n). Factor a(s).
5*(s + 1)*(3*s - 2)
Let i be (-91)/(-5) + (-2)/10. Let q be 6/i - (-5)/3. Let -3/4*c + 9/4*c**q - 1/2 = 0. What is c?
-1/3, 2/3
Let r be ((-10)/(-8))/(1/4). Let -4*p - r*p + 3*p**2 + 6*p = 0. What is p?
0, 1
Let k(o) = 5*o**3 + 90*o**2 + 540*o + 1077. Let g(t) = -10*t**3 - 180*t**2 - 1080*t - 2155. Let j(a) = 3*g(a) + 5*k(a). Factor j(z).
-5*(z + 6)**3
Let n(b) be the third derivative of b**7/2520 + b**6/720 - b**5/60 + b**4/8 - b**2. Let c(v) be the second derivative of n(v). Let c(d) = 0. Calculate d.
-2, 1
Let k be 2/(-4) + 2/2. Suppose 6*a = -4*d + 4*a + 6, a - 3 = 0. Let d*y + k*y**3 + 1/2*y**2 + 0 = 0. What is y?
-1, 0
Let -338/15 - 2/15*g**2 - 52/15*g = 0. Calculate g.
-13
Let z = 18/11 + -68/55. Suppose 0 - z*l**2 - 2/5*l = 0. What is l?
-1, 0
Let v(b) be the first derivative of -b**6/120 + b**4/8 + 2*b**3/3 - 1. Let c(p) be the third derivative of v(p). Factor c(d).
-3*(d - 1)*(d + 1)
Let u = -130 - -134. Factor 0*l + 0 - 1/4*l**5 - 1/4*l**2 - 3/4*l**u - 3/4*l**3.
-l**2*(l + 1)**3/4
Let x(s) = -15*s**2 + 7*s + 9. Let j(k) = -7*k**2 + 3*k + 4. Let v = 5 - 11. Let w(h) = v*x(h) + 13*j(h). What is b in w(b) = 0?
-2, -1
Suppose -2*r - 5 - 7 = 4*c, -13 = c + 3*r. Let p = 4 + c. Determine n so that 0*n**3 - 4*n + 2 + p*n**4 + 4*n**3 - 5*n**4 + 0 = 0.
-1, 1
Let l be (-2)/(-8) - (-9)/(-36). Suppose 2*x - 8 + 0 = l. Find h such that 10/3*h - 20/3*h**3 + 4/3 + 4/3*h**x - 8/3*h**2 + 10/3*h**5 = 0.
-1, -2/5, 1
Let g be ((-6)/(-4))/((-42)/112*-10). Suppose 0 + 2/5*p - 2/5*p**2 + g*p**4 - 2/5*p**3 = 0. What is p?
-1, 0, 1
Let z(m) be the second derivative of m - 1/12*m**3 - 1/2*m**2 + 0 + 1/12*m**4 + 1/40*m**5. Determine k, given that z(k) = 0.
-2, -1, 1
Factor 28/3*d - 2/3*d**2 - 98/3.
-2*(d - 7)**2/3
Let d(n) be the second derivative of -n**6/15 + 4*n**4/3 - 16*n**2 - 5*n - 1. Suppose d(v) = 0. Calculate v.
-2, 2
Let k = 220/819 + 2/117. Factor -2/7*n**3 + 0*n + 0 + k*n**2.
-2*n**2*(n - 1)/7
Let a = -1070 - -7494/7. Solve 0*i + 0*i**2 + 2/7*i**5 + 2/7*i**3 - a*i**4 + 0 = 0 for i.
0, 1
Suppose -10*o + 12*o - 4 = 0. Let -8/9*g + 2/3*g**o - 8/9 = 0. What is g?
-2/3, 2
Let d(r) be the second derivative of r**9/120960 - r**7/20160 + r**4/6 + 7*r. Let c(n) be the third derivative of d(n). Factor c(u).
u**2*(u - 1)*(u + 1)/8
Let l(y) be the first derivative of y**6/1440 - y**4/96 - y**3 - 1. Let w(k) be the third derivative of l(k). Factor w(z).
(z - 1)*(z + 1)/4
Determine q, given that -12/7*q - 12/7 - 3/7*q**2 = 0.
-2
Let o(h) be the first derivative of 1/4*h**4 - 2/3*h**3 + 2*h - 4 - 1/2*h**2. Determine n so that o(n) = 0.
-1, 1, 2
Suppose 33*k + 5*k**2 + 11 - 53*k + 9 = 0. Calculate k.
2
Let q(v) = -v + 12. Let c be q(9). Let s(y) be the third derivative of 0*y + 0 + 0*y**4 - 1/180*y**5 + 0*y**c + 3*y**2. What is w in s(w) = 0?
0
Factor 7*s + 2*s + 5*s - 19*s + 5*s**2.
5*s*(s - 1)
Let j = 48 + -42. Let l(k) be the third derivative of 1/6*k**3 - 2*k**2 - 1/120*k**j + 0 + 0*k - 1/60*k**5 + 1/24*k**4. Factor l(y).
-(y - 1)*(y + 1)**2
Let 4/3*w - 10/9 - 2/9*w**2 = 0. What is w?
1, 5
Let i(u) = u**2 + 6*u - 6. Let x be i(-7). Let -4*q + 6 + q**2 + 1 - 2 - x = 0. What is q?
2
Let y be -2 + 2 - (-3 + 1). Suppose -3*t = -y*t. What is u in t*u**3 + u**4 - 3*u**2 + 4 - 10*u + 2*u**3 + 6*u = 0?
-2, 1
Let h(a) = a**4 - a**3 - a**2 + a + 1. Let m(l) = -4*l**4 + 4*l**3 + 4*l**2 - 4*l - 3. Let k = 5 - 2. Let z(r) = k*h(r) + m(r). Let z(f) = 0. What is f?
-1, 0, 1
Factor 1/3*s + 1/3*s**2 + 0.
s*(s + 1)/3
Suppose 0 = l + 2 - 9. Factor -4*d**2 + d + 12 + 0*d + 0*d + l*d.
-4*(d - 3)*(d + 1)
Let l be (2 + -3 + 1)/2. Suppose -3*v**2 + 2*v**2 + l - v**2 + 2 = 0. What is v?
-1, 1
Let u = 90 - 90. Let m(b) be the second derivative of 1/45*b**6 + 2*b + u + 1/15*b**5 - 2/9*b**3 - 1/18*b**4 + 0*b**2. Suppose m(h) = 0. Calculate h.
-2, -1, 0, 1
Let s(p) be the second derivative of -p**8/120 - 4*p**7/175 - p**6/100 + p**5/75 - p**2 - p. Let g(y) be the first derivative of s(y). What is x in g(x) = 0?
-1, 0, 2/7
Let p(h) be the third derivative of 0*h**3 + 0*h + 3*h**2 - 1/120*h**6 + 0 - 1/72*h**4 + 1/630*h**7 + 1/60*h**5. Factor p(z).
z*(z - 1)**3/3
Let c(h) = 10*h**2 + 6*h - 4. Let m(t) = 11*t**2 + 7*t - 4. Let o(x) = -7*c(x) + 6*m(x). Let o(a) = 0. Calculate a.
-1, 1
Factor 6/7*k - 4/7*k**3 + 6/7*k**4 - 2/7*k**5 - 2/7 - 4/7*k**2.
-2*(k - 1)**4*(k + 1)/7
Let u(c) be the first derivative of -1/4*c**2 + 7/24*c**6 + 1/12*c**3 + 15/16*c**4 + 1 + 0*c + 19/20*c**5. Factor u(d).
d*(d + 1)**3*(7*d - 2)/4
Suppose -q - 3 = -1. Let g be (-57)/(-76) - q/(-8). Find a such that 3/4*a - 1/4*a**2 - g = 0.
1, 2
Factor 9/7 + 6/7*q + 1/7*q**2.
(q + 3)**2/7
Solve 3*r**2 + 5*r - r + 4*r**2 - 9*r**2 = 0.
0, 2
Find a suc