). Suppose -z = 2*z + 3, -4*f - 4*z = -8. Determine x so that -2*x**4 + u*x - 7 + x**4 - 6*x**2 + 6 + 4*x**f = 0.
1
Let u(c) be the third derivative of 0*c**3 + 0 + 1/600*c**5 + c**2 + 1/240*c**4 + 0*c. Find t, given that u(t) = 0.
-1, 0
Let l(r) be the first derivative of r**5/690 + r**4/138 + r**3/69 - 21*r**2 - 13. Let u(j) be the second derivative of l(j). Suppose u(q) = 0. What is q?
-1
Let g = 39 - 52. Let d be 4/(-14)*(g + 6). Factor -2/7 + 2/7*f**d - 2/7*f**3 + 2/7*f.
-2*(f - 1)**2*(f + 1)/7
Factor -92/3 + 88/3*v - 19/3*v**2 - 1/3*v**3.
-(v - 2)**2*(v + 23)/3
Suppose -42/5*m + 2/5*m**2 - 92/5 = 0. Calculate m.
-2, 23
Let a be (8/180)/((-8)/(-10)). Let f(l) be the second derivative of 2*l + 0 + 3*l**2 + a*l**4 - 2/3*l**3. Let f(o) = 0. Calculate o.
3
Let o(d) be the second derivative of -27*d**7/35 + 42*d**6/25 + 34*d**5/25 + 4*d**4/15 + 2*d - 1. Factor o(r).
-2*r**2*(r - 2)*(9*r + 2)**2/5
Let p(a) be the third derivative of 0 + 0*a - 10*a**2 + 1/300*a**5 - 1/30*a**3 + 0*a**4. Factor p(d).
(d - 1)*(d + 1)/5
Let d = -401 + 406. Let z(m) be the third derivative of m**2 + 0 - 9/2*m**4 + 2*m**3 + 81/20*m**d + 0*m. Factor z(x).
3*(9*x - 2)**2
Let y(z) be the second derivative of -z**7/840 + z**6/480 + 3*z**2 + 15*z. Let r(j) be the first derivative of y(j). Suppose r(u) = 0. Calculate u.
0, 1
Let c(d) be the third derivative of d**5/90 - d**4/12 - 36*d**2. Let c(w) = 0. What is w?
0, 3
Let u = -191 - -196. Suppose 0 = u*o + 2*o - 14. Suppose 2/9*n - 2/9*n**o + 0 = 0. What is n?
0, 1
Let p be ((-200)/(-350))/((-12)/(-14)). Determine q, given that -2/15*q**2 - 10/3*q**5 + p*q**4 - 32/15*q - 8/15 + 82/15*q**3 = 0.
-1, -2/5, 1
Suppose 7*w + 13 - 27 = 0. Let -13*c**w - 2 + 3*c**2 + 2 + 15*c - 5*c**3 = 0. What is c?
-3, 0, 1
Suppose 3 = -3*h + 3*c, -2*h + 0*c + 18 = 3*c. Factor 4*i + 3*i**4 - i**3 - 8*i**h + 8*i + 0*i**4.
3*i*(i - 2)**2*(i + 1)
Let x be 5*((-7)/(-5) + 1). Suppose x = 12*q - 8*q. Let 45*v**5 + 6*v**4 + 28*v**3 + 2*v**2 - 8*v**2 - 73*v**q = 0. Calculate v.
-1, -2/15, 0, 1
Let s(t) be the second derivative of t**6/15 + 2*t**5/5 + 2*t**4/3 + 13*t - 1. Factor s(m).
2*m**2*(m + 2)**2
Let k be 2 + 3 + 18/(-6). Suppose -2*i - 3*p + 18 = -4, 0 = k*i + 5*p - 30. Factor 0*a**3 + a**i + a + a**3 - 3*a**3.
a*(a - 1)**2*(a + 1)**2
Let u(m) be the second derivative of 2/11*m**2 + m + 1/66*m**4 - 1/11*m**3 + 0. Determine v, given that u(v) = 0.
1, 2
Let h(l) be the second derivative of -l**6/2700 + l**5/900 + 5*l**3/6 - 2*l. Let p(t) be the second derivative of h(t). Factor p(z).
-2*z*(z - 1)/15
Let q(s) be the first derivative of -2*s**2 - 3 + 0*s**3 - 1/36*s**4 - 2/135*s**5 + 0*s. Let g(v) be the second derivative of q(v). Suppose g(j) = 0. What is j?
-3/4, 0
Let j(l) be the third derivative of l**6/330 + 19*l**5/110 + 35*l**4/11 + 196*l**3/33 + 2*l**2 - 8*l. Factor j(w).
2*(w + 14)**2*(2*w + 1)/11
Suppose -2*h + 22 = -0*h. Let 4*w + 2*w**3 - 2 + 5*w**2 + 4*w - 2*w - h*w**2 = 0. Calculate w.
1
Let m(b) be the third derivative of -b**8/2520 + b**7/630 + 11*b**3/3 - 9*b**2. Let f(j) be the first derivative of m(j). Let f(l) = 0. Calculate l.
0, 2
Let m(o) be the first derivative of -5*o**6/18 - o**5/3 + 5*o**4/12 + 5*o**3/9 - 2. Solve m(v) = 0 for v.
-1, 0, 1
Let w be (-12*(-16)/(-1664))/((-6)/13). Factor 0 + 1/4*m**3 + w*m**5 + 3/4*m**4 - 3/4*m**2 - 1/2*m.
m*(m - 1)*(m + 1)**2*(m + 2)/4
Factor -1/2*h**3 - 2*h + 0 + 2*h**2.
-h*(h - 2)**2/2
Suppose 3*d = k + 17, -2*k - 16 + 2 = -d. Let z(x) be the second derivative of 0*x**2 - 1/12*x**3 - x + 1/40*x**5 + 1/24*x**d - 1/60*x**6 + 0. Factor z(l).
-l*(l - 1)**2*(l + 1)/2
Suppose 8 = 4*k - 0. Suppose 3*f + s - 2 = 0, 2*f - 10 = 2*s + k. What is u in 6 + 0*u**f - u**2 + 0*u**2 - 22 - 8*u = 0?
-4
Let x be 53 + 58330/(-1102) - 251/(-145). Determine f, given that 3/5*f**5 - 9/5*f**2 + x*f**4 - 6/5*f + 3/5*f**3 + 0 = 0.
-2, -1, 0, 1
Let z(a) be the second derivative of a**7/17640 - a**6/1260 + a**5/210 + 41*a**4/12 - 19*a. Let m(c) be the third derivative of z(c). Factor m(u).
(u - 2)**2/7
Let s(p) = -p**3 - 3*p**2 + 34*p + 76. Let b be s(-2). Factor -9*c**2 - 3/2*c**b + 6*c**3 + 6*c - 3/2.
-3*(c - 1)**4/2
Let v = -6 - -1. Let r(w) = -40*w**5 - 18*w**4 + 22*w**3 - 12*w + 12. Let f(z) = -16*z**5 - 7*z**4 + 9*z**3 - 5*z + 5. Let c(u) = v*r(u) + 12*f(u). Factor c(d).
2*d**3*(d + 1)*(4*d - 1)
Let n = -56 + 36. Let i be (-1)/(-6)*16*(-1)/n. Find h, given that 2/15*h**2 - 2/15*h**3 + 0*h - i*h**4 + 2/15*h**5 + 0 = 0.
-1, 0, 1
Let q(b) be the second derivative of -5*b**7/42 - 2*b**6/3 - b**5/2 + 5*b**4/3 + 5*b**3/2 - 58*b. Determine u, given that q(u) = 0.
-3, -1, 0, 1
Suppose 14/3 - 2*k**3 + 3*k - 11/3*k**2 = 0. What is k?
-2, -1, 7/6
Let l(n) be the second derivative of 0 + n**3 - 3/2*n**2 - 4*n - 1/4*n**4. Suppose l(u) = 0. Calculate u.
1
Let m(b) = -15*b + 648. Let u be m(43). What is f in 27/7*f + 18/7*f**2 + 12/7 + 3/7*f**u = 0?
-4, -1
Let m(p) be the first derivative of p**3/9 - 5*p**2/6 + 4*p/3 - 27. Find u such that m(u) = 0.
1, 4
Suppose -32/15*w + 24/5 - 2/15*w**2 = 0. Calculate w.
-18, 2
Let s = -4901 + 4904. Factor 18/5*a - 2*a**s + 6/5*a**2 + 0 + 2/5*a**4.
2*a*(a - 3)**2*(a + 1)/5
Let o(v) be the second derivative of -1/80*v**5 + 1/56*v**7 + 0*v**2 + 0*v**4 - 21*v + 0*v**3 + 0 + 1/60*v**6. Factor o(s).
s**3*(s + 1)*(3*s - 1)/4
Let c(u) be the first derivative of -u**5/5 - 15*u**4/4 + 27. Let c(m) = 0. What is m?
-15, 0
Let o(n) be the third derivative of -n**8/2520 - 4*n**7/525 - 29*n**6/900 - n**5/25 - 120*n**2. Solve o(v) = 0.
-9, -2, -1, 0
Let a(y) be the third derivative of y**8/280 + y**7/30 + 17*y**6/180 + y**5/10 - 10*y**3/3 - 22*y**2. Let s(k) be the first derivative of a(k). Factor s(r).
2*r*(r + 1)*(r + 3)*(3*r + 2)
Find l such that 5*l**3 + 597 + 85*l + 725 - 1182 - 50*l**2 = 0.
-1, 4, 7
Let k be 2*(-2)/(-4)*-1. Let y(m) = m**2 - m. Let c(z) be the first derivative of -7*z**3 + 9*z**2 - 3. Let p(h) = k*c(h) - 18*y(h). Factor p(d).
3*d**2
Let g(x) = -x**3 - 14*x**2 + 13*x - 28. Let h be g(-15). Let v(o) be the second derivative of 4*o + 0 + 3/20*o**5 + 0*o**h - 1/2*o**4 + 0*o**3. Factor v(l).
3*l**2*(l - 2)
Let c(h) be the first derivative of -4/21*h**4 + 1/14*h**5 + 4/21*h**3 + 1 + 0*h**2 - 1/105*h**6 + 2*h. Let g(s) be the first derivative of c(s). Factor g(k).
-2*k*(k - 2)**2*(k - 1)/7
Let o(b) be the first derivative of -25*b**6/6 + 6*b**5 + 35*b**4/2 - 140*b**3/3 + 75*b**2/2 - 10*b - 6. Solve o(v) = 0.
-2, 1/5, 1
Let s(w) = -7*w - 15. Let n be s(-4). Suppose -45*z**3 - 10*z - 30*z**4 - 5*z**5 + n*z**4 - 8*z**4 - 35*z**2 = 0. What is z?
-2, -1, 0
Solve 183 + 10*t**2 - 2*t**5 - 175 - 24*t**2 + 6*t**4 + 2*t**3 = 0 for t.
-1, 1, 2
Let u be (-5)/10 - (-74)/40. Let g = u + 1/4. Solve -4/5*a + 2/5*a**4 + 0 - g*a**3 + 2*a**2 = 0 for a.
0, 1, 2
Let p = 313/12 + -99/4. Let c(j) be the first derivative of j**2 + 1/24*j**4 + p*j + 4 + 1/3*j**3. Factor c(z).
(z + 2)**3/6
Let q(u) = 10*u**3 + 5*u**2 + 20*u - 30. Let j(r) = -7*r**3 - 6*r**2 - 21*r + 30. Let x(o) = -5*j(o) - 4*q(o). Factor x(y).
-5*(y - 3)*(y - 1)*(y + 2)
Find v such that 1/4*v**3 + 9/2*v - 21/4*v**2 + 10 = 0.
-1, 2, 20
Suppose -32*y = -33*y + 12. Factor -13 - 5*q**3 + 2*q**3 - 9*q**3 + 2*q**4 - 3*q**4 + y*q + 14*q**2.
-(q - 1)**2*(q + 1)*(q + 13)
Let i be ((-3)/84 - 2/(-7))*44. Suppose 6*z = i*z. Suppose -3/2*u**3 - 3*u**4 + z + 0*u + 0*u**2 - 3/2*u**5 = 0. Calculate u.
-1, 0
Let r(u) be the first derivative of -u**3/2 - 3*u**2/2 + 9*u/2 - 59. Factor r(q).
-3*(q - 1)*(q + 3)/2
Let f(m) be the second derivative of m**7/21420 - m**6/6120 - 7*m**4/12 + 3*m. Let v(r) be the third derivative of f(r). Let v(t) = 0. Calculate t.
0, 1
Let k = -75 - -83. Determine w so that -6*w**2 + 0*w**2 + 12*w**4 + 9 - 15 - k*w - 19*w + 27*w**3 = 0.
-2, -1, -1/4, 1
Factor -110/17*d**3 - 436/17*d**2 - 424/17*d + 16/17.
-2*(d + 2)**2*(55*d - 2)/17
Let x(u) = -2*u**3 - 10*u**2 + 4*u + 10. Let q(w) = -w**3 + w**2 - 1. Let n(g) = -2*q(g) - x(g). Factor n(v).
4*(v - 1)*(v + 1)*(v + 2)
Let g = 1/82 + 20/41. Factor -3/2*x**2 + g*x + 1.
-(x - 1)*(3*x + 2)/2
Factor -4/9*g**3 + 16/3*g**2 + 4/9*g - 16/3.
-4*(g - 12)*(g - 1)*(g + 1)/9
Let y(h) = -h**3 - 9*h**2 - 9*h - 5. Let u be y(-8). Let c = 762 - 760. Solve -8/5 - 28/5*k**u - 12/5*k**c + 28/5*k + 4*k**4 = 0 f