 = -6*d(v) - 13*i(v). Let s be u(0). Solve 1/2*x + 1/2*x**2 + s = 0 for x.
-1, 0
Let f(g) be the second derivative of 2*g**7/105 - g**6/10 + g**5/5 - g**4/6 + 7*g**2 + 36*g. Let m(h) be the first derivative of f(h). What is v in m(v) = 0?
0, 1
Let j(f) be the first derivative of -f**3/4 - 27*f**2/8 - 25. Let j(z) = 0. What is z?
-9, 0
Let x(h) be the second derivative of -1/45*h**6 + 1/126*h**7 + 0*h**2 + 0*h**5 + 0*h**3 + 0 + 32*h + 0*h**4. Determine r, given that x(r) = 0.
0, 2
Let g(n) = n**3 - 9*n**2 + 9*n - 6. Let i be g(8). Suppose 2*d - i*r + 7*r - 15 = 0, -5*d = 2*r - 27. Solve 30 - 30 - t**d + t**4 = 0 for t.
0, 1
Let g(l) be the first derivative of 1/32*l**4 + 0*l + 1/8*l**2 + 10 - 1/8*l**3. Determine b, given that g(b) = 0.
0, 1, 2
Let v(w) = -3*w**5 + w**4 + 10*w**3 - 4*w - 4. Let f(m) = 5*m**5 - 3*m**4 - 19*m**3 + m**2 + 9*m + 7. Let z(d) = -4*f(d) - 7*v(d). Factor z(x).
x*(x - 1)*(x + 2)**3
Let y(t) be the second derivative of -t**6/3 + 174*t**5/5 - 1995*t**4/2 - 2450*t**3/3 + t + 23. Solve y(k) = 0 for k.
-2/5, 0, 35
Let a(j) be the third derivative of 0 - 229/3*j**5 + 125/336*j**8 - 35/6*j**7 - 160/3*j**3 + 260/3*j**4 + 98/3*j**6 + 0*j + 7*j**2. Suppose a(w) = 0. What is w?
2/5, 1, 4
Let l(a) = -a + 14. Let q be l(9). Factor q + 15*x - 12*x**2 - 7*x**3 - 21 + 9*x + 9*x**3.
2*(x - 2)**3
Suppose -72*f + 81 - 9*f**2 - 23*f - 8*f**2 + 2*f**2 - 31*f = 0. Calculate f.
-9, 3/5
Let m be (1/(-9))/(1/(-2)). Let n be 120/(-8) + 21 - (-104)/(-18). Solve -m*w**2 + n*w + 4/9 = 0 for w.
-1, 2
Factor 0*a**2 - 16*a + 5*a**2 - 577 + 124*a + 127 + 107*a.
5*(a - 2)*(a + 45)
Let w be (-22)/(-18) + -1 + (-579)/(-27). Let k = 23 - w. Factor -2/3*n**2 - k*n - 2/3.
-2*(n + 1)**2/3
Let q(g) be the first derivative of 3/4*g**4 + 1/4*g**2 + 0*g - 2/3*g**3 - 2/5*g**5 + 1/12*g**6 + 25. Find i such that q(i) = 0.
0, 1
Determine a so that -2*a**3 + 1/3*a**5 - 4/3*a**2 + 0 + 5/3*a + 4/3*a**4 = 0.
-5, -1, 0, 1
Let o(d) be the third derivative of -d**6/420 - d**5/21 + 23*d**4/84 - 4*d**3/7 - 130*d**2 - 2. Solve o(f) = 0 for f.
-12, 1
Let m be (-2*(-1)/(-8))/(1/(-4)). Let g(j) = 6*j**4 + 8*j**3 + 8*j**2 - 8*j - 10. Let h(f) = f**4 + f**2 - 1. Let d(q) = m*g(q) - 4*h(q). Factor d(u).
2*(u - 1)*(u + 1)**2*(u + 3)
Let x = -107 + 110. Suppose 2*w - 6 = x*p, -3*w + 4*p + 3 = -6. Factor -10/9*s**2 - 2/3*s**w + 2/9*s**4 - 4/9*s + 0 + 2/9*s**5.
2*s*(s - 2)*(s + 1)**3/9
Let i(q) be the third derivative of -q**7/525 + q**6/300 + q**5/150 - q**4/60 - 31*q**2. Factor i(s).
-2*s*(s - 1)**2*(s + 1)/5
Let k(t) be the second derivative of 3/40*t**5 + 11*t - 1/8*t**4 - 1/4*t**3 + 0 + 3/4*t**2. What is o in k(o) = 0?
-1, 1
Let t(f) = -7*f**3 + 326*f**2 - 3793*f + 1058. Let b(j) = -42*j**3 + 1957*j**2 - 22757*j + 6348. Let p(v) = -6*b(v) + 39*t(v). Factor p(h).
-3*(h - 23)**2*(7*h - 2)
Suppose 3*t - 2*l - 19 - 7 = 0, 3*t + 4*l - 2 = 0. Let b(f) be the first derivative of 0*f - f**3 + t + 3/2*f**2. Factor b(x).
-3*x*(x - 1)
Let b(v) be the third derivative of 0 + 0*v**4 - 1/180*v**5 - 10*v**2 + 1/18*v**3 + 0*v. Factor b(s).
-(s - 1)*(s + 1)/3
Find h, given that 2/7*h**2 + 32/7*h + 8 = 0.
-14, -2
Let h(j) be the first derivative of -j**5/90 - j**4/18 + j**3/3 + 31*j**2/2 - 21. Let s(l) be the second derivative of h(l). Factor s(n).
-2*(n - 1)*(n + 3)/3
Let c = 259/6 + -43. Let t(m) be the first derivative of c*m**3 - 3/4*m**2 + m - 4. Let t(d) = 0. What is d?
1, 2
Find z, given that -3/4*z**2 + 87/2 + 81/4*z = 0.
-2, 29
Suppose -2*p + 6*p + 3*s = 106, 2*p + 5*s - 60 = 0. Suppose 2*f + p = 33. Factor 2/7*v**2 + 0*v + 2/7*v**f + 4/7*v**3 + 0.
2*v**2*(v + 1)**2/7
Let s(i) be the second derivative of -i**7/4620 - i**6/990 + 14*i**3/3 - 27*i. Let b(h) be the second derivative of s(h). Determine l so that b(l) = 0.
-2, 0
Let k be ((-74)/20 + 4)/((60/(-80))/(-1)). Factor -1/5*x**2 + k*x - 1/5.
-(x - 1)**2/5
Let u(a) = 3*a**3 - a**2 - a + 3. Let h(p) = -25*p**3 + 8*p**2 + 8*p - 25. Let o(v) = 6*h(v) + 51*u(v). Factor o(s).
3*(s - 1)**2*(s + 1)
Let o = -1615 + 1617. Find m such that -2*m + 2*m**3 + 2/3*m**o + 2/3*m**4 - 4/3 = 0.
-2, -1, 1
Factor 867/7 - 102/7*l + 3/7*l**2.
3*(l - 17)**2/7
Let c(t) be the third derivative of -t**5/210 + t**4/14 - 5*t**3/21 - 4*t**2 - 2. Determine z so that c(z) = 0.
1, 5
What is v in 8*v**4 + 7*v**2 + 1/2*v**5 + 29/2*v**3 + 0 + 0*v = 0?
-14, -1, 0
Suppose -5*t + 2*r = -0*r - 11, 4*r - 8 = 0. Find u such that -4*u**t + 12*u**2 - u + 2*u + 2 + 3*u - 4*u**4 - 10 = 0.
-2, -1, 1
Let w be 65/15 - 2/(-3). Factor 15*s**3 - 2*s**2 + 11*s**2 + 3*s**4 - 10*s**w + 7*s**5.
-3*s**2*(s - 3)*(s + 1)**2
Suppose 15*y - 21 = 8*y. Suppose 4*a = -5*t + 13, -2*a + t - y = -3*a. Find g such that 8/15 - 2/15*g**a - 2/15*g**3 + 8/15*g = 0.
-2, -1, 2
Suppose -19*w + 33 + 43 = 0. Suppose -w*u = -8 - 0. Factor -25*v**3 + 20*v**u - 7/2*v**5 - 15/2*v + 1 + 15*v**4.
-(v - 1)**4*(7*v - 2)/2
Suppose 0*n - 10 = -n - 2*t, 0 = 5*n - 5*t + 10. Suppose 4*y + n*f = -f + 48, y - 23 = 2*f. Solve -3 - 2*r**2 - y - 49*r + 37*r = 0.
-3
Let v = 15 + -13. Factor -2 - 119*r + r**3 + 122*r + 6*r**2 - 3*r**4 + 3*r**v.
-(r - 2)*(r + 1)**2*(3*r - 1)
Let s(p) be the second derivative of 2*p**7/21 - 14*p**6/15 + 3*p**5 - 3*p**4 + 35*p. What is v in s(v) = 0?
0, 1, 3
Let j be (460 - 5)/(((-2)/1)/(-6)). Let i be (520/j)/(1 - 14/18). Determine z, given that 8/7*z**2 + 12/7*z - i*z**4 + 4/7 - 4/7*z**5 - 8/7*z**3 = 0.
-1, 1
Let h(t) be the second derivative of t + 1/40*t**5 + 0*t**2 + 1/12*t**3 + 0 + 1/12*t**4. Factor h(c).
c*(c + 1)**2/2
Let a be (-121)/(-17) - 4/34. Let g(s) = -8*s + 2. Let k(m) = 5 + 0*m**2 - 25*m - m**3 + 0*m**2. Let o(c) = a*g(c) - 2*k(c). Factor o(x).
2*(x - 1)**2*(x + 2)
Suppose -m + 6 = -k, -2*m = 5*k + 2 + 7. Factor 6*r**m + 1/4*r**5 - 8*r**2 + 4*r - 2*r**4 + 0.
r*(r - 2)**4/4
Let d(t) = -8*t**3 - 8*t**2 - 6*t. Let p(c) = 3*c**3 + 3*c**2 + 2*c. Let g = 36 + -40. Let a(j) = g*d(j) - 11*p(j). Factor a(o).
-o*(o - 1)*(o + 2)
Let g(p) be the second derivative of -p**5/30 + 2*p**4/3 - 16*p**3/3 + 11*p**2/2 + 12*p. Let s(x) be the first derivative of g(x). Solve s(c) = 0.
4
Let m(g) be the third derivative of g**8/252 + 4*g**7/63 + 13*g**6/30 + 74*g**5/45 + 34*g**4/9 + 16*g**3/3 + 627*g**2. Factor m(u).
4*(u + 1)*(u + 2)**3*(u + 3)/3
Solve 1196*q - 110 - 5*q**3 + 25*q**2 + 0*q**2 - 1186*q - 10 = 0 for q.
-2, 3, 4
Let u(x) be the second derivative of -x**4/3 - 34*x**3/7 - 4*x**2 - x + 61. Factor u(b).
-4*(b + 7)*(7*b + 2)/7
Let m(c) = -c**5 + c**4 + c**3 - 2*c**2 - 1. Let o(v) = -v**5 - 2*v**4 - 2*v**3 + 4*v**2 + 2. Let a(u) = -2*m(u) - o(u). Factor a(i).
3*i**5
Factor 0*l**3 - 2*l**3 - 73*l**2 + 37*l**2 + 28*l**2.
-2*l**2*(l + 4)
Let d = 18 - 12. Suppose -d = -6*h + 3*h. Let 0 + k**3 + 4/3*k - 8/3*k**h = 0. What is k?
0, 2/3, 2
Let i(d) be the first derivative of d**5/5 + d**4/2 - d**3 - 4*d**2 - 4*d - 161. Factor i(p).
(p - 2)*(p + 1)**2*(p + 2)
Let f be 9*(-7 - (-424)/60). Let g(l) be the first derivative of f*l**5 + 0*l - 6*l**2 - 15/4*l**4 - 4 + 8*l**3. Factor g(d).
3*d*(d - 2)**2*(d - 1)
Let n(o) be the third derivative of 11*o**6/240 - 19*o**5/40 + 5*o**4/24 + 111*o**2. Determine r so that n(r) = 0.
0, 2/11, 5
Let k be (-11 + -1)/(14 - (26 - 9)). Factor -12/5*j**2 - 8/5*j**3 - 2/5 - 2/5*j**k - 8/5*j.
-2*(j + 1)**4/5
Let u(z) be the second derivative of -z**7/5040 - z**6/360 + z**4/3 + 6*z. Let j(f) be the third derivative of u(f). Find p such that j(p) = 0.
-4, 0
Let d = -43 + 59. Let -5*s**2 - 8*s + 3*s + 5*s**3 - d + 21 = 0. What is s?
-1, 1
Let s(y) be the second derivative of -y**6/60 + y**5/10 + y**4/4 - 3*y**3 + 27*y**2/4 - 9*y - 5. Factor s(w).
-(w - 3)**2*(w - 1)*(w + 3)/2
Let y(z) be the second derivative of 1/33*z**3 + 0*z**2 + 2/33*z**4 + 0 + 27*z. Factor y(g).
2*g*(4*g + 1)/11
Suppose -1 = 3*i - 5*a, -3*a = -5*i - 2*a + 13. What is k in -50*k**3 - 24*k**2 - 49*k**i + 12*k**5 - 76*k**4 - 17*k**3 + 4*k**5 = 0?
-1, -1/4, 0, 6
Find w, given that -2/7*w**2 - 11552/7 - 304/7*w = 0.
-76
Factor 5/2*j + 1/4*j**2 - 11/4.
(j - 1)*(j + 11)/4
Let f be (-6)/(-10) - 6*(-128)/120. Let j(z) be the second derivative of -f*z + 1/48*z**4 + 0 + 0*z**2 - 1/12*z**3 + 3/80*z**5. Factor j(o).
o*(o + 1)*(3*o - 2)/4
Let i = -34157/40040 + 101/91. Let t = i + -3/40. Factor 2/11*q**3 - t + 2/11*q**2 - 2