) be the first derivative of r(a). Find s such that t(s) = 0.
0
Let t(v) be the first derivative of v**8/4200 - v**6/450 + v**4/60 + v**3 + 1. Let b(h) be the third derivative of t(h). Find f, given that b(f) = 0.
-1, 1
Suppose a - 4 = -0. Factor -2 - 4*v**3 + 2*v**2 + 11*v - 9*v**4 + a + 5*v**2 - 7*v**3.
-(v - 1)*(v + 1)**2*(9*v + 2)
Let y be 1 - (-3)/(-5) - 0. Suppose -4/5 + 6/5*h**2 + y*h = 0. Calculate h.
-1, 2/3
Let z(d) be the first derivative of -343*d**5/5 + 147*d**4/2 - 28*d**3 + 4*d**2 + 11. Factor z(s).
-s*(7*s - 2)**3
Let j(h) be the second derivative of -h**6/240 - h**5/72 - h**4/72 - 3*h**2/2 + 4*h. Let v(c) be the first derivative of j(c). Factor v(r).
-r*(r + 1)*(3*r + 2)/6
Suppose 0*u + 2*u = 0. Let v(i) = -i**2 - 5*i + 18. Let n be v(-7). Factor 2/7*j + u + 2/7*j**2 - 2/7*j**3 - 2/7*j**n.
-2*j*(j - 1)*(j + 1)**2/7
Let j(m) be the first derivative of m**6/18 - 7*m**5/15 + 19*m**4/12 - 25*m**3/9 + 8*m**2/3 - 4*m/3 - 9. Find z such that j(z) = 0.
1, 2
Let -7 + 3*x**3 + 19 + x**3 - 12*x**2 - 15*x + 11*x = 0. Calculate x.
-1, 1, 3
Let g = 14 + -77. Let o be -2 - 7/(g/30). Factor o + 6*r + 14/3*r**2.
2*(r + 1)*(7*r + 2)/3
Let i(v) be the first derivative of 4*v**3/3 - 4*v**2 + 4*v - 5. Solve i(h) = 0.
1
Let s(c) = -c - 10. Let k be s(-12). Factor 2*t**k - 1 + t + t - 3.
2*(t - 1)*(t + 2)
Find k such that -8*k**3 - 71 - 12*k**2 + 55 + 4*k**4 + 24*k + 8*k = 0.
-2, 1, 2
Determine k so that -3/2*k - 3/2*k**3 + 0 - 1/4*k**4 - 11/4*k**2 = 0.
-3, -2, -1, 0
Let h = 13/7 + -25/21. Let j = 1/4 - -5/12. Let 0 - j*f - h*f**2 = 0. What is f?
-1, 0
Let z = 45 + -223/5. Let 8/5*d - z*d**2 - 8/5 = 0. Calculate d.
2
Let f(m) = -2*m**2 + 13*m - 6. Let p be f(6). Let i be 3 + -1 - (-3 - -3). Find k such that 2/9*k**5 + p*k + 2/3*k**4 - 8/9*k**i + 0*k**3 + 0 = 0.
-2, 0, 1
Let q(z) = -12*z**3 + 66*z**2 + 12*z - 66. Let h(n) = -n**3 + 5*n**2 + n - 5. Let c(a) = -27*h(a) + 2*q(a). Let c(b) = 0. Calculate b.
-1, 1
Let r(l) = 3*l**5 - 12*l**4 + 6*l**2 - 6*l + 6. Let p(f) = 8*f**5 - 35*f**4 + 17*f**2 - 17*f + 17. Let a(v) = -6*p(v) + 17*r(v). Suppose a(i) = 0. Calculate i.
-2, 0
Let k = -1 - -3. Factor w**3 + 4*w**2 + 0*w**2 + w**4 - 5*w**2 - k*w**3 + w**5.
w**2*(w - 1)*(w + 1)**2
Suppose 3*r = 2*r. Suppose -3*o = -r*o - 6. Suppose -m**2 + 0*m**4 + 10*m**4 + 9*m**o - 2*m**5 - 16*m**3 = 0. What is m?
0, 1, 2
Let w(u) = u**5 - u**4 + 4*u**3 - 4*u**2 + u - 1. Let v(m) = -m**5 + m**4 - m + 1. Let b(t) = 6*v(t) + 2*w(t). Factor b(l).
-4*(l - 1)**3*(l + 1)**2
Let i(a) be the first derivative of 2*a**5/25 + 2*a**4/5 + 2*a**3/3 + 2*a**2/5 + 17. Factor i(p).
2*p*(p + 1)**2*(p + 2)/5
Let v(w) = 18*w**5 - 5*w**4 - 12*w**3 - 2*w**2 - 5. Let c(i) = -i**5 - i**3 + i**2 + i + 1. Let l(j) = 6*c(j) + v(j). Determine q so that l(q) = 0.
-1, -1/3, -1/4, 1
Let w(s) = 2*s - 11. Let o be w(5). Let h be (o/5)/((-3)/10). Factor -h*t**2 - 8/3*t - 8/3.
-2*(t + 2)**2/3
Let n(h) = 1 - 4*h**2 + h**3 + 4*h**2. Let p(d) = 9*d**3 - 24*d**2 + 18*d - 5. Let w(y) = -n(y) - p(y). What is t in w(t) = 0?
2/5, 1
Let 0*r - 2/19 + 2/19*r**2 = 0. What is r?
-1, 1
Suppose -5*n = 5*s - 35, -26 = -2*s - 2*s - 2*n. Factor 6*z - 2*z**5 + 3 + 3*z**4 + 5*z**5 - 4*z - s*z**2 + z - 6*z**3.
3*(z - 1)**2*(z + 1)**3
Let a = -19 - -23. Let l(k) be the first derivative of 2*k - 7/3*k**3 - 3/2*k**2 - 1 + 3/4*k**a + k**5. What is b in l(b) = 0?
-1, 2/5, 1
Let u = -87 - -89. Let z(t) be the third derivative of 0 + 1/240*t**6 - 1/48*t**4 + 0*t + 1/120*t**5 - t**u + 0*t**3 - 1/420*t**7. Determine p so that z(p) = 0.
-1, 0, 1
Let o(g) be the third derivative of 0*g - 1/6*g**4 + g**2 - 1/3*g**3 + 0 - 1/30*g**5. Solve o(w) = 0 for w.
-1
Let l = -23/3 - -8. Let t(h) be the second derivative of -l*h**3 + 0 - h**2 + 1/10*h**5 - 2*h + 1/6*h**4. Determine x, given that t(x) = 0.
-1, 1
Determine c, given that 0*c + 5/2*c**2 - 5/2 = 0.
-1, 1
Let l(y) = -y**4 + y**3 - y**2. Let d(b) = 8*b**4 + 4*b**2. Let p(s) = -d(s) - 12*l(s). Factor p(k).
4*k**2*(k - 2)*(k - 1)
Let c be 1 + -1 + (-2 - -4). Factor 2*p**c - 1 + 4*p - 2 + 4 + 1.
2*(p + 1)**2
Let q(a) = -a**2 - 4*a + 4. Suppose 5*r - 2*r = -4*o + 8, o - 17 = 3*r. Let u be q(r). Factor 1/5*l**2 + 0 + 0*l + 1/5*l**u - 2/5*l**3.
l**2*(l - 1)**2/5
Let r be 7/3 + (-6)/(-18). Let w = 1/257 + 2567/771. Suppose -r - w*q**2 + 8*q = 0. What is q?
2/5, 2
Let k be (4/2 + -2)/1. Let o be (1 - 0 - k) + -3. Let y(f) = 1. Let r(m) = m**2 - m + 11. Let u(v) = o*r(v) + 22*y(v). Let u(c) = 0. Calculate c.
0, 1
Let n = 30 - 18. Let k be 15/n + -1 - 0. Solve -1/2*p + 1/4*p**2 + k = 0 for p.
1
Let r(h) be the first derivative of -h**4/8 + h**3/3 + 3. Factor r(q).
-q**2*(q - 2)/2
Let i = 713/4 + -178. Factor 1/2 + 1/4*j - i*j**2.
-(j - 2)*(j + 1)/4
Suppose b - 14 = -3*u, -4*u + 2*b = 7*b - 26. Let -2*a**2 - 4/3*a - 4/3*a**3 - 1/3*a**u - 1/3 = 0. Calculate a.
-1
Suppose -4*n + 5*n = -2*p - 7, -15 = 5*n. Let j be (-3)/((12/10)/p). Factor 0*g**4 - 2/3*g**j + 4/3*g**3 + 0 + 0*g**2 - 2/3*g.
-2*g*(g - 1)**2*(g + 1)**2/3
Let d(p) be the third derivative of p**6/600 - p**5/75 + p**4/24 - p**3/15 + 5*p**2. Determine n so that d(n) = 0.
1, 2
Let u(o) be the third derivative of o**7/10 - 13*o**6/20 + 27*o**5/20 - o**4/2 - 2*o**3 - o**2 + o. Factor u(d).
3*(d - 2)*(d - 1)**2*(7*d + 2)
Let a = -1587/5 + 319. Factor -8/5*b**3 + a*b + 2/5*b**2 - 2/5.
-2*(b - 1)*(b + 1)*(4*b - 1)/5
Factor 9*i**4 + 0*i**2 + i**5 + 13*i**2 - 27*i + 26*i**3 - 27 - 7*i**2 + 12*i**2.
(i - 1)*(i + 1)*(i + 3)**3
Let o(k) be the second derivative of -k**7/70 - k**6/10 - 27*k**5/100 - 7*k**4/20 - k**3/5 - 7*k. Factor o(a).
-3*a*(a + 1)**3*(a + 2)/5
Factor -8*t**3 - 7*t**4 - 9 - 9*t - 15*t + 6*t**4 - 22*t**2.
-(t + 1)**2*(t + 3)**2
Suppose 3 = 7*r + 3. Find d, given that 0*d**2 + r*d + 0 - 2/7*d**3 = 0.
0
Let z = -12 + 18. Factor 6*x + 3 - 2*x**2 + z*x**2 - x**2.
3*(x + 1)**2
Let b(n) be the first derivative of -2*n**5/25 + n**4/5 - 2*n**2/5 + 2*n/5 - 12. Find p, given that b(p) = 0.
-1, 1
Suppose -15 = 5*b - 8*b. Factor -3/5*u**3 + 3/5*u**4 + 0 + 3/5*u**b + 0*u - 3/5*u**2.
3*u**2*(u - 1)*(u + 1)**2/5
Suppose 87 + 5*g + 10*g**3 + 21*g**2 + 4*g**2 - 97 = 0. Calculate g.
-2, -1, 1/2
What is q in -2/7*q**2 - 12/7 - 10/7*q = 0?
-3, -2
Let g(q) be the second derivative of q**5/40 - q**4/9 + q**3/12 + q**2/6 - 8*q. Determine i, given that g(i) = 0.
-1/3, 1, 2
Let l(n) be the third derivative of n**7/315 - n**6/180 - n**5/90 + n**4/36 - 12*n**2. Factor l(t).
2*t*(t - 1)**2*(t + 1)/3
Let n(a) = a**2 + 2. Let z be n(0). Suppose v + 1 - 3 = 0. Factor -z*y**2 + y**2 - 1 + v*y**2.
(y - 1)*(y + 1)
Let p be (-4 + 4 + 0)/3. Suppose -6 = -3*t - p. Find z such that t*z - 1/2 - 1/2*z**4 + 2*z**3 - 3*z**2 = 0.
1
Let f(k) be the first derivative of 2*k**5/5 + 13*k**4/8 + 11*k**3/6 + k**2/2 - 5. Factor f(p).
p*(p + 1)*(p + 2)*(4*p + 1)/2
Let k(m) = 2*m - 2. Let u be k(-5). Let n be (u/(-21))/((-18)/(-21)). Suppose n*f - 2/3*f**2 + 0 = 0. What is f?
0, 1
Let a(t) be the first derivative of -t**6/540 + t**4/36 + 2*t**3 + 5. Let z(m) be the third derivative of a(m). Let z(h) = 0. Calculate h.
-1, 1
Let g be -1 - 33/(-567)*17. Let c = g - -326/189. Solve -2/7*x**4 + 0 - 10/7*x**3 + 0*x + 4/7*x**2 + c*x**5 = 0 for x.
-1, 0, 1/2, 2/3
Let v(j) be the second derivative of j**6/120 + j**5/20 + j**4/12 + 5*j**2/2 + 5*j. Let f(z) be the first derivative of v(z). Find a, given that f(a) = 0.
-2, -1, 0
Let u = 175 - 175. Let -5/4*i**5 + 1/2*i**2 + 3*i**4 - 9/4*i**3 + 0*i + u = 0. What is i?
0, 2/5, 1
Suppose -5*f = -2*d + 9 - 3, -9 = -3*d + 2*f. Factor 2*x**3 - 4*x**d + x**2 - 2*x + x**3 + 4*x.
-x*(x - 2)*(x + 1)
Let x be 2*1 + (-780)/18. Let d = x - -42. Factor 4/3*k**2 + 0 + 2/3*k + d*k**3.
2*k*(k + 1)**2/3
What is z in -7/5*z**2 - 6*z - 8/5 = 0?
-4, -2/7
Let a(u) = 6*u**3 + 6*u**2 - 4*u. Let k(o) = 7*o**3 + 6*o**2 - 4*o. Let f(i) = 3*a(i) - 4*k(i). Factor f(m).
-2*m*(m + 1)*(5*m - 2)
Let s(k) be the second derivative of -k**8/6720 - k**7/2520 + k**6/360 + k**4/6 + 5*k. Let j(p) be the third derivative of s(p). Factor j(q).
-q*(q - 1)*(q + 2)
Factor -24*r - 57/2*r**3 - 21/2*r**4 - 75/2*r**2 - 6 - 3/2*r**5.
-3*(r + 1)**3*(r + 2)**2/2
Factor -b**4 + 19/7*b**3 + 16/7*b - 4/7 + 1/7*b**5 - 25/7*b**2.
(b - 2)**2*(b - 1)**3/7
Let y(w) be the first derivative of -1/9*w**3 - 1/2