erivative of -f**7/210 - f**6/50 + f**5/100 + f**4/20 - 12*f. Suppose v(a) = 0. Calculate a.
-3, -1, 0, 1
Let q be 5*((-423)/(-105) - 2*2). Factor 2/7 + 3/7*f + 0*f**2 - q*f**3.
-(f - 2)*(f + 1)**2/7
Let x(d) be the third derivative of -d**6/210 + 4*d**5/105 - 5*d**4/42 + 4*d**3/21 - 10*d**2. Suppose x(v) = 0. Calculate v.
1, 2
Let w(r) be the third derivative of r**6/420 - r**5/30 + r**4/14 + 2*r**2 - 39. Suppose w(o) = 0. What is o?
0, 1, 6
Factor 4*a**3 + 14*a**2 + 7*a**4 + 0*a**4 - 3*a**4 + 8*a - 6*a**4.
-2*a*(a - 4)*(a + 1)**2
Let k = 8 - 2. Let g = 10 - k. Let i**2 + g - 7 + 2 = 0. What is i?
-1, 1
Let d(r) = r**4 - 2*r**5 - 2 - 5*r**5 - 2*r**2 + 3*r + 3*r**4. Let c(j) = -j**5 - j**3 + j**2 + j - 1. Let l(s) = 4*c(s) - d(s). Factor l(h).
(h - 1)**3*(h + 1)*(3*h + 2)
Let m(i) = 9*i**2 - 4. Let n(z) = -19*z**2 + 9. Let q(h) = -9*m(h) - 4*n(h). Solve q(r) = 0 for r.
0
Let h = -115/2 - -58. Suppose 1/2*j**2 + h - j = 0. Calculate j.
1
Determine d so that -4*d**2 - 8/7*d + 0 - 12/7*d**3 = 0.
-2, -1/3, 0
Let k(j) be the second derivative of -4*j**7/147 - j**6/105 + 4*j**5/35 + j**4/21 - 4*j**3/21 - j**2/7 - 12*j. Find h such that k(h) = 0.
-1, -1/4, 1
Let k(r) be the second derivative of -r**5/360 + r**4/144 - r**2 + r. Let y(x) be the first derivative of k(x). Let y(t) = 0. Calculate t.
0, 1
Let m(u) be the third derivative of -u**7/945 - u**6/270 - u**5/270 - 2*u**2. Solve m(a) = 0 for a.
-1, 0
Let r(n) be the third derivative of 0*n + 3/80*n**6 + 0 + 1/32*n**4 - 1/20*n**5 + 3*n**2 - 1/70*n**7 + 1/448*n**8 + 0*n**3. Determine f so that r(f) = 0.
0, 1
Let w(d) = d**2 - 6*d + 5. Let f(u) = -u + 1. Let x(j) = 3*f(j) + w(j). Let o(v) = 3*v - 3. Let i(a) = 8*o(a) + 3*x(a). Let i(y) = 0. What is y?
0, 1
Suppose 0 = 3*p - 8 - 16. Factor -4 + 6*x - p*x**2 - 2*x**3 - 9*x - 7*x.
-2*(x + 1)**2*(x + 2)
Let b(p) be the first derivative of -5*p**4/4 + 20*p**3/3 - 15*p**2/2 + 7. Determine w, given that b(w) = 0.
0, 1, 3
Factor 26/5*b**3 + 56/5*b**2 - 252/5*b**4 + 0 + 162/5*b**5 + 8/5*b.
2*b*(b - 1)**2*(9*b + 2)**2/5
Let u be (-2009)/5*(-1 - -2). Let l = u - -403. Factor -4/5 - l*f - 2/5*f**2.
-2*(f + 1)*(f + 2)/5
Let h(u) be the third derivative of -u**6/780 + u**5/390 + u**4/39 - 4*u**3/39 - 18*u**2. What is a in h(a) = 0?
-2, 1, 2
Factor -5*j**2 - 60 + 4*j + 45*j - 9*j.
-5*(j - 6)*(j - 2)
Let k(s) be the first derivative of s**6/1440 + 4*s**3/3 - 1. Let b(u) be the third derivative of k(u). What is q in b(q) = 0?
0
Let r = -25 + 35. Let n be (-70)/(-6)*2/r. Factor 2/3 - 4*k**2 - k - n*k**3.
-(k + 1)**2*(7*k - 2)/3
Let a(c) be the second derivative of -c**6/20 + 3*c**5/40 + c**4/8 - c**3/4 + 11*c. Factor a(h).
-3*h*(h - 1)**2*(h + 1)/2
Factor -1/5*m**3 - 3/5*m + 3/5*m**2 + 1/5.
-(m - 1)**3/5
Let g(y) be the first derivative of -y**8/1512 - y**7/315 - y**6/180 - y**5/270 - 3*y**2/2 + 1. Let b(k) be the second derivative of g(k). Factor b(i).
-2*i**2*(i + 1)**3/9
Let g = -10485/11 - -955. Determine w, given that -10/11*w + 10/11*w**4 - 20/11*w**3 + 2/11 + g*w**2 - 2/11*w**5 = 0.
1
Let b(y) be the third derivative of y**7/42 + y**6/6 + y**5/4 - 5*y**4/6 - 10*y**3/3 - 6*y**2. Factor b(t).
5*(t - 1)*(t + 1)*(t + 2)**2
Let y be 48/(-64) - 22/(-8). Let s(r) be the first derivative of 2*r + 2/3*r**3 + y*r**2 + 2. Factor s(g).
2*(g + 1)**2
Let m(d) be the second derivative of -d**5/4 + 5*d**4/6 + 25*d**3/6 - 15*d**2 - 26*d. Factor m(z).
-5*(z - 3)*(z - 1)*(z + 2)
Let p(a) = -a**3 + 12*a**2 - 26*a - 6. Let x be p(9). Factor 0 + 1/3*g**4 - 5/3*g**x + 7/3*g**2 - g.
g*(g - 3)*(g - 1)**2/3
Let u(x) be the third derivative of x**5/180 - 5*x**4/36 + 25*x**3/18 - 4*x**2 - 2*x. Let u(w) = 0. What is w?
5
Let f = 40 - 17. Factor 0*p**2 - 4*p**2 - 5*p**4 + f*p**4 - 10*p**3 - 4*p**3.
2*p**2*(p - 1)*(9*p + 2)
Let w(n) be the second derivative of 3*n**5/20 + n**4/6 - 6*n. Find u such that w(u) = 0.
-2/3, 0
Let w(i) = -i**5 - i**4 + i**2 + i - 1. Let p(z) = 5*z**5 - 4*z**4 + 22*z**3 - 28*z**2 + 5*z + 4. Let m(y) = -p(y) - 4*w(y). Factor m(q).
-q*(q - 3)**2*(q - 1)**2
Suppose r = 3*r - 8. Find b such that 0*b**3 + 0 + 1/2*b**5 + 0*b - 1/2*b**r + 0*b**2 = 0.
0, 1
Let i(j) be the second derivative of -j**5/20 + j**4/6 - j**3/6 - 7*j. Determine l, given that i(l) = 0.
0, 1
Let z(d) be the first derivative of -d**7/4620 - d**6/1980 + d**5/660 + d**4/132 - d**3 + 2. Let h(q) be the third derivative of z(q). Factor h(y).
-2*(y - 1)*(y + 1)**2/11
Let a(d) be the second derivative of -d**8/1344 + d**7/840 + d**2 - 3*d. Let m(g) be the first derivative of a(g). Factor m(h).
-h**4*(h - 1)/4
Let v = 1/225 + 1991/7650. Let s = 249/170 - v. What is z in -6/5*z + 2/5*z**2 - 2/5 + s*z**3 = 0?
-1, -1/3, 1
Let p(v) = v**3 - 7*v**2 + 6*v + 3. Let r be p(6). Suppose r*a + y = 11, 4*a + y - 8 = 2*a. Factor -2/7*i**a + 0 + 2/7*i + 0*i**2.
-2*i*(i - 1)*(i + 1)/7
Let a = -300 + 302. Find n, given that -6/7*n**4 + 3/7*n + 3/7*n**5 - 6/7*n**3 + 12/7*n**a - 6/7 = 0.
-1, 1, 2
Let c = 384/7 + -54. Factor -4/7*g + c - 2/7*g**2.
-2*(g - 1)*(g + 3)/7
Let y = 4 + -4. Suppose 5*i - 16 + 6 = y. Solve i*u**2 + u - u**3 + 0*u**2 + 2*u**3 = 0 for u.
-1, 0
Let p(f) be the first derivative of f**2/2 - f + 3. Let u be p(4). Factor -2*s**2 + 2*s**4 - 3 + u + 0.
2*s**2*(s - 1)*(s + 1)
Let c(p) = 4*p**5 + 2*p**4 - 15*p**3 - 14*p**2 + 12*p + 12. Let k(n) = n**5 - n**4 + n**2. Let t(l) = c(l) - k(l). Find g, given that t(g) = 0.
-2, -1, 1, 2
Factor 16/5*u**3 + 14/5*u**2 + 6/5*u**4 + 0 + 4/5*u.
2*u*(u + 1)**2*(3*u + 2)/5
Let t = -204 + 613/3. Suppose 2/3 + z + t*z**2 = 0. Calculate z.
-2, -1
Suppose -2*o + 6*o = -300. Let m = -221/3 - o. Factor -10/3*u - 8/3*u**2 - m - 2/3*u**3.
-2*(u + 1)**2*(u + 2)/3
Let t(r) be the first derivative of 1/6*r**2 - 3 - 1/12*r**4 + 1/3*r - 1/9*r**3. Factor t(m).
-(m - 1)*(m + 1)**2/3
Let r(y) be the first derivative of -2*y**5/35 - 9*y**4/14 - 16*y**3/7 - 20*y**2/7 + 40. Factor r(l).
-2*l*(l + 2)**2*(l + 5)/7
Let q(v) be the third derivative of v**8/420 + v**7/140 - v**5/60 + v**3/2 - v**2. Let m(n) be the first derivative of q(n). Factor m(j).
2*j*(j + 1)**2*(2*j - 1)
Suppose -6*a - 15*a = -0*a. Let f(s) be the second derivative of a*s**2 + 7/30*s**5 + s + 0 - 1/2*s**4 + 2/9*s**3. Suppose f(z) = 0. What is z?
0, 2/7, 1
Let p = -7/24 + 25/24. Let i be (-4 - -4)/(-2 + 6 + -2). Factor 3/4*u - p*u**2 + i.
-3*u*(u - 1)/4
Let b be (-11)/33*(-9)/20. Let l(s) be the second derivative of b*s**5 + 0 - 1/30*s**6 + 0*s**2 + 0*s**4 + 4*s - 2/3*s**3. Factor l(o).
-o*(o - 2)**2*(o + 1)
Let k(p) = 3*p**2 + 6*p + 4. Let x(a) = 12*a**2 + 24*a + 15. Let z(y) = -15*k(y) + 4*x(y). Factor z(w).
3*w*(w + 2)
Determine r, given that 2/5*r + 2/5*r**2 - 2/5 - 2/5*r**3 = 0.
-1, 1
Let g(f) be the first derivative of 7*f**3/3 - 9*f**2/2 + 2*f - 4. Let t(v) = -2*v**2 + 3*v - 1. Let a(j) = 3*g(j) + 8*t(j). Suppose a(z) = 0. Calculate z.
-2/5, 1
Let p(z) = -z**3 - 5*z**2 - 5*z - 7. Let d(y) = 2*y**3 + 15*y**2 + 15*y + 19. Let n(k) = -6*d(k) - 17*p(k). Factor n(c).
5*(c - 1)**2*(c + 1)
Find l, given that -2376*l**2 - 33*l**3 + 275*l - 6*l - 2916*l**4 + 4893*l**3 + 195*l - 32 = 0.
2/9, 1
Suppose a = 7*a. Let r(s) be the first derivative of -1 + 0*s**3 - 1/9*s**4 + 0*s - 2/15*s**5 + a*s**2 + 5/27*s**6. Find l such that r(l) = 0.
-2/5, 0, 1
Let p(a) be the second derivative of a**8/16800 - a**6/600 - a**5/150 - a**4/6 - 2*a. Let l(k) be the third derivative of p(k). Suppose l(j) = 0. Calculate j.
-1, 2
Let 7/2*t**5 - t + 0 - 19/2*t**4 - 1/2*t**2 + 15/2*t**3 = 0. Calculate t.
-2/7, 0, 1
Let s be (-54)/9*1/(-3). Solve -7/2*d**3 + 9/2*d**s - d + 0 = 0.
0, 2/7, 1
Let w(s) be the first derivative of 4/21*s**3 - 1/2*s**4 - 4/35*s**5 + 0*s + 0*s**2 - 3 + 1/3*s**6. What is o in w(o) = 0?
-1, 0, 2/7, 1
Let q(p) = -3*p**3 - p**2 + 1. Let v be q(1). Let i be 0/(((-12)/(-4))/v). Factor i - 2/3*h - 2/3*h**2.
-2*h*(h + 1)/3
Let x = 20 + -18. Suppose -1 - 3 - 5*t**2 + 9*t**x + 6*t**3 - 6*t = 0. What is t?
-1, -2/3, 1
Let b be (-1 + 0)/((-10)/2). Let r(z) be the first derivative of 1/9*z**3 - 2 + 1/4*z**4 + b*z**5 + 0*z + 1/18*z**6 + 0*z**2. Solve r(a) = 0.
-1, 0
Solve -9/4 - 3/4*j**4 + 3*j**2 + 3/2*j**3 - 3/2*j = 0 for j.
-1, 1, 3
Let s = -480 + 482. Factor 0 + 3/2*k - 9/2*k**s + 3*k**3.
3*k*(k - 1)*(2*k - 1)/2
Let v(p) be the first deri