, 0, 2/5
Let h(m) be the third derivative of m**7/735 + m**6/105 + m**5/105 - m**4/21 - m**3/7 - 4*m**2. Factor h(s).
2*(s - 1)*(s + 1)**2*(s + 3)/7
Let n(v) be the first derivative of -v**6/21 - 38*v**5/35 - 53*v**4/7 - 20*v**3/3 + 77*v**2 - 98*v + 62. Solve n(h) = 0.
-7, 1
Solve -2/13*q**2 + 0 + 0*q + 2/13*q**3 = 0 for q.
0, 1
Suppose 5*k = 4*k + 4. Factor -6*t - 9 + 13*t**2 - 6*t**2 - k*t**2.
3*(t - 3)*(t + 1)
Let y be 4/4 + 2 + -3. Factor 0*q**2 + y + 2/7*q - 2/7*q**3.
-2*q*(q - 1)*(q + 1)/7
Let b(t) be the first derivative of 1 - 1/5*t**5 + 0*t - 1/9*t**3 - 1/18*t**6 + 0*t**2 - 1/4*t**4. Factor b(a).
-a**2*(a + 1)**3/3
Let i = -1390/9 + 466/3. Suppose -i + 10/9*j**2 + 16/9*j = 0. What is j?
-2, 2/5
Let g(l) be the third derivative of l**5/210 + 5*l**4/84 - 2*l**3/7 - 15*l**2. Determine m, given that g(m) = 0.
-6, 1
Let c(o) = -7*o**2 + 20*o - 19. Let j(h) = 15*h**2 - 40*h + 39. Let f(x) = -7*c(x) - 3*j(x). Factor f(n).
4*(n - 4)*(n - 1)
Let u be 3 - (3 + -2)/1. Suppose -2*o = u*s + 1 - 3, -3*o = -2*s - 8. Find f, given that -1/3 + 4/3*f - f**o = 0.
1/3, 1
Let i(j) = 2*j - 8. Let x be i(10). Let u = -8 + x. Solve -2/3*r**3 - 10/9*r**2 + 2/9 + 2/3*r + 8/9*r**u = 0 for r.
-1, -1/4, 1
Suppose 4*v + 2*n - 3*n + 1 = 0, 5*v - 3*n + 3 = 0. Suppose v = 7*u - 3*u. Factor u*c**3 - 1/4*c**5 - 1/2*c**2 + 1/4*c + 1/2*c**4 + 0.
-c*(c - 1)**3*(c + 1)/4
Let j be 0 - ((-2)/(-3) - (-25)/(-6)). Let a(r) be the first derivative of j*r**2 + 2*r + 5/3*r**3 - 3. Factor a(k).
(k + 1)*(5*k + 2)
Let p(o) be the second derivative of o**5/10 + o**4/3 + o**2 - 3*o. Let z(t) = -8*t**3 - 16*t**2 + t - 9. Let v(b) = -9*p(b) - 2*z(b). Factor v(w).
-2*w*(w + 1)**2
Let q = -3 + 5. Factor 3*x + q*x**2 + 2*x - 6*x + 3*x.
2*x*(x + 1)
Let s(d) be the first derivative of -4*d**2 - 2*d**6 + 14*d**2 - 10*d**4 + 5 - 8*d**5 + 0*d**2 + 8*d. Suppose s(y) = 0. Calculate y.
-1, 2/3
Let o(v) = -9*v**3 - 3*v**2 + 9*v - 4. Let j(q) = -q**2 - 5*q**3 - 2 + 6*q + 5*q - 6*q. Let n(t) = -7*j(t) + 3*o(t). Factor n(s).
2*(s - 1)*(s + 1)*(4*s - 1)
Let n(z) be the third derivative of -z**7/1365 + z**6/390 - z**4/78 + z**3/39 + z**2. Solve n(l) = 0 for l.
-1, 1
Factor 0*b - 625*b**5 - 104*b**2 + 300*b**3 - 250*b**4 + 5*b + 34*b**2.
-5*b*(b + 1)*(5*b - 1)**3
Let i(n) be the second derivative of n**7/70 + n**6/20 - n**4/4 - n**3/2 - n**2 + n. Let s(f) be the first derivative of i(f). Find g, given that s(g) = 0.
-1, 1
Suppose 7*p - 27 = 8. Let r(u) be the third derivative of 3*u**2 + 0*u + 1/3*u**3 + 1/8*u**4 + 0 + 1/60*u**p. Determine x, given that r(x) = 0.
-2, -1
Let p = 1803 - 315524/175. Let i(o) be the third derivative of 0*o**4 + 0*o + 1/100*o**6 + 0*o**3 + 1/840*o**8 + 0 - p*o**7 - 2*o**2 - 1/150*o**5. Factor i(c).
2*c**2*(c - 1)**3/5
Factor 36*u**2 - 2 - 37*u**2 + 4*u - 1.
-(u - 3)*(u - 1)
Let k(n) be the first derivative of 0*n**2 - 1/36*n**4 + 2*n - 1/18*n**3 + 2. Let f(h) be the first derivative of k(h). Let f(d) = 0. What is d?
-1, 0
Let w(x) be the second derivative of x**5/40 - x**3/4 - x**2/2 + 3*x. Determine c, given that w(c) = 0.
-1, 2
Suppose 70*p - 5*p - 25*p + 5*p**2 + 35 = 0. Calculate p.
-7, -1
Let g be (-1)/6*(-3)/6. Let h(r) be the second derivative of 0 - 1/4*r**2 - 5/24*r**3 + 4*r - g*r**4 - 1/80*r**5. What is c in h(c) = 0?
-2, -1
Let a be (16/648)/((-2)/(-6)). Let b(p) be the first derivative of a*p**3 - 2/9*p + 1/9*p**2 - 1/18*p**4 - 1. Factor b(j).
-2*(j - 1)**2*(j + 1)/9
Find c, given that 14/19*c**4 + 130/19*c**3 + 414/19*c**2 + 486/19*c + 108/19 = 0.
-3, -2/7
Suppose -9*r**3 + 35*r + 8*r**3 - 37*r + 3*r**2 = 0. Calculate r.
0, 1, 2
Let f(u) = -9*u**2 - 21*u - 16. Let n = 11 + -3. Let p = n + -10. Let z(k) = -4*k**2 - 10*k - 8. Let y(i) = p*f(i) + 5*z(i). Let y(w) = 0. What is w?
-2
Let o be -1 - (-4 + 25/10). Factor p**4 + o*p**3 + 1/2*p**5 + 0*p + 0 + 0*p**2.
p**3*(p + 1)**2/2
Let f = -136/11 + 1018/77. Let -f*j**4 - 6/7*j**3 + 0 + 0*j - 2/7*j**5 - 2/7*j**2 = 0. Calculate j.
-1, 0
Let r = -8 - -11. Factor -7*z - 86*z**r - 1/2 - 32*z**5 - 73/2*z**2 - 88*z**4.
-(z + 1)**2*(4*z + 1)**3/2
Factor 35/3*y**3 - 44/3*y + 46/3*y**2 + 8/3.
(y + 2)*(5*y - 2)*(7*y - 2)/3
Let m(c) be the first derivative of -1/4*c - 1 + 1/12*c**3 + 3/16*c**4 - 3/8*c**2. Let m(i) = 0. Calculate i.
-1, -1/3, 1
Let i(l) = -l**2 - 1. Suppose n = 3*n + 4. Let u(k) = 6*k**2 - k + 1. Let s(o) = n*u(o) - 6*i(o). Find r such that s(r) = 0.
-2/3, 1
Let g(o) be the second derivative of -3/20*o**5 - 3*o + 0*o**2 + 0 + 1/10*o**6 + 0*o**3 + 1/14*o**7 - 1/4*o**4. Suppose g(z) = 0. What is z?
-1, 0, 1
Let m(r) be the third derivative of -r**7/120 - r**6/40 + r**5/60 + 4*r**2. Factor m(n).
-n**2*(n + 2)*(7*n - 2)/4
Let a(h) be the second derivative of 3*h**5/20 + h**4/2 + h. What is o in a(o) = 0?
-2, 0
Let s = -115 + 1151/10. Let z(g) be the second derivative of 0 - 2/15*g**6 + 0*g**3 + 1/21*g**7 + s*g**5 + 0*g**2 + g + 0*g**4. Factor z(t).
2*t**3*(t - 1)**2
Let b(x) = x**2 + 8*x + 9. Let y(p) = -p**3 + 2*p**2 + 2. Let m be y(3). Let w be b(m). Find f, given that f**2 + 2*f**2 + 4*f**3 + f**w + f**4 = 0.
-2, 0
Let q(s) = s**2 + s. Let j(m) = -4*m**2 - 11*m - 16. Let b(f) = -j(f) - 3*q(f). Find y such that b(y) = 0.
-4
Let r = 8 - 6. Suppose -r = x - 4. Solve 2*w + x*w + 0*w - 4 - w**2 = 0.
2
Suppose 3*i - 8*k + 8 = -13*k, -5*i = -5*k - 40. Factor -4/5*p**3 + 2/15*p**i + 2/5 + 8/5*p**2 - 4/3*p.
2*(p - 3)*(p - 1)**3/15
Suppose 2*p = -3*p + 25. Solve -20*d**p - 53/4*d**3 + 7*d**2 + 7/4*d - 1/2 - 38*d**4 = 0 for d.
-1, -2/5, 1/4
Let h(n) be the third derivative of 0*n + 0 - 1/12*n**4 - 1/6*n**3 - 1/60*n**5 + 9*n**2. What is g in h(g) = 0?
-1
Suppose -11*p + 12*p - 5 = -4*u, -5*u = 4*p + 2. Factor -10/7*l**u + 2*l**3 + 0 - 4/7*l.
2*l*(l - 1)*(7*l + 2)/7
Let o(t) be the first derivative of 3*t**4/4 - 9*t**2/2 - 6*t + 7. Find a such that o(a) = 0.
-1, 2
Factor 2*z**3 - 4/3*z**2 - 2/3*z**4 + 0*z + 0.
-2*z**2*(z - 2)*(z - 1)/3
Let 0 - 2/7*z**3 + 4/7*z**2 + 0*z = 0. Calculate z.
0, 2
Factor 0*b**3 + 3*b**2 + 3/2 - 1/2*b**4 + 4*b.
-(b - 3)*(b + 1)**3/2
Let t be (-11)/(-12) + 6/(-9). Let u(c) be the second derivative of 0*c**5 - c - t*c**2 + 0 - 1/60*c**6 + 0*c**3 + 1/12*c**4. Factor u(g).
-(g - 1)**2*(g + 1)**2/2
Let c(h) = 2*h**4 + 9*h**2 + 4*h - 9. Let s(b) = -5*b**4 - 18*b**2 - 8*b + 17. Let q(k) = 14*c(k) + 6*s(k). Factor q(n).
-2*(n - 3)*(n - 1)*(n + 2)**2
Suppose 9 = 3*k - z - 2, 5*k - 19 = 2*z. Factor 9/2*b**k - 3/2*b**2 + 0 + 0*b.
3*b**2*(3*b - 1)/2
Suppose 0 - 27/7*a**2 + 6/7*a + 3*a**3 = 0. What is a?
0, 2/7, 1
Determine s so that -20/9 + 28/9*s**2 + 2/3*s**3 - 14/9*s = 0.
-5, -2/3, 1
Factor 3/2*k**4 + 0*k**2 + 0 + 0*k - 3/2*k**3.
3*k**3*(k - 1)/2
Let a(d) be the third derivative of d**6/30 + d**5/15 - 7*d**2. Factor a(t).
4*t**2*(t + 1)
Let b(x) be the first derivative of -x**6/6 + 16*x**5/5 - 25*x**4 + 304*x**3/3 - 224*x**2 + 256*x - 28. Factor b(t).
-(t - 4)**3*(t - 2)**2
Let h(q) = -q. Let v(i) = 2*i**2 - 10*i + 4. Let f(z) = -4*h(z) + v(z). Find o, given that f(o) = 0.
1, 2
Let b(y) be the second derivative of -11*y**7/70 + 13*y**6/50 - 3*y**5/50 + y. Suppose b(j) = 0. Calculate j.
0, 2/11, 1
Suppose -5*r = 5*j - 25, 3*j - j = 4. Let m(z) be the second derivative of 0 - 1/6*z**4 + 0*z**r + 0*z**2 - 1/10*z**5 + 3*z. Factor m(u).
-2*u**2*(u + 1)
Let h(x) be the first derivative of x**4/4 + x**3/3 - x**2/2 - x - 7. Factor h(r).
(r - 1)*(r + 1)**2
Let i(j) be the first derivative of j**3/18 - j**2/3 + 2*j/3 - 10. Factor i(m).
(m - 2)**2/6
Suppose 2*c = -2*z, -3*c = z - 0*c + 4. Suppose -t - 12 = -8*w + 5*w, 4 = w. Factor t*h - 2/3 + 2/3*h**z.
2*(h - 1)*(h + 1)/3
Let f = -35/2 + 18. Let v(m) be the first derivative of 3/4*m**2 + 1/8*m**4 + 1/2*m**3 - 1 + f*m. Find l such that v(l) = 0.
-1
Suppose -3*u**4 + 14*u**3 + 2*u**5 - 16*u**3 + 0*u**4 = 0. What is u?
-1/2, 0, 2
Suppose 41*l - 11*l = 90. Suppose 0*r - 3/4*r**5 + 0*r**l + 1/4*r**4 + 0*r**2 + 0 = 0. Calculate r.
0, 1/3
Let z(n) = n - 5. Let g be z(7). Factor -16*k - 29 - 9*k**g - k**3 + 10 - 11*k - 8.
-(k + 3)**3
Suppose 0*r - r + 3 = 0. Suppose p + 25 = 5*b, 0*b - r*p - 10 = -2*b. Let -3*a - b + 1 - 3*a - 2*a**2 = 0. What is a?
-2, -1
Factor -17*m**2 + 20*m + 5*m**2 - m**4 - 3*m**4 - 12*m**3 - 8*m**3 + 16.
-4*(m - 1)*(m + 1)**2*(m + 4)
Let r(p) be the s