1
Let k(r) be the first derivative of r**8/1120 - r**7/280 + r**6/240 + r**3/3 + 7. Let s(x) be the third derivative of k(x). Factor s(z).
3*z**2*(z - 1)**2/2
Let w(c) = 2*c + 16. Let m be w(-9). Let f be (-5)/(1*(-3 - m)). Factor 7*z**4 + 4*z**3 + f*z**4 + 2*z**4.
2*z**3*(7*z + 2)
Let z be 126/26 - 4/(-26). Suppose -2 - 13 = -z*y + 2*r, -3*y + 9 = -5*r. Suppose 1/2*n**2 - y*n + 9/2 = 0. Calculate n.
3
Let g = -16 + 10. Let b(n) = n**2 + 7*n + 9. Let t be b(g). Factor -t*i**2 + 2*i - i - 3 - 3*i - 4*i.
-3*(i + 1)**2
Let f(q) = 3*q**3 + 12*q**2 + 17*q + 4. Let s = -9 + 11. Let v(a) = 11*a**3 + 63 - 35*a + 192*a**2 + 308*a + 37*a**3. Let u(k) = s*v(k) - 33*f(k). Factor u(d).
-3*(d + 1)**2*(d + 2)
Let x = 4569 - 13706/3. Factor x - 1/6*q**2 + 1/6*q.
-(q - 2)*(q + 1)/6
Let u be 736/299 - (-12)/(-26). Let o(t) be the first derivative of 0*t - 2/35*t**5 + 0*t**u + 2/21*t**3 + 2 - 1/14*t**4 + 1/21*t**6. Find c such that o(c) = 0.
-1, 0, 1
Let n = -369 - -747/2. Let j(u) be the first derivative of 1/2*u**6 - 6*u + 0*u**5 - 3*u**4 + 2*u**3 + n*u**2 - 1. Factor j(r).
3*(r - 1)**3*(r + 1)*(r + 2)
Let q(z) be the first derivative of z**6/540 + 11*z**3/3 + 9. Let v(x) be the third derivative of q(x). Factor v(o).
2*o**2/3
Let l(p) be the third derivative of p**7/945 + p**6/30 + 9*p**5/20 + 7*p**4/24 + 11*p**2. Let m(u) be the second derivative of l(u). Factor m(g).
2*(2*g + 9)**2/3
Factor 0 + 12/7*p**3 - 12/7*p - 3/7*p**2 + 3/7*p**4.
3*p*(p - 1)*(p + 1)*(p + 4)/7
Let q(j) be the first derivative of -2*j**6/3 - 12*j**5/5 + j**4 + 44*j**3/3 + 24*j**2 + 16*j + 314. Solve q(i) = 0.
-2, -1, 2
Let f(v) be the first derivative of -4 + 1/16*v**2 + 1/40*v**5 - 1/32*v**4 - 1/24*v**3 + 0*v. Determine a, given that f(a) = 0.
-1, 0, 1
Let a(n) = n**3 - 20*n**2 + 23*n - 74. Let h be a(19). Let s(l) be the first derivative of 1/3*l**3 + 7 - h*l**2 + 4*l. Factor s(t).
(t - 2)**2
Let g = 19 - 21. Let t be ((-8)/3 - g)/(2/(-8)). Suppose f**5 + 2*f**2 - 7/3*f + 2/3 - t*f**4 + 4/3*f**3 = 0. What is f?
-1, 2/3, 1
Factor 47/7*v + 18/7 + 13/7*v**3 + 1/7*v**4 + 41/7*v**2.
(v + 1)**2*(v + 2)*(v + 9)/7
Let l(x) be the second derivative of -20*x**7/21 + 67*x**6/15 + 7*x**5 - 59*x**4/6 - 50*x**3/3 - 8*x**2 + 123*x. Find p such that l(p) = 0.
-1, -2/5, -1/4, 1, 4
Let p be (15 + -3 + 1)*4/26. Factor 51/2*m**p + 6 + 6*m**3 + 30*m.
3*(m + 2)**2*(4*m + 1)/2
Let 2/11*m**2 + 4/11*m + 2/11 = 0. What is m?
-1
Let i(a) be the first derivative of 3*a**4/4 + 33*a**3 + 1089*a**2/2 + 3993*a - 280. Factor i(s).
3*(s + 11)**3
Let c(g) be the second derivative of 40/21*g**4 + 0 - 9/35*g**5 + 1/105*g**6 + 6/7*g**3 - 51*g - 81/7*g**2. Factor c(m).
2*(m - 9)**2*(m - 1)*(m + 1)/7
Suppose 5*v + 5*w = 5, 6*v - 5 = v + 3*w. Let n be (-1)/v*0/(-1 - -2). Solve 0*k**2 + 0 + n*k**4 + 0*k + 2/9*k**3 - 2/9*k**5 = 0 for k.
-1, 0, 1
Let q(f) be the second derivative of -f**7/21 + 2*f**6/15 - f**5/10 + 3*f - 3. Factor q(z).
-2*z**3*(z - 1)**2
Suppose -k = -3*k + u - 22, 0 = 2*u + 8. Let x(h) = -3*h**2 + 6*h - 36. Let o(w) = -7*w**2 + 11*w - 72. Let g(f) = k*x(f) + 6*o(f). Factor g(m).
-3*(m - 2)*(m + 6)
Factor 2/5*n**2 + 0 + 32/5*n.
2*n*(n + 16)/5
Let s(l) be the first derivative of -l**4/2 + 76*l**3/9 + 5*l**2 - 52*l/3 - 480. What is t in s(t) = 0?
-1, 2/3, 13
Let x(u) be the first derivative of -2*u**3/15 - 36*u**2/5 + 74*u/5 - 831. Factor x(k).
-2*(k - 1)*(k + 37)/5
Suppose 2*t - 22 = -4*a, 2 = 2*t + 6*a - 7*a. Suppose 5*s**4 + 7*s**t + 18*s**3 + 5*s**2 + 25*s**2 = 0. Calculate s.
-3, -2, 0
Let v = 21884 + -21882. Factor -16/3*o + 20/3*o**v + 0 - 4/3*o**3.
-4*o*(o - 4)*(o - 1)/3
Suppose -3*a + 3 + 3 = n, 3*a + 54 = 4*n. Suppose 2*k = -0*k + 2*i + n, 2*k + 4*i = -12. Factor -9*c**2 + 3*c**k + 4*c + 0*c**3 + 2*c**3 + 0*c.
2*c*(c - 2)*(c - 1)
Let r(a) be the second derivative of 8*a + 1/10*a**2 + 0 + 49/60*a**4 + 7/15*a**3. Factor r(m).
(7*m + 1)**2/5
Let f(u) be the first derivative of -11*u**6/10 - 111*u**5/25 - 3*u**4/20 + 37*u**3/5 + 18*u**2/5 - 149. Find v such that f(v) = 0.
-3, -1, -4/11, 0, 1
Let w(i) = 10*i**2 + 231*i + 266. Let l(k) = -4*k**2 - 116*k - 132. Let c(o) = -9*l(o) - 4*w(o). Let c(h) = 0. What is h?
-1, 31
Let l(s) be the third derivative of s**6/40 + 9*s**5/10 + 77*s**4/8 + 30*s**3 - 702*s**2. Find d, given that l(d) = 0.
-12, -5, -1
Let b be -5 + 9 + -1 + (-45)/26. Let q = -10/13 + b. Factor -3*y**2 - 2*y - q*y**4 - 2*y**3 - 1/2.
-(y + 1)**4/2
Let s = -1516 - -1516. Let q(o) be the first derivative of 3/32*o**4 + 13 + 0*o + s*o**3 + 0*o**2. Find t such that q(t) = 0.
0
Factor -1/5*d**3 + 1/5*d + 1/5*d**4 - 1/5*d**2 + 0.
d*(d - 1)**2*(d + 1)/5
Let j(n) be the third derivative of n**5/330 - 35*n**4/33 + 4900*n**3/33 + 226*n**2. Factor j(h).
2*(h - 70)**2/11
Let i(b) = 2*b + 28. Let v be i(-13). Factor 9*r + 11*r + 2*r**v - 6*r**2.
-4*r*(r - 5)
Let k(z) be the second derivative of -21*z**6/20 + 15*z**5/2 + 119*z**4/24 - 56*z**3/3 + 5*z**2 + 1009*z. Solve k(p) = 0.
-1, 2/21, 2/3, 5
Determine n, given that -2094*n**2 + 2118*n**2 + 33*n + 27*n - 3*n**3 = 0.
-2, 0, 10
Let d(f) = -f**4 - f**2 - 4*f**3 - f + 9*f**3 - 7*f**3 + 3*f**3. Let s(i) = 15*i**4 - 15*i**3 + 10*i**2 + 10*i. Let p(v) = -10*d(v) - s(v). Solve p(h) = 0.
0, 1
Let p be ((-10)/4)/((-93)/124) + -3. What is d in 2/3*d + 0 + p*d**4 - 1/3*d**2 + 1/3*d**5 - d**3 = 0?
-2, -1, 0, 1
Let s(v) be the first derivative of 2*v**5/5 - 5*v**4/4 + v**3/3 + v**2 - 65. Find t such that s(t) = 0.
-1/2, 0, 1, 2
Factor 2/3*p**3 + 4606/3*p + 4418/3 + 190/3*p**2.
2*(p + 1)*(p + 47)**2/3
Let i(t) be the first derivative of t**6/27 - 4*t**5/45 - 7*t**4/18 - 8*t**3/27 - 23. Let i(m) = 0. What is m?
-1, 0, 4
Let q(n) = -n**4 + n + 1. Let o(p) = -2*p**4 - 6*p**3 - 5*p**2 + p + 1. Let r(v) = -4*o(v) + 4*q(v). Suppose r(x) = 0. Calculate x.
-5, -1, 0
Let d(x) be the third derivative of x**8/560 + x**7/140 - x**6/30 - x**5/5 + 3*x**3 - 2*x**2. Let t(a) be the first derivative of d(a). Factor t(v).
3*v*(v - 2)*(v + 2)**2
Let v(o) be the first derivative of -2/3*o - 12 + 0*o**2 + 2/9*o**3. Determine z so that v(z) = 0.
-1, 1
Let n(r) be the third derivative of r**8/60480 - r**7/5040 - 8*r**5/15 + 29*r**2. Let b(k) be the third derivative of n(k). Factor b(o).
o*(o - 3)/3
Let n(y) be the first derivative of -y**8/4200 + y**6/300 - y**5/150 + 2*y**3/3 - 1. Let z(o) be the third derivative of n(o). Factor z(c).
-2*c*(c - 1)**2*(c + 2)/5
Suppose -49*d**3 - 12*d**2 + 15 + 9 + 53*d**3 - 8 = 0. What is d?
-1, 2
Let a(r) be the second derivative of -r**4/54 - 100*r**3/27 - 2500*r**2/9 + 243*r. What is u in a(u) = 0?
-50
Let b be (12/21)/((-2)/(-7)). Suppose -a = 2 - 4. Find p such that 4*p**b + 12*p + 2*p**a + 6*p**3 + 2*p**4 - 10*p = 0.
-1, 0
Let c(a) be the second derivative of a**7/84 - a**6/15 - a**5/5 + 8*a**4/3 - 28*a**3/3 + 16*a**2 - 3*a - 4. Factor c(j).
(j - 2)**4*(j + 4)/2
Factor -11*t**2 + 9 - 11*t**2 + 6*t + 27*t**2 - 4*t**2.
(t + 3)**2
Let s = 997/620 + -1/124. Let v(w) be the first derivative of -8/5*w - 2/5*w**3 + 2/25*w**5 - s*w**2 + 5 + 1/5*w**4. Factor v(g).
2*(g - 2)*(g + 1)**2*(g + 2)/5
Let d be (-1)/(((-1)/(-5))/(-1)). Suppose 3*p + 7 = 2*y - 3*y, 15 = -d*p. Factor -6 - 5*l - 8*l - 3*l**y + 4*l.
-3*(l + 1)*(l + 2)
Find w such that -257 + 76*w + 257 + 4*w**2 - 12*w = 0.
-16, 0
Let c be (4 - (-33)/(-6))/((-6)/20). Suppose 1 + c + 7 + 7 - 15*j - 5*j**2 = 0. Calculate j.
-4, 1
Suppose -15*g = -8*g - 3*x - 17, 0 = 2*x - 12. Factor 5*t**2 + 5/3 + 5/3*t**3 + g*t.
5*(t + 1)**3/3
Let g = -19384 + 19386. Suppose 2*s = 7*s. Factor 1/6 + 1/6*c**4 + s*c + 0*c**3 - 1/3*c**g.
(c - 1)**2*(c + 1)**2/6
Let f(g) be the first derivative of -g**5/60 + g**4/12 - g**3/6 + 21*g**2/2 + 24. Let t(l) be the second derivative of f(l). Solve t(s) = 0.
1
Suppose -3*x - 1 - 14 = -4*t, -12 = -4*x. Suppose -3*q**2 - 4*q**3 + t*q**5 + 4*q**3 + 5*q**4 + 4*q**4 = 0. What is q?
-1, 0, 1/2
Let m(g) be the third derivative of g**7/210 - g**6/30 + g**5/60 + g**4/4 - 19*g**2. Let m(f) = 0. What is f?
-1, 0, 2, 3
Suppose -36 + 36 = -101*o. Solve 2/5*y**3 + 0*y - 24/5*y**2 + o = 0.
0, 12
Let t(a) be the third derivative of -1/3*a**4 - 19*a**2 + 1/20*a**6 + 0 + 2/15*a**5 + 1/168*a**8 + 0*a - 4/105*a**7 + 0*a**3. Suppose t(k) = 0. Calculate k.
-1, 0, 1, 2
Let d = 10 - 24. Let l = d + 14. Find v