6*x**2.
2*x*(x - 3)
Suppose -15*h + 58*h = 0. Factor -3/5*i**5 + 6/5*i**4 + 0 - 6/5*i**2 + 3/5*i + h*i**3.
-3*i*(i - 1)**3*(i + 1)/5
Let f be ((-888)/9620)/(3/(-5)). Suppose -1 = -k + 1. Let -2/13*h**k - 2/13*h**3 + f*h + 2/13 = 0. What is h?
-1, 1
Find h such that 12*h**3 + 9*h**2 - 40*h + 13*h**3 + 20 + 12*h**4 - 17*h**4 - 5*h**5 - 4*h**2 = 0.
-2, 1
Let w(x) be the second derivative of -x**7/420 + x**6/180 + x**5/60 - x**4/12 - x**3/6 - 3*x. Let r(m) be the second derivative of w(m). Factor r(q).
-2*(q - 1)**2*(q + 1)
Let f(h) be the third derivative of h**6/2340 - 4*h**5/195 + 16*h**4/39 - h**3/2 + 20*h**2. Let m(x) be the first derivative of f(x). Factor m(j).
2*(j - 8)**2/13
Let j = -30047/24 + 1252. Let q(s) be the second derivative of 1/80*s**5 - 8*s + 1/8*s**2 + 0 - 1/48*s**4 - j*s**3. Solve q(r) = 0.
-1, 1
Suppose -3*g + 6 + 6 = 0. Let q be 6 - (g + (-2 - -1)). Factor 4 + q*t - 3*t**2 + 4 + t - t**2.
-4*(t - 2)*(t + 1)
Suppose -106*n**3 + 37*n**3 + 3*n**2 - 40 + 36*n**3 + 34*n**3 - 18*n = 0. Calculate n.
-5, -2, 4
Let y = -953 - -957. Let g(p) be the first derivative of -3/10*p**y + 0*p**2 + 1/10*p**6 + 3/25*p**5 + 0*p**3 + 10 + 0*p. Factor g(m).
3*m**3*(m - 1)*(m + 2)/5
Let h(g) be the third derivative of g**5/5 - 11*g**4/3 + 14*g**3/3 - 202*g**2. Let h(a) = 0. Calculate a.
1/3, 7
Let z(l) be the first derivative of -l**6/3 + 66*l**5/35 - 11*l**4/14 - 82*l**3/21 + 18*l**2/7 + 16*l/7 - 379. Solve z(j) = 0 for j.
-1, -2/7, 1, 4
Let i(z) be the second derivative of -z**6/30 - 21*z**5/20 - 10*z**4 + 32*z**3/3 + 768*z**2 - 14*z - 4. Factor i(p).
-(p - 3)*(p + 8)**3
Let b be -10*(-6)/15*2. Let v be (28/b)/((-4)/(-24)). Find q, given that -4*q - v*q + 3*q**2 + 12 + 13*q = 0.
2
Let z(x) be the first derivative of 7/6*x**3 + 3/8*x**2 - 7/24*x**6 - 1/2*x - 11 - 3/5*x**5 + 1/4*x**4. Let z(p) = 0. Calculate p.
-1, 2/7, 1
Let y(r) = r + 1. Let f be y(4). Suppose j - 2 = b, 2*j + f*b = 3 + 1. Determine i so that 2/7*i**j - 4/7 + 2/7*i = 0.
-2, 1
Let g be (-8944)/4480 - 2/(3/(-3)). Let t(r) be the third derivative of 1/56*r**4 + 1/70*r**5 - 3*r**2 + 0*r - g*r**6 + 0 - 1/7*r**3. Factor t(x).
-3*(x - 2)*(x - 1)*(x + 1)/7
Let y(s) = -8*s**3 - 2*s**2 - 2*s - 1. Let w be y(-2). What is b in 40*b - b**2 + w*b - 3*b**2 - 484 - 11*b = 0?
11
Let s(b) be the second derivative of b**4/12 + 19*b**3/6 - 21*b**2 + 22*b. Find h such that s(h) = 0.
-21, 2
Let m = -2/7599 - -5068/7599. Let -2/9 + m*z**2 - 4/9*z**3 + 0*z = 0. What is z?
-1/2, 1
Let c(r) be the second derivative of 3*r**5/40 - 13*r**4/8 + 12*r**3 - 27*r**2 - 100*r. Factor c(y).
3*(y - 6)**2*(y - 1)/2
Factor 8/7*g + 8/21 + 22/21*g**2 + 2/7*g**3.
2*(g + 1)*(g + 2)*(3*g + 2)/21
Let h be (-2)/(-3) + 4/3. Solve 3*l**2 - 12*l + 5 - 3*l**2 + 4*l**h + 3 = 0 for l.
1, 2
Let z = 31/245 - -1/147. Let t(x) be the second derivative of 0 + 1/50*x**5 + 10*x - z*x**3 + 0*x**2 + 1/30*x**4. Let t(r) = 0. Calculate r.
-2, 0, 1
Suppose 0 = -48*p + 7*p. Let d(y) be the first derivative of -5 + 0*y - 1/8*y**4 + p*y**2 + 0*y**3. Factor d(g).
-g**3/2
Let v(y) = -60*y + 303. Let h be v(5). Solve 15/4*x + 5/4 + 15/4*x**2 + 5/4*x**h = 0.
-1
Let a(m) be the third derivative of -1/96*m**4 + 0 + 0*m - 1/240*m**5 - 18*m**2 + 0*m**3. Let a(r) = 0. What is r?
-1, 0
Factor 7/4*p**3 + 0*p + 0 + 5/2*p**2 + 1/4*p**4.
p**2*(p + 2)*(p + 5)/4
Let h(o) be the third derivative of -5/12*o**4 - 1/21*o**7 + o**2 + 0 - 1/168*o**8 - 1/3*o**5 - 1/3*o**3 + 0*o - 1/6*o**6. Factor h(c).
-2*(c + 1)**5
Let m be ((-66)/(-374))/((-26)/(-442)). Find x, given that 64/3*x - 8*x**4 + 68/3*x**2 - 4/3*x**m + 16/3 = 0.
-1, -2/3, -1/2, 2
Let z(v) be the first derivative of 25*v**6/3 - 42*v**5 + 79*v**4/2 + 30*v**3 - 32*v**2 - 24*v - 32. Find h such that z(h) = 0.
-2/5, 1, 3
Let c be 4 - (3 + (-32)/(-18)) - 12/(-12). Find n such that c - 26/9*n**2 - 8/3*n = 0.
-1, 1/13
Factor -4*n**3 + 2*n**4 - 11*n + 3*n**2 + 15*n - 2*n**2 - 3*n**4.
-n*(n - 1)*(n + 1)*(n + 4)
Let l(d) be the second derivative of -2*d**6/75 - 7*d**5/50 - d**4/10 + 8*d**3/15 + 4*d**2/5 - 40*d - 2. Solve l(q) = 0.
-2, -1/2, 1
Let v be (-2)/((-20)/(-22)) + 2/10. Let t be v/(-6) + 0 + 42/9. Factor 5/2*k**2 + 5/4*k**t - 9/4*k + 1/2 - 3*k**4 + k**3.
(k - 1)**3*(k + 1)*(5*k - 2)/4
Let m = 3727/420 - 62/7. Let c(k) be the second derivative of 0 + 0*k**2 - 2/9*k**3 - m*k**5 + 1/9*k**4 - 5*k. Suppose c(h) = 0. Calculate h.
0, 2
Let z(p) be the third derivative of -p**9/90720 - p**8/30240 + p**7/3780 + 7*p**5/60 + 35*p**2. Let t(g) be the third derivative of z(g). Factor t(n).
-2*n*(n - 1)*(n + 2)/3
Let i(s) = -2 + 0 - 3*s + 2*s + s**2. Let q be i(3). Find k, given that -10*k**q + 34*k**2 + 8 - 32*k**4 - 48*k - 107*k**5 + 146*k**3 + 9*k**5 = 0.
-1, 2/7, 1
Let k(c) be the third derivative of c**9/83160 - c**8/12320 + c**7/6930 - 5*c**4/12 + 12*c**2. Let b(r) be the second derivative of k(r). Factor b(a).
2*a**2*(a - 2)*(a - 1)/11
Let -6 - 1/2*b**2 - 4*b = 0. Calculate b.
-6, -2
Let n(u) be the second derivative of u**4/78 - 2*u**3/39 - 3*u**2/13 - 60*u. Factor n(w).
2*(w - 3)*(w + 1)/13
Let 16/5 - 2*w**3 - 34/5*w**2 + 28/5*w = 0. What is w?
-4, -2/5, 1
Let d(a) be the third derivative of a**5/210 + a**4/7 + 20*a**3/21 - 453*a**2. What is j in d(j) = 0?
-10, -2
Let q = -1053 - -126361/120. Let i(a) be the third derivative of 0 + 0*a - 1/24*a**4 + 0*a**3 + 0*a**5 + q*a**6 + 2*a**2. Suppose i(k) = 0. What is k?
-1, 0, 1
Let y(f) be the first derivative of f**5/35 - 5*f**4/28 + 2*f**3/21 + 4*f**2/7 - 470. Factor y(t).
t*(t - 4)*(t - 2)*(t + 1)/7
Let b(s) be the first derivative of 2*s**5/15 + s**4/6 - 8*s**3/9 - 4*s**2/3 + 97. Suppose b(u) = 0. What is u?
-2, -1, 0, 2
Let c be (-80)/60 + (-19962)/(-270). Find a such that 3/5*a**2 + c + 66/5*a = 0.
-11
Let h(f) = -96*f - 672. Let t be h(-7). Factor 1/2*z**3 + t + z + 3/2*z**2.
z*(z + 1)*(z + 2)/2
Let i be (-11 - (-117)/12) + (-13)/(-4). Let o = -256 + 2818/11. Factor -o*w + 2/11*w**i + 0.
2*w*(w - 1)/11
Let y(l) be the first derivative of l**3 - 6*l**2 + 12*l - 32. Determine t so that y(t) = 0.
2
Suppose -45*x = -41*x - 60. Let k = -13 + x. Determine t so that -1/3*t**5 - 1/3*t**k + 0*t + 0 - t**3 - t**4 = 0.
-1, 0
Let u(p) be the second derivative of 0*p**4 + 13*p - 1/120*p**6 + 0*p**3 - 1/80*p**5 + 0*p**2 + 0. Factor u(h).
-h**3*(h + 1)/4
Let n(b) be the second derivative of -3*b**5/20 - 7*b**4/4 + 17*b**3/2 - 27*b**2/2 - 124*b. Find h, given that n(h) = 0.
-9, 1
Let x = -8149 + 16301/2. Factor 0 - x*v**4 - 3/2*v + 3/2*v**3 + 3/2*v**2.
-3*v*(v - 1)**2*(v + 1)/2
Let h(a) be the third derivative of 35*a**2 + 50/3*a**4 + 0*a + 0 + 0*a**3 + 1/30*a**6 - 4/3*a**5. Factor h(p).
4*p*(p - 10)**2
Let m(q) = 11*q**3 - 7*q**2 - 16*q + 8. Let z(l) = -4*l**3 + 2*l**2 + 6*l - 3. Let b(t) = 3*m(t) + 8*z(t). Factor b(f).
f**2*(f - 5)
Suppose 2*d + 9 = -15. Let j = -4 - d. Determine b, given that -4*b**3 + 25*b - 9*b - 18*b - 8*b**2 + 6*b**5 + j*b**4 = 0.
-1, -1/3, 0, 1
Let m(x) be the first derivative of x**5/30 + x**4/9 + x**3/9 - 18*x - 13. Let c(u) be the first derivative of m(u). Factor c(r).
2*r*(r + 1)**2/3
Let z be 0/(0 - (1 + 0)). Let f(q) = q**2 + q + 2. Let p be f(z). Determine v, given that -3 + 1 + 2*v**3 - 2*v - 6*v**p + 8*v**2 = 0.
-1, 1
Let v(z) = -3*z - 13. Let t be v(-5). Suppose -100*n**4 - 10*n**2 - 16*n**3 - 2*n**t + 48*n**4 + 48*n**4 = 0. What is n?
-3, -1, 0
Factor -10/3*t**3 + 8/3*t + 2/3*t**4 - 16/3 + 4*t**2.
2*(t - 2)**3*(t + 1)/3
Let m(h) = -8*h**2 + 452*h - 12604. Let z(y) = y**2 - y + 15. Let n(o) = -m(o) - 4*z(o). Factor n(b).
4*(b - 56)**2
Let j be ((-14)/(-84))/(2/4). Suppose -u - 4 = -4*b, 2*u + 5*b = -0*b + 5. Determine c, given that 2/3*c**3 + u*c**2 - j - 2/3*c + 1/3*c**4 = 0.
-1, 1
Let u(q) = -39*q - 3*q**3 - 4 + 24*q**2 + 15 + 1. Let h(n) = 3*n**3 - 23*n**2 + 38*n - 13. Let o(x) = 6*h(x) + 5*u(x). Factor o(z).
3*(z - 3)*(z - 2)*(z - 1)
Let c(v) = v**2 + v. Let z(w) = 7*w**2 - 2*w + 16. Let p(m) = -6*c(m) + z(m). Factor p(b).
(b - 4)**2
Let r(v) be the first derivative of v**6/60 - 2*v**5/15 - 5*v**4/12 - 4*v**2 - 18. Let c(n) be the second derivative of r(n). Let c(g) = 0. What is g?
-1, 0, 5
Suppose 0 = -3*p - 4*h + 28, p - 32 = -2*p - 5*h. Let b(m) be the second derivative of 1/42*m**p - 4*m + 0*m**2 + 0*m**3 + 0. Suppose b(u) = 0. Wh