 1)/11
Factor 90 - 69/2*f + 3/2*f**2.
3*(f - 20)*(f - 3)/2
Let a(i) = -i**4 + 4*i**3 - 2*i**2 - i - 1. Let m(h) = 25*h**3 - 80*h**2 - 155*h + 485. Let y(g) = -5*a(g) - m(g). Factor y(u).
5*(u - 4)**2*(u - 3)*(u + 2)
Let f(a) be the first derivative of 1/2*a**4 + 0*a - 1/5*a**5 + 11 - 1/3*a**3 + 0*a**2. Factor f(n).
-n**2*(n - 1)**2
Let v(g) = -4*g**4 + 2*g**3 + g**2 + 4*g. Let h(r) = -9*r**4 + 5*r**3 + 2*r**2 + 9*r. Let f(k) = -3*h(k) + 7*v(k). Factor f(s).
-s*(s - 1)*(s + 1)**2
Let k(s) be the first derivative of -s**4/6 + 14*s**3/9 - 11*s**2/3 + 10*s/3 - 110. Factor k(q).
-2*(q - 5)*(q - 1)**2/3
Let v = 12 + 13. Factor -9 - 27*r**4 - 16*r**2 + 41 - v*r**3 - 23*r**3 + 64*r + 45*r**4.
2*(r - 2)**2*(3*r + 2)**2
Let g(m) be the third derivative of -m**6/420 + m**5/70 - m**4/42 - 2*m**2 - 156*m. Find w, given that g(w) = 0.
0, 1, 2
Suppose 0 - 2/15*t + 2/15*t**2 = 0. Calculate t.
0, 1
Let v(x) be the first derivative of -x**5/40 - 17*x**4/48 - 5*x**3/6 - x**2/2 - 4*x - 31. Let h(i) be the second derivative of v(i). Factor h(r).
-(r + 5)*(3*r + 2)/2
Let x = -166 + 178. Suppose -4*d - x = 5*g, -2*g + 6 = g - 2*d. Factor -y**2 + y**4 - 1/2*y + g + 0*y**3 + 1/2*y**5.
y*(y - 1)*(y + 1)**3/2
Suppose -3 = 12*s - 75. Suppose -4*z + s = -j, 3*j + 3 = 2*z + 5. Determine t, given that 3/5*t**z - 24/5*t + 48/5 = 0.
4
Solve 2/9*j**3 - 2/9*j**2 + 0 + 0*j = 0 for j.
0, 1
Let s(b) = 4*b**4 - 4*b**2 + 4*b - 2. Let v(n) = n**4 + n**3 - n**2 + n - 1. Suppose 0 = 4*t + 6 - 2. Let g(c) = t*s(c) + 2*v(c). Suppose g(m) = 0. Calculate m.
-1, 0, 1
Let t be 1 + -2 + 3 - 0. What is z in 2*z - 2*z**3 + 4*z**2 - 6 + t + 5 - 5 = 0?
-1, 1, 2
Let r(o) be the third derivative of o**6/1080 - o**5/30 + o**4/2 + 10*o**3/3 - 33*o**2. Let p(j) be the first derivative of r(j). Solve p(k) = 0.
6
Let d(l) = -5*l**4 - 17*l**3 + 52*l**2 - 24*l + 3. Let u(w) = -w**3 + w**2 - 2*w - 1. Let r(t) = d(t) + 3*u(t). Factor r(z).
-5*z*(z - 1)**2*(z + 6)
Let o(x) be the first derivative of -3*x**4/8 - 5*x**3/2 + 6*x**2 + 18*x - 54. Solve o(v) = 0 for v.
-6, -1, 2
Let k(t) = t - 19. Let x be k(12). Let u be (3/(-18)*-3)/(-5 - x). Factor l + u*l**2 + 1.
(l + 2)**2/4
Let r = 120 + -116. Let b be r/(5 + -9)*(-3 + 1). Determine m so that 0*m**b + 1/4*m**4 + 0*m + 0 - 1/4*m**3 = 0.
0, 1
Let q(j) = 6*j**5 + 10*j**4 - 14*j**3 + 22*j**2 + 28*j - 12. Let n(k) = -2*k**5 - 3*k**4 + 5*k**3 - 7*k**2 - 9*k + 4. Let v(r) = -10*n(r) - 3*q(r). Factor v(p).
2*(p - 1)**3*(p + 1)*(p + 2)
Let p be 0*(-7)/(-49)*7. Let g(f) be the first derivative of -1/4*f**4 + p*f**2 + 0*f - 4 + 0*f**3 - 1/5*f**5. Solve g(d) = 0.
-1, 0
Let f(m) = -m + 19. Let p be f(17). Factor 13*d**p - 222*d + 222*d + 12*d**2 + d**4 - 10*d**3.
d**2*(d - 5)**2
Factor 15/7*x + 1/7*x**3 - 9/7*x**2 - 1.
(x - 7)*(x - 1)**2/7
Let v = -71 + 64. Let k(g) = 2*g**3 - 2*g**2 - 2*g. Let h(m) = -6*m**3 + 7*m**2 + 7*m. Let a(s) = v*k(s) - 2*h(s). Factor a(z).
-2*z**3
Let l(b) be the second derivative of -b**7/2940 + b**6/1260 - 13*b**3/6 + 6*b. Let n(f) be the second derivative of l(f). Let n(g) = 0. What is g?
0, 1
Let v(m) be the second derivative of -5*m**4/3 + 16*m**3/3 + 8*m**2 - 4*m + 10. Factor v(o).
-4*(o - 2)*(5*o + 2)
Let x(p) be the third derivative of -p**6/300 - 7*p**5/75 - 5*p**4/12 - 4*p**3/5 + 10*p**2 + 2*p. Factor x(h).
-2*(h + 1)**2*(h + 12)/5
Let h(g) = -g**2 - 12*g - 23. Let u(k) = k + 3. Let v(t) = -5*h(t) - 15*u(t). Find n, given that v(n) = 0.
-7, -2
Let u(y) be the second derivative of y**10/15120 - y**9/2520 + y**8/1680 + y**4/4 + 11*y. Let c(t) be the third derivative of u(t). Factor c(w).
2*w**3*(w - 2)*(w - 1)
Let m(o) be the second derivative of o**4/3 + 232*o**3/3 - 5*o - 47. Find d such that m(d) = 0.
-116, 0
Let q(v) = 3*v**2 - 9*v - 12. Let w(i) = -2*i + 4. Let o be w(0). Let u(t) = 2*t**2 - 9*t - 11. Let f(r) = o*u(r) - 3*q(r). Suppose f(l) = 0. Calculate l.
-8, -1
Let k(q) be the second derivative of -3/110*q**5 + 7/66*q**4 + 0*q**2 - 45*q - 2/33*q**3 + 0. Find j, given that k(j) = 0.
0, 1/3, 2
Suppose 0 = 7*f - 0 - 35. Factor -25/3*u**3 - 1/3 + 3*u - f*u**2.
-(u + 1)*(5*u - 1)**2/3
Let o(r) be the first derivative of 8/5*r - 14/15*r**3 - 8 + 12/5*r**2. Solve o(u) = 0.
-2/7, 2
Let s(b) be the third derivative of 9*b**5/80 - 5*b**4/32 - 12*b**2 + 16*b. Find z, given that s(z) = 0.
0, 5/9
Let i be (18/10)/(2 - 14/10). Find f such that 2*f**i - 21*f - 13*f + 0 + 22*f + 6*f**2 - 16 = 0.
-4, -1, 2
Let a = 145 - -90. Let w = a - 1643/7. Factor 2/7*h**3 - 2/7*h**2 - 2/7*h + w.
2*(h - 1)**2*(h + 1)/7
Let j(o) be the second derivative of -o**7/147 - o**6/21 + o**5/14 + 25*o**4/42 - 40*o**3/21 + 16*o**2/7 + o + 5. Suppose j(p) = 0. Calculate p.
-4, 1
Let j(r) be the first derivative of 4*r**3/15 - 18*r**2/5 - 122. Let j(z) = 0. What is z?
0, 9
Let u = -1953/5 - -391. Let 4/5*d**2 - 2/5*d**4 - 2/5*d - 2/5*d**5 - u + 4/5*d**3 = 0. Calculate d.
-1, 1
Let i(z) = z + 3. Let x be i(-1). Let t(b) = b**2 - b. Let m be t(x). Factor -3*n**2 - m*n**2 - 6*n - 2 - 2*n**2 + 3*n**2.
-2*(n + 1)*(2*n + 1)
Suppose 2*j = -4*o - 4, -5*o - 8 - 11 = -j. Let z be (j - -1)/(-40)*-6. Factor z*s**5 - 1/2*s**3 + 3/2*s**2 - 5/4*s**4 - 1/4*s - 1/4.
(s - 1)**3*(s + 1)*(3*s + 1)/4
Let f = 13321/8880 - 1/8880. Suppose 15/4*g**4 + 0 + f*g**5 + 3/4*g**2 + 3*g**3 + 0*g = 0. Calculate g.
-1, -1/2, 0
Let y = 36 - 31. Let a be (-1)/(y/(-70) - 0). Factor 6*j**2 + 6*j**2 - 14*j - a*j - 11 - 13.
4*(j - 3)*(3*j + 2)
Let g(p) be the second derivative of 0*p**6 + 0*p**3 + 0*p**4 - 1/100*p**5 + 1/210*p**7 + 0 - 3*p + 0*p**2. Factor g(f).
f**3*(f - 1)*(f + 1)/5
Let b = -4683/76 + 1204/19. Factor 9/4*m**2 + 5/4*m**3 + 1/4*m**4 + b*m + 1/2.
(m + 1)**3*(m + 2)/4
Let t(q) be the first derivative of q**8/336 - 5*q**7/168 - q**6/12 - 10*q**3 + 24. Let o(d) be the third derivative of t(d). Let o(j) = 0. What is j?
-1, 0, 6
Let o(s) = -s + 10. Let g be o(6). Suppose -4 = -h + 2. Let d(t) = 3*t**2 - 2*t + 3. Let n(l) = -4*l**2 + 2*l - 4. Let u(w) = g*n(w) + h*d(w). Factor u(y).
2*(y - 1)**2
Let m(f) be the first derivative of 2*f**3/39 + 2*f**2/13 + 2*f/13 - 102. Factor m(o).
2*(o + 1)**2/13
Let n be -2 + (1 - (3 + -7)). Let i(x) be the third derivative of 0*x + 0 - 5*x**2 + 3/8*x**4 - x**n - 1/20*x**5. Suppose i(j) = 0. Calculate j.
1, 2
Suppose 21 = 30*o - 37*o. Let m be ((-32)/24)/(o/9). Solve -m*t**2 + 8/5*t + 16/5 + 6/5*t**3 = 0 for t.
-2/3, 2
Let m(g) be the second derivative of -4/15*g**6 - 28*g + 0 - 47/36*g**4 + 97/120*g**5 + 11/9*g**3 + 1/28*g**7 - 2/3*g**2. What is s in m(s) = 0?
2/3, 1, 2
Find o, given that -8/3*o**2 - 392/3*o - 4802/3 = 0.
-49/2
Find l such that -14/19*l - 2/19*l**4 - 10/19*l**3 - 4/19 - 18/19*l**2 = 0.
-2, -1
Let v(k) = -k**5 - 4*k**4 + 9*k**3 + 11*k**2 + 8*k + 6. Let j(f) = -f**2 + f**3 + 7 - f - f**4 + 2 - 8. Let c(g) = 3*j(g) - v(g). Factor c(m).
(m - 3)*(m + 1)**4
Factor 9 - 2*m**2 + 3/2*m - 1/2*m**3.
-(m - 2)*(m + 3)**2/2
Factor 2*y**2 - 2/5*y - 2 + 2/5*y**3.
2*(y - 1)*(y + 1)*(y + 5)/5
Suppose 0 = 4*d + 12, -2*b + 2*d + 38 = 0. Factor -16*a**2 + 4*a**5 - 16*a**3 + 18*a**3 + b*a - 14*a**3 + 8*a**4.
4*a*(a - 1)**2*(a + 2)**2
Suppose 204*r**2 + 4*r + 5*r - 12 - 201*r**2 = 0. What is r?
-4, 1
Let u(m) be the first derivative of -21*m**4/4 - 114*m**3 + 330*m**2 + 216*m - 92. Suppose u(l) = 0. What is l?
-18, -2/7, 2
Let o(t) = 7*t**2 - 124*t - 262. Let u(w) = 15*w**2 - 250*w - 525. Let x(j) = -5*o(j) + 2*u(j). Factor x(d).
-5*(d - 26)*(d + 2)
Let v(u) = 3*u**3 - 3*u**2 + 4*u. Let x(t) = 6*t + 9. Let k be x(-2). Let s(z) = 2*z**3 - 3*z**2 + 3*z. Let o(q) = k*v(q) + 4*s(q). Suppose o(a) = 0. What is a?
-3, 0
Let o(m) = -m - 20. Let s be o(-24). Let l be (-287)/(-308) - s/22. Factor 0 - 3/4*n - l*n**2.
-3*n*(n + 1)/4
Let r(a) be the third derivative of a**7/420 + a**6/180 - a**5/12 + a**4/4 + 5*a**3/2 - 8*a**2. Let k(w) be the first derivative of r(w). Factor k(y).
2*(y - 1)**2*(y + 3)
Let q(j) be the first derivative of j**3/3 + 5*j**2/2 + 6*j - 128. Factor q(l).
(l + 2)*(l + 3)
Let n(i) be the first derivative of -3*i**6/25 + 21*i**5/100 - i**4/10 - 17*i - 1. Let a(j) be the first derivative of n(j). Determine g so that a(g) = 0.
0, 1/2, 2/3
Let w be (-900)/(-48)*(-14)/(-175). Solve 3/2*m**2 - 3/2*m**3 - w + 3/2*m = 0 for m.
-1, 1
Let p(k) = 4*k**2 + 7*k - 25