23*r**2 - 35*r**2 - 16*r**2 + i*r + 24.
-4*(r - 3)*(7*r + 2)
Let h(m) be the third derivative of -m**6/540 - m**5/54 - 7*m**4/108 - m**3/9 - 84*m**2 - 6*m. Solve h(w) = 0.
-3, -1
Let q be -1*((0 - 1) + 3/3). Let d(i) be the third derivative of 0 + q*i + 25*i**2 - 1/360*i**6 + 0*i**3 + 0*i**4 + 0*i**5. Determine r, given that d(r) = 0.
0
Let i(a) be the second derivative of -3/4*a**4 + 0*a**2 + 33/80*a**5 + 1/112*a**7 - 4*a - 1 - 1/10*a**6 + 9/16*a**3. Suppose i(p) = 0. What is p?
0, 1, 3
Let k(f) = -11*f**2 - 24*f - 61. Let p(y) = -13*y**2 - 23*y - 62. Let h(c) = -6*k(c) + 5*p(c). Let w be h(-27). Let 0 + 2/3*a + 2/3*a**w = 0. Calculate a.
-1, 0
Suppose -y - 14 = r, -10823*r = 2*y - 10828*r - 70. Factor y*i - 36/5*i**2 - 3/5*i**4 - 24/5*i**3 + 0.
-3*i**2*(i + 2)*(i + 6)/5
Let h(l) be the second derivative of -1/90*l**5 - 3*l + 0*l**3 + 13 + 0*l**2 - 4/27*l**4. Determine q, given that h(q) = 0.
-8, 0
Let z(w) be the third derivative of -2*w**2 + 0*w - 1/48*w**6 + 7 - 15/16*w**4 - 1/4*w**5 - 5/3*w**3. Factor z(l).
-5*(l + 1)**2*(l + 4)/2
Factor -4/7*h**4 - 17844/7*h**3 - 26534028/7*h**2 + 0 - 13152033212/7*h.
-4*h*(h + 1487)**3/7
Let a = -15367 - -461011/30. Let c(p) be the third derivative of -25/48*p**4 + 0 + 6*p - 4*p**2 - 1/2*p**3 - a*p**5. What is i in c(i) = 0?
-6, -1/4
Let q(i) be the second derivative of i**7/147 - 2*i**6/105 - 5*i**5/2 - 56*i**4/3 + i - 140. Factor q(n).
2*n**2*(n - 16)*(n + 7)**2/7
Let 12*u**4 + 1807141*u**3 + 2778*u**2 - 394*u + 1114*u - 1807546*u**3 = 0. What is u?
-1/4, 0, 10, 24
Let v(f) = 45*f**2 - 268*f - 513. Let k(t) = -19*t**2 + 134*t + 257. Let y(r) = 7*k(r) + 3*v(r). Find x such that y(x) = 0.
-65, -2
Let y(f) be the second derivative of -f**3 - 1/12*f**6 - 4/3*f**4 - 23/40*f**5 - 63*f + 0 + 0*f**2. Factor y(g).
-g*(g + 2)**2*(5*g + 3)/2
Let k(l) = -13*l**2 + 17*l + 18. Let o be (-8 - -19)/(2/(-4)). Let r(f) = -f**2 + f + 2. Let z(x) = o*r(x) + 2*k(x). Factor z(p).
-4*(p - 2)*(p - 1)
Let l(v) be the third derivative of 0*v - 1/8*v**4 + 0*v**3 + 0 - 26*v**2 + 1/180*v**5. Factor l(k).
k*(k - 9)/3
Let j(c) = c**2 - 4490*c + 1008009. Let x(h) = -8980*h + 2016020. Let n(m) = 5*j(m) - 2*x(m). Find t such that n(t) = 0.
449
Let s be 5*-2*(-52)/(-130) - -7. Let w(v) be the second derivative of 0 - 1/9*v**2 + 2/27*v**s - 1/54*v**4 - 26*v. Factor w(h).
-2*(h - 1)**2/9
What is d in 75*d**4 + 962 + 2516*d + 3429*d**2 - 7539*d - 2753*d + 11*d**5 - 14*d**5 - 729*d**3 + 5842 = 0?
3, 6, 7
Let w(z) = z**4 + 24*z**3 + 5*z**2 - 10*z - 4. Let m(f) = 2*f**4 + f**2 + f + 1. Let r = 234 + -238. Let i(q) = r*m(q) - w(q). Suppose i(o) = 0. Calculate o.
-2, -1, 0, 1/3
Determine o, given that 3/5*o**2 - 1428/5 + 69*o = 0.
-119, 4
Suppose -77*j + 8*j + 17 = -121. Let g(k) be the first derivative of -2*k**5 + 4/5*k**j + 1/2*k**4 + 15 + 0*k + 32/15*k**3. Find u, given that g(u) = 0.
-2/5, 0, 1
Suppose 2*n - 3*h - 15 = 4, 4*n + 4*h = -12. Let l(m) be the first derivative of -1/9*m**n + 15 + 1/27*m**3 - 1/3*m. Factor l(k).
(k - 3)*(k + 1)/9
Suppose -29*j - 9*j = -76. Let -34*c**4 - 96*c + 30*c**4 + 24*c**3 - 7 - 4*c**j - 57 = 0. What is c?
-1, 4
Find m such that -17*m**3 + 16*m**3 - 2*m**2 - 16*m**2 = 0.
-18, 0
Let w(m) be the second derivative of m**5/70 - m**4/6 + 10*m**3/21 + 751*m - 1. Factor w(a).
2*a*(a - 5)*(a - 2)/7
Let f(i) be the second derivative of -i**4/60 - 893*i**3/15 - 797449*i**2/10 - 5199*i. Solve f(d) = 0 for d.
-893
Let j be (5/((-45)/12))/(52/(-117)). Suppose -28*c**4 - 9*c**5 - 7*c**j + 56*c**3 - 17*c**3 + 5*c**5 = 0. What is c?
-8, 0, 1
Let k(t) be the second derivative of t**4/6 + 125*t**3/3 - 126*t**2 - 3*t + 115. Factor k(h).
2*(h - 1)*(h + 126)
Factor 0 + 102/13*f - 2/13*f**3 + 100/13*f**2.
-2*f*(f - 51)*(f + 1)/13
Let u = 401149/4 - 100287. Solve -1/4*j**4 + u*j**2 + 0 - 1/4*j**3 + 1/4*j = 0.
-1, 0, 1
Let y(w) be the second derivative of 3/70*w**5 - 1/14*w**4 + 0*w**2 - 1/105*w**6 + 1/21*w**3 + 0 - 148*w. Suppose y(j) = 0. Calculate j.
0, 1
What is g in 1/6*g**3 + 0 + 1/6*g - 1/3*g**2 = 0?
0, 1
Let p = 445 + -377. Let c(z) = 7*z**2 - 32*z - 59. Let l(n) = 80*n**2 - 352*n - 650. Let f(r) = p*c(r) - 6*l(r). Factor f(x).
-4*(x + 2)*(x + 14)
Let r(o) = 11*o**2 + 8*o - 24. Let v be r(-5). Suppose 61 - v = -30*f. Find l such that 7/4*l**4 + 1 + 1/4*l**f + 4*l + 25/4*l**2 + 19/4*l**3 = 0.
-2, -1
Suppose -1454/9*y - 2740/9*y**2 - 8*y**3 + 340/3 + 184/9*y**4 - 10/9*y**5 = 0. Calculate y.
-3, -1, 2/5, 5, 17
Let y(a) be the third derivative of -13*a**6/24 - 99*a**5/4 - 105*a**4 + 84*a**2 + a + 10. Solve y(x) = 0.
-21, -24/13, 0
Let z(k) be the first derivative of k**4/66 + 10*k**3/33 + 16*k**2/11 + 41*k + 82. Let a(x) be the first derivative of z(x). Solve a(g) = 0.
-8, -2
Let o(a) be the first derivative of -5/42*a**4 + 0*a**2 + 13 - 23*a + 1/21*a**3. Let g(i) be the first derivative of o(i). Factor g(c).
-2*c*(5*c - 1)/7
Let u(r) be the third derivative of -r**5/330 - 211*r**4/44 + 1270*r**3/33 - 25*r**2 - 6*r - 4. Let u(c) = 0. Calculate c.
-635, 2
Let t(m) = m**3 - 5*m**2 - 13*m + 65. Let v be t(5). Let g be -5 + (0 - -4) + 1. Factor -3/7*i**5 + 3/7*i**4 + 3/7*i**3 + g + v*i - 3/7*i**2.
-3*i**2*(i - 1)**2*(i + 1)/7
Let w(x) = -12*x**2 + 56*x - 8. Let q be 7 - (3 - (1 - (1 - 0))). Let a(g) = q*g**2 + 5 + g - 2 + g - 21*g. Let o(l) = -8*a(l) - 3*w(l). Factor o(y).
4*y*(y - 4)
Let a(n) be the first derivative of n**7/280 - n**6/72 - n**5/45 + 2*n**4/9 - 25*n**3 + 71. Let k(t) be the third derivative of a(t). Factor k(q).
(q + 1)*(3*q - 4)**2/3
Let c(s) = -s**3 - 23*s**2 - 92*s - 7. Let g be c(-5). Determine i, given that -12/5*i**2 + 4/5*i**4 + 4*i - 8/5 - 4/5*i**g = 0.
-2, 1
Let d(g) be the first derivative of -g**3/5 - 24*g**2 - 237*g/5 - 1152. What is a in d(a) = 0?
-79, -1
Let q(h) be the third derivative of 13*h**8/2520 + 41*h**7/1575 - 7*h**6/900 - 41*h**5/450 - h**4/30 + 9496*h**2. Let q(w) = 0. Calculate w.
-3, -1, -2/13, 0, 1
Suppose 2*b - 5*i = -4, b + 4*b + 5*i = 25. Suppose 4*o - 5*l = 26, b*o + o = -5*l + 6. Find c such that -1546*c - 2*c**2 + 2*c**o - c**3 + 1546*c + c**5 = 0.
-2, -1, 0, 1
Factor c**2 + 1847*c + 1628*c - 821066 + 65*c + 3130*c + 11943291.
(c + 3335)**2
Let j(c) = c**5 - 20*c**4 + 55*c**3 + 20*c**2 - 71*c. Let o(y) = -y**5 + 20*y**4 - 54*y**3 - 20*y**2 + 67*y. Let d(s) = -4*j(s) - 5*o(s). What is u in d(u) = 0?
-1, 0, 1, 3, 17
Let t(x) be the second derivative of -5*x**5/34 + 245*x**4/34 - 957*x**3/17 + 3025*x**2/17 + 6807*x. Factor t(w).
-2*(w - 25)*(5*w - 11)**2/17
Let i(f) be the first derivative of 35*f**4/4 + 20*f**3/3 - 35*f**2/2 + 40*f - 75. Let b(u) = -u**3 - u**2 + u - 1. Let p(c) = -30*b(c) - i(c). Factor p(n).
-5*(n - 2)*(n - 1)*(n + 1)
Let s be 272/72 + -4 - (-116)/198. Let n = -23817 - -23819. Factor 2/11*q**3 + s*q + 6/11*q**n + 0.
2*q*(q + 1)*(q + 2)/11
Suppose 54*r - 37*r = 51. Let n(x) be the first derivative of -1/2*x**2 + 14 - 2*x + 1/3*x**r. Factor n(s).
(s - 2)*(s + 1)
Let g(s) be the second derivative of -s**5/4 + 3185*s**4 - 16230760*s**3 + 41355976480*s**2 - 5422*s. Factor g(r).
-5*(r - 2548)**3
Suppose -12*k + 25 = -7*k. Let x be -2 + k - (1 - 1). Factor -z + 3*z - z**3 - 2*z + 1 - x*z + 3*z**2.
-(z - 1)**3
Let f = -316 + 324. What is a in -f*a**2 - 8*a**2 - 24*a**2 + 25*a**4 + 5*a**5 + 10*a**3 = 0?
-4, -2, 0, 1
Let s be 4/3 - (-2)/3. Let x be -19 + ((-679)/(-175))/((-31)/(-155)). Determine p, given that -x*p**s + 0 + 0*p + 2/5*p**3 = 0.
0, 1
Let i(a) be the third derivative of a**5/360 - 59*a**4/9 + 55696*a**3/9 + 5086*a**2. Factor i(y).
(y - 472)**2/6
Let d = -2544 + 2546. Suppose -4*k = -13*w + 9*w - 8, k = d*w + 4. Find n such that -3/2*n**3 - n + k + 1/2*n**5 + 5/2*n**2 - 1/2*n**4 = 0.
-2, 0, 1
Let w(c) be the first derivative of -c**3/7 - 2640*c**2/7 - 2323200*c/7 - 1942. Factor w(b).
-3*(b + 880)**2/7
Let m be (4/(-10))/((-1)/4). Let t be 2 + 4 + (41 - 25) - 2914/155. Find y such that -m*y + 1/5*y**2 + t = 0.
4
Let o(l) = -3*l**3 - l**2 - l. Let p(z) = 14*z**3 - 218*z**2 + 6052*z + 6272. Let a(d) = -4*o(d) - p(d). Solve a(n) = 0 for n.
-1, 56
Suppose -42 = -15*f + f. Solve -18*m**3 + 9*m**2 - 3*m - 3*m**2 + 15*m**f = 0.
0, 1
Let a(h) be the third derivative of -h**7/630 + h**5/180 + 2*h**2 + h + 59. Determine v so that a(v) = 0.
-1, 0, 1
Let n(j) be the fi