16
Determine k so that 68 - 2*k**2 - 91 + 93 + 4*k = 0.
-5, 7
Let i = 1/2456 - -2449/17192. Let a(x) be the first derivative of 1/14*x**4 + 15 + 12/7*x - i*x**2 - 4/7*x**3. Factor a(p).
2*(p - 6)*(p - 1)*(p + 1)/7
Let c(t) be the third derivative of t**7/945 + t**6/36 + t**5/5 + 10*t**4/27 + 1352*t**2 - 2*t. Factor c(p).
2*p*(p + 1)*(p + 4)*(p + 10)/9
Let p(a) be the second derivative of 0 + 50*a - 5/12*a**4 + 0*a**3 - 1/4*a**5 + 0*a**2. Factor p(f).
-5*f**2*(f + 1)
Let s(d) = -d**3 + 29*d**2 - 31*d + 904. Let k be s(29). Let o be (-3)/7*7/(-4). Factor -9/4*r**4 + 9/4*r - 3/2*r**3 + 3/2*r**2 - 3/4*r**k + o.
-3*(r - 1)*(r + 1)**4/4
Let q = -289 - -294. Let a(n) be the second derivative of 5/168*n**7 + 1/12*n**6 - 1/16*n**q - 5/24*n**4 + 0*n**3 + 13*n + 0 + 0*n**2. Let a(k) = 0. What is k?
-2, -1, 0, 1
Let n be (-1319)/1320 - 4*26/(-104). Let i(l) be the third derivative of n*l**6 - 11*l**2 - 1/88*l**4 + 0 + 0*l**3 + 1/330*l**5 + 0*l. Solve i(q) = 0 for q.
-3, 0, 1
Suppose 29*p - 4*v = 27*p - 44, p - 3*v = -17. Let u be 4/64 - 126/p. Factor 0 + 0*x**u - 2/13*x**5 + 0*x**2 + 2/13*x**3 + 0*x.
-2*x**3*(x - 1)*(x + 1)/13
Let m(s) = 2*s**4 + 6*s**3 - 26*s**2 + 10*s - 8. Let l(n) = -3*n**4 - 13*n**3 + 50*n**2 - 21*n + 15. Let o(k) = -4*l(k) - 7*m(k). Suppose o(i) = 0. What is i?
1, 2
Suppose 4*h + 2*q = 28, -16*h + 3*q - 15 = -13*h. Solve 6 - 15/4*w**h - 9/2*w**2 + 3*w - 3/4*w**4 = 0 for w.
-2, 1
Let o = 473 + -470. Suppose 5*h**2 - 1/2*h**o + 16 - 16*h = 0. Calculate h.
2, 4
Let v(u) be the first derivative of -10*u - 11 + 0*u**2 + 0*u**3 - 1/54*u**4. Let a(y) be the first derivative of v(y). Find i, given that a(i) = 0.
0
Let s(w) be the first derivative of -5*w**7/8 - 3*w**6/10 + w**5/10 - 166*w**3/3 - 125. Let n(l) be the third derivative of s(l). Factor n(d).
-3*d*(7*d + 2)*(25*d - 2)
Suppose -5*u - 377 = c + 698, -5*u + 4*c - 1075 = 0. Let v = 215 + u. Suppose 0*x + 1/3*x**4 + v + 2/3*x**2 - x**3 = 0. Calculate x.
0, 1, 2
Suppose 2*m + 5 = -99*s + 102*s, 3*s - 7 = m. Suppose -4*r + r + 2*k = -11, 16 = 5*r - k. Factor -134*o**r - 69*o + 72 + 32*o**2 - 15*o + 65*o**s + 65*o**3.
-4*(o - 3)**2*(o - 2)
Let h(o) be the first derivative of -o**5/4 + 25*o**4/12 - 20*o**3/3 + 10*o**2 - 20*o - 17. Let q(m) be the first derivative of h(m). Factor q(z).
-5*(z - 2)**2*(z - 1)
Factor 21*h**2 + 94*h**2 + h**3 + 180*h**2 - 330*h + 34*h.
h*(h - 1)*(h + 296)
Suppose -3 = -4*k + 9. Suppose 2*i = 4*h - 5*h + 3, h + 5*i = k. Factor -768*y - 83*y**4 + 131*y**4 + 768*y**2 - 188*y**h - 3*y**5 - 100*y**3.
-3*y*(y - 4)**4
Let g(n) be the third derivative of 16*n**7/105 - 8798*n**6/5 + 174187201*n**5/30 - 14512301*n**4/2 + 10883401*n**3/3 - 2*n**2 - 2*n + 271. Factor g(d).
2*(d - 3299)**2*(4*d - 1)**2
Let a(t) be the second derivative of 1/14*t**7 + 0*t**3 + 0*t**4 + 2*t + 0*t**2 - 77 + 1/40*t**5 + 1/12*t**6. Factor a(m).
m**3*(2*m + 1)*(3*m + 1)/2
Let r(i) be the second derivative of -96*i + 0 - 8/9*i**3 - 7/9*i**4 + 0*i**2 - 3/10*i**5 - 1/252*i**7 - 1/18*i**6. Let r(o) = 0. What is o?
-4, -2, 0
Factor 83/2*p - 1/2*p**2 - 41.
-(p - 82)*(p - 1)/2
Let q(u) be the first derivative of 2*u + 2/3*u**3 + 2*u**2 + 139. Determine n, given that q(n) = 0.
-1
Suppose 3*d + 141 = -5235. Let h = d - -1796. Suppose 0*y + 0 - 1/4*y**2 + 1/4*y**h + 0*y**3 = 0. What is y?
-1, 0, 1
Let b = 3389 - 2323. Determine n so that b*n**2 - 1280 - 160*n - 539*n**2 - 532*n**2 = 0.
-16
Let i = 75 - 75. Let y = -18/1039 - -2312/13507. What is p in 0 + 2/13*p**2 - y*p**3 + i*p = 0?
0, 1
Let j(s) be the third derivative of -7*s**5/60 - 3*s**4/4 - 27*s**3/2 - s**2 + 5. Let r(u) = 3*u**2. Let a(o) = 3*j(o) + 6*r(o). Factor a(f).
-3*(f + 9)**2
Let u(o) = -o**2 + 92*o + 285. Let q be u(-3). Let v(w) be the third derivative of q + 0*w**5 - 2*w**2 + 1/6*w**3 - 1/720*w**6 + 7/144*w**4 + 0*w. Factor v(k).
-(k - 3)*(k + 1)*(k + 2)/6
Let b = 90 + -88. Factor 19 + 50*k**2 + 80*k - 15 - 15*k**b + k**3 + 4*k**3 + 56.
5*(k + 2)**2*(k + 3)
Let i(u) = -23*u**2 - 53*u - 22. Let l(g) = 8*g**2 + 18*g + 7. Let h be (11/(-5) + 2)/((-45)/675). Let j(f) = h*i(f) + 8*l(f). What is m in j(m) = 0?
-2, -1
Let t be ((-17255)/27 + -2)*12/(-6920). Let w = -1/1730 + t. Determine m so that 16/9 - 4*m - w*m**2 = 0.
-4, 2/5
Let w(t) be the first derivative of t**7/28 - t**6/4 + 9*t**5/40 + 9*t**4/8 + 5*t - 27. Let a(k) be the first derivative of w(k). Factor a(z).
3*z**2*(z - 3)**2*(z + 1)/2
Let i be 1 + 11 + 0 + 0. Factor -12*y**3 - i + 12*y + 17 - 4*y**4 + 3 - 4*y**2.
-4*(y - 1)*(y + 1)**2*(y + 2)
Factor 3/7*x**3 - 12/7*x + 0 - 4/7*x**2 + 1/7*x**4.
x*(x - 2)*(x + 2)*(x + 3)/7
Factor 19392*b - 192/5*b**3 - 8206/5*b**2 - 51005 - 1/5*b**4.
-(b - 5)**2*(b + 101)**2/5
Let 585*y + 966/5*y**2 + 0 - 3/5*y**3 = 0. Calculate y.
-3, 0, 325
Let o be (990/81)/(165/90). Factor -68/3*b - 7/3*b**2 + o.
-(b + 10)*(7*b - 2)/3
Let s(l) be the first derivative of 5*l**4/12 + 605*l**3/9 - 4355*l**2/3 - 11793. Factor s(t).
5*t*(t - 13)*(t + 134)/3
Let b(a) be the first derivative of a**4/18 - 332*a**3/9 + 331*a**2/3 - 992*a/9 + 4013. Factor b(m).
2*(m - 496)*(m - 1)**2/9
Let h(s) be the first derivative of s**8/1344 + s**7/210 + s**6/96 + s**5/120 + 6*s**2 - 9*s + 71. Let w(c) be the second derivative of h(c). Factor w(j).
j**2*(j + 1)**2*(j + 2)/4
Let -88/7*k - 968/7 - 2/7*k**2 = 0. What is k?
-22
Let q(i) be the third derivative of -1/48*i**4 + 1/240*i**6 + 0 - 1/60*i**5 + 1/840*i**7 - i**2 + 1/8*i**3 + 2*i. Factor q(r).
(r - 1)**2*(r + 1)*(r + 3)/4
Let s(n) = n**2 + n - 10. Let j be s(-4). Let t(y) be the first derivative of y**3 + 57*y - 6 + 33*y**j - 9*y - 45*y**2. Let t(v) = 0. Calculate v.
4
Let g(v) be the second derivative of 71*v + 4/9*v**3 + 0 - 1/20*v**5 + 2*v**2 - 17/36*v**4. Solve g(j) = 0 for j.
-6, -2/3, 1
Solve -4*j**5 - 20600*j - 24*j**3 - 32*j**4 + 32*j**2 + 41237*j - 20609*j = 0 for j.
-7, -1, 0, 1
Let l(b) be the second derivative of -b**5/4 - 600*b**4 + 7205*b**3/6 + 6*b - 364. Factor l(r).
-5*r*(r - 1)*(r + 1441)
Let s be (26 - -1)*(-16 - -17). Find q, given that -q**4 - 45*q**2 - s*q - 3*q**3 - 2*q**4 - 18*q**3 = 0.
-3, -1, 0
Let 329672/3 - 268*y**2 - 2/3*y**3 - 26390*y = 0. What is y?
-203, 4
Let n = -15749/180 - -5263/60. Determine b, given that 0 - 4/9*b**5 - 14/9*b**4 + 14/9*b**2 + 2/3*b - n*b**3 = 0.
-3, -1, -1/2, 0, 1
Let o be (-20)/(170/(-17))*4. Let l(k) be the first derivative of 0*k - o - 3/5*k**2 - 9/20*k**4 + k**3. Solve l(h) = 0.
0, 2/3, 1
Let h(s) be the second derivative of -1/84*s**4 + 0 - 288*s + 5/7*s**3 + 31/14*s**2. Factor h(y).
-(y - 31)*(y + 1)/7
Let r(o) be the first derivative of 0*o - 12*o**4 + 144 - 147/2*o**2 + 56*o**3. Factor r(s).
-3*s*(4*s - 7)**2
Find b, given that -b**2 - b**2 - 100174 + 100030 + 146*b = 0.
1, 72
Let z(b) = 40*b**2 + 136*b + 57. Let y(u) = 28 + 20*u**2 + 7*u + 14*u + 47*u. Let v(o) = -9*y(o) + 4*z(o). Factor v(g).
-4*(g + 3)*(5*g + 2)
Let d(x) be the third derivative of 4 + 0*x**3 - 17/60*x**6 + 0*x**4 - 5*x**2 + 3/70*x**7 - 2/15*x**5 + 0*x. Factor d(t).
t**2*(t - 4)*(9*t + 2)
Let s(d) be the second derivative of d**4/8 + 218*d**3 + 142572*d**2 - 2199*d. Solve s(y) = 0 for y.
-436
What is q in 18465*q**2 + 75*q**3 - 5*q**4 - 9557*q**2 + 450 - 9193*q**2 + 85*q = 0?
-1, 2, 5, 9
Let n(t) be the third derivative of t**8/588 + 6*t**7/245 - 8*t**6/105 - 4*t**5/7 + 3444*t**2. Suppose n(p) = 0. What is p?
-10, -2, 0, 3
Let c(q) = 3*q**2 + 2*q - 4. Let b(l) = 2*l**2 - 5. Let w(d) = 3*b(d) - 3*c(d). Determine f, given that w(f) = 0.
-1
Determine j, given that 138/5*j + 22/5*j**3 - 72/5 - 86/5*j**2 - 2/5*j**4 = 0.
1, 3, 4
Let m = -137 + 143. Solve n**3 + 790*n + 90 - 398*n - m*n**3 - 377*n - 20*n**2 = 0 for n.
-3, 2
Let w(c) be the second derivative of -9/4*c**4 + 405/2*c**3 - 18225/2*c**2 + 1/100*c**5 + 0 + 135*c. Factor w(n).
(n - 45)**3/5
Suppose -2*f + 3*f = 3. Let m = -982280 + 8840522/9. Factor m*g**f + 2/9*g**2 - 4/9*g + 0.
2*g*(g - 1)*(g + 2)/9
Suppose 3237 = -7*d + 3251. Let m(i) be the second derivative of -1/4*i**3 + 18*i + 3/2*i**d - 1/8*i**4 + 0. Find l such that m(l) = 0.
-2, 1
Let p be 14 + -9 + 1 + 3. Factor -2*f**2 + 4*f + f**5 - 5*f**3 + f**2 + p*f**4 - 12*f**4 + 4*f**2.
f*(f - 4)*(f - 1)*(f + 1)**2
Let k(w) be the third derivative of 2/105*w**5 - 25/21*w**3 + 1 + 33/28*w**